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Sample records for korteweg de vries equation

  1. Simple Numerical Schemes for the Korteweg-deVries Equation

    SciTech Connect

    C. J. McKinstrie; M. V. Kozlov

    2000-12-01

    Two numerical schemes, which simulate the propagation of dispersive non-linear waves, are described. The first is a split-step Fourier scheme for the Korteweg-de Vries (KdV) equation. The second is a finite-difference scheme for the modified KdV equation. The stability and accuracy of both schemes are discussed. These simple schemes can be used to study a wide variety of physical processes that involve dispersive nonlinear waves.

  2. Multiple soliton production and the Korteweg-de Vries equation.

    NASA Technical Reports Server (NTRS)

    Hershkowitz, N.; Romesser, T.; Montgomery, D.

    1972-01-01

    Compressive square-wave pulses are launched in a double-plasma device. Their evolution is interpreted according to the Korteweg-de Vries description of Washimi and Taniuti. Square-wave pulses are an excitation for which an explicit solution of the Schrodinger equation permits an analytical prediction of the number and amplitude of emergent solitons. Bursts of energetic particles (pseudowaves) appear above excitation voltages greater than an electron thermal energy, and may be mistaken for solitons.

  3. On exact traveling-wave solutions for local fractional Korteweg-de Vries equation

    NASA Astrophysics Data System (ADS)

    Yang, Xiao-Jun; Tenreiro Machado, J. A.; Baleanu, Dumitru; Cattani, Carlo

    2016-08-01

    This paper investigates the Korteweg-de Vries equation within the scope of the local fractional derivative formulation. The exact traveling wave solutions of non-differentiable type with the generalized functions defined on Cantor sets are analyzed. The results for the non-differentiable solutions when fractal dimension is 1 are also discussed. It is shown that the exact solutions for the local fractional Korteweg-de Vries equation characterize the fractal wave on shallow water surfaces.

  4. On exact traveling-wave solutions for local fractional Korteweg-de Vries equation.

    PubMed

    Yang, Xiao-Jun; Tenreiro Machado, J A; Baleanu, Dumitru; Cattani, Carlo

    2016-08-01

    This paper investigates the Korteweg-de Vries equation within the scope of the local fractional derivative formulation. The exact traveling wave solutions of non-differentiable type with the generalized functions defined on Cantor sets are analyzed. The results for the non-differentiable solutions when fractal dimension is 1 are also discussed. It is shown that the exact solutions for the local fractional Korteweg-de Vries equation characterize the fractal wave on shallow water surfaces. PMID:27586629

  5. Negative-order Korteweg-de Vries equations.

    PubMed

    Qiao, Zhijun; Fan, Engui

    2012-07-01

    In this paper, based on the regular Korteweg-de Vries (KdV) system, we study negative-order KdV (NKdV) equations, particularly their Hamiltonian structures, Lax pairs, conservation laws, and explicit multisoliton and multikink wave solutions thorough bilinear Bäcklund transformations. The NKdV equations studied in our paper are differential and actually derived from the first member in the negative-order KdV hierarchy. The NKdV equations are not only gauge equivalent to the Camassa-Holm equation through reciprocal transformations but also closely related to the Ermakov-Pinney systems and the Kupershmidt deformation. The bi-Hamiltonian structures and a Darboux transformation of the NKdV equations are constructed with the aid of trace identity and their Lax pairs, respectively. The single and double kink wave and bell soliton solutions are given in an explicit formula through the Darboux transformation. The one-kink wave solution is expressed in the form of tanh while the one-bell soliton is in the form of sech, and both forms are very standard. The collisions of two-kink wave and two-bell soliton solutions are analyzed in detail, and this singular interaction differs from the regular KdV equation. Multidimensional binary Bell polynomials are employed to find bilinear formulation and Bäcklund transformations, which produce N-soliton solutions. A direct and unifying scheme is proposed for explicitly building up quasiperiodic wave solutions of the NKdV equations. Furthermore, the relations between quasiperiodic wave solutions and soliton solutions are clearly described. Finally, we show the quasiperiodic wave solution convergent to the soliton solution under some limit conditions. PMID:23005555

  6. Soliton fractals in the Korteweg-de Vries equation.

    PubMed

    Zamora-Sillero, Elias; Shapovalov, A V

    2007-10-01

    We have studied the process of creation of solitons and generation of fractal structures in the Korteweg-de Vries (KdV) equation when the relation between the nonlinearity and dispersion is abruptly changed. We observed that when this relation is changed nonadiabatically the solitary waves present in the system lose their stability and split up into ones that are stable for the set of parameters. When this process is successively repeated the trajectories of the solitary waves create a fractal treelike structure where each branch bifurcates into others. This structure is formed until the iteration where two solitary waves overlap just before the breakup. By means of a method based on the inverse scattering transformation, we have obtained analytical results that predict and control the number, amplitude, and velocity of the solitary waves that arise in the system after every change in the relation between the dispersion and the nonlinearity. This complete analytical information allows us to define a recursive L system which coincides with the treelike structure, governed by KdV, until the stage when the solitons start to overlap and is used to calculate the Hausdorff dimension and the multifractal properties of the set formed by the segments defined by each of the two "brothers" solitons before every breakup. PMID:17995132

  7. Explicit solutions and conservation laws of the coupled modified Korteweg-de Vries equation

    NASA Astrophysics Data System (ADS)

    Xue, Bo; Li, Fang; Yang, Gang

    2015-08-01

    With the aid of the gauge transformation between the corresponding 3 × 3 matrix spectral problem, Darboux transformation for the coupled modified Korteweg-de Vries (cmKdV) equation is derived. Depending on the Darboux transformation, explicit solutions for this equation are given and some figures are plotted. Finally, infinitely many conservation laws of the cmKdV equation are constructed.

  8. Note on the single-shock solutions of the Korteweg-de Vries-Burgers equation

    NASA Astrophysics Data System (ADS)

    Kourakis, Ioannis; Sultana, Sharmin; Verheest, Frank

    2012-04-01

    The well-known shock solutions of the Korteweg-de Vries-Burgers equation are revisited, together with their limitations in the context of plasma (astro)physical applications. Although available in the literature for a long time, it seems to have been forgotten in recent papers that such shocks are monotonic and unique, for a given plasma configuration, and cannot show oscillatory or bell-shaped features. This uniqueness is contrasted to solitary wave solutions of the two parent equations (Korteweg-de Vries and Burgers), which form a family of curves parameterized by the excess velocity over the linear phase speed.

  9. Cylindrical nonlinear Schroedinger equation versus cylindrical Korteweg-de Vries equation

    SciTech Connect

    Fedele, Renato; De Nicola, Sergio; Grecu, Dan; Visinescu, Anca; Shukla, Padma K.

    2008-10-15

    A correspondence between the family of cylindrical nonlinear Schroedinger (cNLS) equations and the one of cylindrical Korteweg-de Vries (cKdV) equations is constructed. It associates non stationary solutions of the first family with the ones of the second family. This is done by using a correspondence, recently found, between the families of generalized NLS equation and generalized KdV equation, and their solutions in the form of travelling waves, respectively. In particular, non-stationary soliton-like solutions of the cNLS equation can be associated with non-stationary soliton-like solutions of cKdV equation.

  10. Chaos in the perturbed Korteweg-de Vries equation with nonlinear terms of higher order

    NASA Astrophysics Data System (ADS)

    Pan, Wei-Zhen; Song, Xiang-Jiong; Yu, Jun

    2010-03-01

    The dynamical behaviour of the generalized Korteweg-de Vries (KdV) equation under a periodic perturbation is investigated numerically. The bifurcation and chaos in the system are observed by applying bifurcation diagrams, phase portraits and Poincaré maps. To characterise the chaotic behaviour of this system, the spectra of the Lyapunov exponent and Lyapunov dimension of the attractor are also employed.

  11. Darboux transformation for a generalized Hirota-Satsuma coupled Korteweg-de Vries equation

    SciTech Connect

    Geng Xianguo; Ren Hongfeng; He Guoliang

    2009-05-15

    A Darboux transformation for the generalized Hirota-Satsuma coupled Korteweg-de Vries (KdV) equation is derived with the aid of the gauge transformation between the corresponding 4x4 matrix spectral problems with three potentials, by which some explicit solutions of the generalized Hirota-Satsuma coupled KdV equation are constructed. As a reduction, a Darboux transformation of the complex coupled KdV equation and its explicit solutions are obtained.

  12. The zero dispersion limit for the Korteweg-deVries KdV equation.

    PubMed

    Lax, P D; Levermore, C D

    1979-08-01

    We use the inverse scattering method to determine the weak limit of solutions of the Korteweg-deVries equation as dispersion tends to zero. The limit, valid for all time, is characterized in terms of a quadratic programming problem which can be solved with the aid of function theoretic methods. For large t, the solutions satisfy Whitham's averaged equations at some times and the equations found by Flaschka et al. at other times. PMID:16592690

  13. Darboux transformation for a generalized Hirota-Satsuma coupled Korteweg-de Vries equation.

    PubMed

    Geng, Xianguo; Ren, Hongfeng; He, Guoliang

    2009-05-01

    A Darboux transformation for the generalized Hirota-Satsuma coupled Korteweg-de Vries (KdV) equation is derived with the aid of the gauge transformation between the corresponding 4x4 matrix spectral problems with three potentials, by which some explicit solutions of the generalized Hirota-Satsuma coupled KdV equation are constructed. As a reduction, a Darboux transformation of the complex coupled KdV equation and its explicit solutions are obtained. PMID:19518577

  14. Nonlocal Symmetries, Explicit Solutions, and Wave Structures for the Korteweg-de Vries Equation

    NASA Astrophysics Data System (ADS)

    Ma, Zheng-Yi; Fei, Jin-Xi

    2016-08-01

    From the known Lax pair of the Korteweg-de Vries (KdV) equation, the Lie symmetry group method is successfully applied to find exact invariant solutions for the KdV equation with nonlocal symmetries by introducing two suitable auxiliary variables. Meanwhile, based on the prolonged system, the explicit analytic interaction solutions related to the hyperbolic and Jacobi elliptic functions are derived. Figures show the physical interaction between the cnoidal waves and a solitary wave.

  15. Reduction of dispersionless coupled Korteweg-de Vries equations to the Euler-Darboux equation

    NASA Astrophysics Data System (ADS)

    Matsuno, Yoshimasa

    2001-04-01

    A quasilinear hyperbolic system of two first-order equations is introduced. The system is linearized by means of the hodograph transformation combined with Riemann's method of characteristics. In the process of linearization, the main step is to explicitly express the characteristic velocities in terms of the Riemann invariants. The procedure is shown to be performed by quadrature only for specific combinations of the parameters in the system. We then apply the method developed here to the dispersionless versions of the typical coupled Korteweg-de Vries (cKdV) equations including the Broer-Kaup, Ito, Hirota-Satsuma, and Bogoyavlenskii equations and show that these equations are transformed into the classical Euler-Darboux equation. A more general quasilinear system of equations is also considered with application to the dispersionless cKdV equations for the Jaulent-Miodek and Nutku-Ög˜uz equations.

  16. Nonlinear dynamics of a soliton gas: Modified Korteweg-de Vries equation framework

    NASA Astrophysics Data System (ADS)

    Shurgalina, E. G.; Pelinovsky, E. N.

    2016-05-01

    Dynamics of random multi-soliton fields within the framework of the modified Korteweg-de Vries equation is considered. Statistical characteristics of a soliton gas (distribution functions and moments) are calculated. It is demonstrated that the results sufficiently depend on the soliton gas properties, i.e., whether it is unipolar or bipolar. It is shown that the properties of a unipolar gas are qualitatively similar to the properties of a KdV gas [Dutykh and Pelinovsky (2014) [1

  17. Soliton management for a variable-coefficient modified Korteweg-de Vries equation.

    PubMed

    Sun, Zhi-Yuan; Gao, Yi-Tian; Liu, Ying; Yu, Xin

    2011-08-01

    The concept of soliton management has been explored in the Bose-Einstein condensate and optical fibers. In this paper, our purpose is to investigate whether a similar concept exists for a variable-coefficient modified Korteweg-de Vries equation, which arises in the interfacial waves in two-layer liquid and Alfvén waves in a collisionless plasma. Through the Painlevé test, a generalized integrable form of such an equation has been constructed under the Painlevé constraints of the variable coefficients based on the symbolic computation. By virtue of the Ablowitz-Kaup-Newell-Segur system, a Lax pair with time-dependent nonisospectral flow of the integrable form has been established under the Lax constraints which appear to be more rigid than the Painlevé ones. Under such Lax constraints, multisoliton solutions for the completely integrable variable-coefficient modified Korteweg-de Vries equation have been derived via the Hirota bilinear method. Moreover, results show that the solitons and breathers with desired amplitude and width can be derived via the different choices of the variable coefficients. PMID:21929127

  18. Exact solutions of unsteady Korteweg-de Vries and time regularized long wave equations.

    PubMed

    Islam, S M Rayhanul; Khan, Kamruzzaman; Akbar, M Ali

    2015-01-01

    In this paper, we implement the exp(-Φ(ξ))-expansion method to construct the exact traveling wave solutions for nonlinear evolution equations (NLEEs). Here we consider two model equations, namely the Korteweg-de Vries (KdV) equation and the time regularized long wave (TRLW) equation. These equations play significant role in nonlinear sciences. We obtained four types of explicit function solutions, namely hyperbolic, trigonometric, exponential and rational function solutions of the variables in the considered equations. It has shown that the applied method is quite efficient and is practically well suited for the aforementioned problems and so for the other NLEEs those arise in mathematical physics and engineering fields. PACS numbers: 02.30.Jr, 02.70.Wz, 05.45.Yv, 94.05.Fq. PMID:25810953

  19. Solution of the pulse width modulation problem using orthogonal polynomials and Korteweg-de Vries equations.

    PubMed

    Chudnovsky, D V; Chudnovsky, G V

    1999-10-26

    The mathematical underpinning of the pulse width modulation (PWM) technique lies in the attempt to represent "accurately" harmonic waveforms using only square forms of a fixed height. The accuracy can be measured using many norms, but the quality of the approximation of the analog signal (a harmonic form) by a digital one (simple pulses of a fixed high voltage level) requires the elimination of high order harmonics in the error term. The most important practical problem is in "accurate" reproduction of sine-wave using the same number of pulses as the number of high harmonics eliminated. We describe in this paper a complete solution of the PWM problem using Pade approximations, orthogonal polynomials, and solitons. The main result of the paper is the characterization of discrete pulses answering the general PWM problem in terms of the manifold of all rational solutions to Korteweg-de Vries equations. PMID:10535909

  20. The Korteweg-de Vries equation on the half-line

    NASA Astrophysics Data System (ADS)

    Fokas, Athanassios S.; Alexandrou Himonas, A.; Mantzavinos, Dionyssios

    2016-02-01

    The initial-boundary value problem (ibvp) for the Korteweg-de Vries (KdV) equation on the half-line with data in Sobolev spaces is analysed by combining the unified transform method with a contraction mapping approach. First, the linear KdV ibvp with initial and boundary data in Sobolev spaces is solved and the basic space and time estimates of the solution are derived. Then, further linear estimates in a new norm, motivated by the KdV bilinear term, are obtained. Finally, well-posedness of the KdV ibvp with data (u(x, 0), u(0, t)) in Hxs≤ft(0,∞ \\right)× Ht(s+1)/3(0,T) , \\frac{3}{4}, is established via a fixed point argument in an appropriate solution space.

  1. Korteweg-de Vries Burgers equation for magnetosonic wave in plasma

    SciTech Connect

    Hussain, S.; Mahmood, S.

    2011-05-15

    Korteweg-de Vries Burgers (KdVB) equation for magnetosonic wave propagating in the perpendicular direction of the magnetic field is derived for homogeneous electron-ion magneto-plasmas. The dissipation in the system is taken into account through the kinematic viscosity of the ions. The effects of kinematic viscosity of ions, plasma density, and magnetic field strength on the formation of magnetosonic shocks are investigated. It is found that the shock strength is enhanced with the increase in the plasma density of the system. However, the increase in magnetic field strength decreases the amplitude of magnetosonic shock wave. The critical value of the dissipative coefficient to form oscillatory profile and monotonic shock is also discussed. The numerical results have also been plotted by taking the parameters from laboratory plasma experiments.

  2. Some mathematical aspects of the correspondence between the generalized nonlinear Schroedinger equation and the generalized Korteweg-de Vries equation

    SciTech Connect

    Fedele, Renato; De Nicola, Sergio; Grecu, Dan; Visinescu, Anca; Shukla, Padma K.

    2009-11-10

    A review of the recent studies on the correspondence between a wide family of the generalized nonlinear Schroedinger equations and a wide family of the generalized Korteweg-de Vries equations is presented. It was constructed some years ago within the framework of a recently-developed approach based on the Madelung's fluid representation of the generalized nonlinear Schroedinger equation. The present analysis extends the former approach, developed for nonlinear Schroedinger equation with a nonlinear term proportional to a multiplicative operator, to the cases of derivative operators and the ones corresponding to cylindrical nonlinear Schroedinger equations.

  3. Compacton solutions in a class of generalized fifth-order Korteweg--de Vries equations

    SciTech Connect

    Cooper, Fred; Hyman, James M.; Khare, Avinash

    2001-08-01

    Solitons play a fundamental role in the evolution of general initial data for quasilinear dispersive partial differential equations, such as the Korteweg--de Vries (KdV), nonlinear Schroedinger, and the Kadomtsev-Petviashvili equations. These integrable equations have linear dispersion and the solitons have infinite support. We have derived and investigate a new KdV-like Hamiltonian partial differential equation from a four-parameter Lagrangian where the nonlinear dispersion gives rise to solitons with compact support (compactons). The new equation does not seem to be integrable and only mass, momentum, and energy seem to be conserved; yet, the solitons display almost the same modal decompositions and structural stability observed in integrable partial differential equations. The compactons formed from arbitrary initial data, are nonlinearly self-stabilizing, and maintain their coherence after multiple collisions. The robustness of these compactons and the inapplicability of the inverse scattering tools, that worked so well for the KdV equation, make it clear that there is a fundamental mechanism underlying the processes beyond integrability. We have found explicit formulas for multiple classes of compact traveling wave solutions. When there are more than one compacton solution for a particular set of parameters, the wider compacton is the minimum of a reduced Hamiltonian and is the only one that is stable.

  4. Compacton solutions in a class of generalized fifth-order Korteweg-de Vries equations.

    PubMed

    Cooper, F; Hyman, J M; Khare, A

    2001-08-01

    Solitons play a fundamental role in the evolution of general initial data for quasilinear dispersive partial differential equations, such as the Korteweg-de Vries (KdV), nonlinear Schrödinger, and the Kadomtsev-Petviashvili equations. These integrable equations have linear dispersion and the solitons have infinite support. We have derived and investigate a new KdV-like Hamiltonian partial differential equation from a four-parameter Lagrangian where the nonlinear dispersion gives rise to solitons with compact support (compactons). The new equation does not seem to be integrable and only mass, momentum, and energy seem to be conserved; yet, the solitons display almost the same modal decompositions and structural stability observed in integrable partial differential equations. The compactons formed from arbitrary initial data, are nonlinearly self-stabilizing, and maintain their coherence after multiple collisions. The robustness of these compactons and the inapplicability of the inverse scattering tools, that worked so well for the KdV equation, make it clear that there is a fundamental mechanism underlying the processes beyond integrability. We have found explicit formulas for multiple classes of compact traveling wave solutions. When there are more than one compacton solution for a particular set of parameters, the wider compacton is the minimum of a reduced Hamiltonian and is the only one that is stable. PMID:11497731

  5. Soliton evolution and radiation loss for the Korteweg--de Vries equation

    SciTech Connect

    Kath, W.L.; Smyth, N.F. Department of Mathematics and Statistics, University of Edinburgh, The King's Buildings, Mayfield Road, Edinburgh EH93JZ, Scotland )

    1995-01-01

    The time-dependent behavior of solutions of the Korteweg--de Vries (KdV) equation for nonsoliton initial conditions is considered. While the exact solution of the KdV equation can in principle be obtained using the inverse scattering transform, in practice it can be extremely difficult to obtain information about a solution's transient evolution by this method. As an alternative, we present here an approximate method for investigating this transient evolution which is based upon the conservation laws associated with the KdV equation. Initial conditions which form one or two solitons are considered, and the resulting approximate evolution is found to be in good agreement with the numerical solution of the KdV equation. Justification for the approximations employed is also given by way of the linearized inverse scattering solution of the KdV equation. In addition, the final soliton state determined from the approximate equations agrees very well with the final state determined from the exact inverse scattering transform solution.

  6. A Hamiltonian preserving discontinuous Galerkin method for the generalized Korteweg-de Vries equation

    NASA Astrophysics Data System (ADS)

    Liu, Hailiang; Yi, Nianyu

    2016-09-01

    The invariant preserving property is one of the guiding principles for numerical algorithms in solving wave equations, in order to minimize phase and amplitude errors after long time simulation. In this paper, we design, analyze and numerically validate a Hamiltonian preserving discontinuous Galerkin method for solving the Korteweg-de Vries (KdV) equation. For the generalized KdV equation, the semi-discrete formulation is shown to preserve both the first and the third conserved integrals, and approximately preserve the second conserved integral; for the linearized KdV equation, all the first three conserved integrals are preserved, and optimal error estimates are obtained for polynomials of even degree. The preservation properties are also maintained by the fully discrete DG scheme. Our numerical experiments demonstrate both high accuracy of convergence and preservation of all three conserved integrals for the generalized KdV equation. We also show that the shape of the solution, after long time simulation, is well preserved due to the Hamiltonian preserving property.

  7. Quartic B-spline collocation method applied to Korteweg de Vries equation

    NASA Astrophysics Data System (ADS)

    Zin, Shazalina Mat; Majid, Ahmad Abd; Ismail, Ahmad Izani Md

    2014-07-01

    The Korteweg de Vries (KdV) equation is known as a mathematical model of shallow water waves. The general form of this equation is ut+ɛuux+μuxxx = 0 where u(x,t) describes the elongation of the wave at displacement x and time t. In this work, one-soliton solution for KdV equation has been obtained numerically using quartic B-spline collocation method for displacement x and using finite difference approach for time t. Two problems have been identified to be solved. Approximate solutions and errors for these two test problems were obtained for different values of t. In order to look into accuracy of the method, L2-norm and L∞-norm have been calculated. Mass, energy and momentum of KdV equation have also been calculated. The results obtained show the present method can approximate the solution very well, but as time increases, L2-norm and L∞-norm are also increase.

  8. Shallow-water soliton dynamics beyond the Korteweg-de Vries equation.

    PubMed

    Karczewska, Anna; Rozmej, Piotr; Infeld, Eryk

    2014-07-01

    An alternative way for the derivation of the new Korteweg-de Vries (KdV)-type equation is presented. The equation contains terms depending on the bottom topography (there are six new terms in all, three of which are caused by the unevenness of the bottom). It is obtained in the second-order perturbative approach in the weakly nonlinear, dispersive, and long wavelength limit. Only treating all these terms in the second-order perturbation theory made the derivation of this KdV-type equation possible. The motion of a wave, which starts as a KdV soliton, is studied according to the new equation in several cases by numerical simulations. The quantitative changes of a soliton's velocity and amplitude appear to be directly related to bottom variations. Changes of the soliton's velocity appear to be almost linearly anticorrelated with changes of water depth, whereas correlation of variation of soliton's amplitude with changes of water depth looks less linear. When the bottom is flat, the new terms narrow down the family of exact solutions, but at least one single soliton survives. This is also checked by numerics. PMID:25122360

  9. Derivation of electrostatic Korteweg-deVries equation in fully relativistic two-fluid plasmas

    SciTech Connect

    Lee, Nam C.

    2008-08-15

    A second order Korteweg-deVries (KdV) equation that describes the evolution of nonlinear electrostatic waves in fully relativistic two-fluid plasmas is derived without any assumptions restricting the magnitudes of the flow velocity and the temperatures of each species. In the derivation, the positive and negative species of plasmas are treated with equal footings, not making any species specific assumptions. Thus, the resulting equation, which is expressed in transparent form symmetric in particle species, can be applied to any two-fluid plasmas having arbitrarily large flow velocity and ultrarelativistically high temperatures. The phase velocity of the nonlinear electrostatic waves found in this paper is shown to be related to the flow velocity and the acoustic wave velocity through the Lorentz addition law of velocities, revealing the relativistic nature of the formulation in the present study. The derived KdV equation is applied to some limiting cases, and it is shown that it can be reduced to existing results in nonrelativistic plasmas, while there are some discrepancies from the results in the weak relativistic approximations.

  10. Rare-event Simulation for Stochastic Korteweg-de Vries Equation

    SciTech Connect

    Xu, Gongjun; Lin, Guang; Liu, Jingchen

    2014-01-01

    An asymptotic analysis of the tail probabilities for the dynamics of a soliton wave $U(x,t)$ under a stochastic time-dependent force is developed. The dynamics of the soliton wave $U(x,t)$ is described by the Korteweg-de Vries Equation with homogeneous Dirichlet boundary conditions under a stochastic time-dependent force, which is modeled as a time-dependent Gaussian noise with amplitude $\\epsilon$. The tail probability we considered is $w(b) :=P(\\sup_{t\\in [0,T]} U(x,t) > b ),$ as $b\\rightarrow \\infty,$ for some constant $T>0$ and a fixed $x$, which can be interpreted as tail probability of the amplitude of water wave on shallow surface of a fluid or long internal wave in a density-stratified ocean. Our goal is to characterize the asymptotic behaviors of $w(b)$ and to evaluate the tail probability of the event that the soliton wave exceeds a certain threshold value under a random force term. Such rare-event calculation of $w(b)$ is very useful for fast estimation of the risk of the potential damage that could caused by the water wave in a density-stratified ocean modeled by the stochastic KdV equation. In this work, the asymptotic approximation of the probability that the soliton wave exceeds a high-level $b$ is derived. In addition, we develop a provably efficient rare-event simulation algorithm to compute $w(b)$. The efficiency of the algorithm only requires mild conditions and therefore it is applicable to a general class of Gaussian processes and many diverse applications.

  11. Energy invariant for shallow-water waves and the Korteweg-de Vries equation: Doubts about the invariance of energy.

    PubMed

    Karczewska, Anna; Rozmej, Piotr; Infeld, Eryk

    2015-11-01

    It is well known that the Korteweg-de Vries (KdV) equation has an infinite set of conserved quantities. The first three are often considered to represent mass, momentum, and energy. Here we try to answer the question of how this comes about and also how these KdV quantities relate to those of the Euler shallow-water equations. Here Luke's Lagrangian is helpful. We also consider higher-order extensions of KdV. Though in general not integrable, in some sense they are almost so within the accuracy of the expansion. PMID:26651809

  12. Energy invariant for shallow-water waves and the Korteweg-de Vries equation: Doubts about the invariance of energy

    NASA Astrophysics Data System (ADS)

    Karczewska, Anna; Rozmej, Piotr; Infeld, Eryk

    2015-11-01

    It is well known that the Korteweg-de Vries (KdV) equation has an infinite set of conserved quantities. The first three are often considered to represent mass, momentum, and energy. Here we try to answer the question of how this comes about and also how these KdV quantities relate to those of the Euler shallow-water equations. Here Luke's Lagrangian is helpful. We also consider higher-order extensions of KdV. Though in general not integrable, in some sense they are almost so within the accuracy of the expansion.

  13. Korteweg de Vries Burgers equation in multi-ion and pair-ion plasmas with Lorentzian electrons

    SciTech Connect

    Hussain, S.; Akhtar, N.

    2013-01-15

    Korteweg de Vries Burgers equation for multi-ion and pair-ion plasmas has been derived using reductive perturbation technique. The kinematic viscosities of both positive and negative ions are taken into account. Generalized Lorentzian distribution is assumed for the electron component, accounting for deviation from Maxwellian equilibrium, parametrized via a real parameter {kappa}. The modification in the strength of shock structure is presented. A comprehensive comparison between the profiles of shock wave structure in multi-ion and pair-ion plasmas, (for the Maxwellian electrons to Lorentzian electrons), is discussed.

  14. Supersymmetric quantum mechanics and the Korteweg--de Vries hierarchy

    SciTech Connect

    Grant, A.K.; Rosner, J.L. )

    1994-05-01

    The connection between supersymmetric quantum mechanics and the Korteweg--de Vries (KdV) equation is discussed, with particular emphasis on the KdV conservation laws. It is shown that supersymmetric quantum mechanics aids in the derivation of the conservation laws, and gives some insight into the Miura transformation that converts the KdV equation into the modified KdV equation. The construction of the [tau] function by means of supersymmetric quantum mechanics is discussed.

  15. On a hierarchy of nonlinearly dispersive generalized Korteweg - de Vries evolution equations

    SciTech Connect

    Christov, Ivan C.

    2015-08-20

    We propose a hierarchy of nonlinearly dispersive generalized Korteweg–de Vries (KdV) evolution equations based on a modification of the Lagrangian density whose induced action functional the KdV equation extremizes. Two recent nonlinear evolution equations describing wave propagation in certain generalized continua with an inherent material length scale are members of the proposed hierarchy. Like KdV, the equations from the proposed hierarchy possess Hamiltonian structure. Unlike KdV, the solutions to these equations can be compact (i.e., they vanish outside of some open interval) and, in addition, peaked. Implicit solutions for these peaked, compact traveling waves (“peakompactons”) are presented.

  16. N=2 supersymmetric a=4-Korteweg-de Vries hierarchy derived via Gardner's deformation of Kaup-Boussinesq equation

    SciTech Connect

    Hussin, V.; Kiselev, A. V.; Krutov, A. O.; Wolf, T.

    2010-08-15

    We consider the problem of constructing Gardner's deformations for the N=2 supersymmetric a=4-Korteweg-de Vries (SKdV) equation; such deformations yield recurrence relations between the super-Hamiltonians of the hierarchy. We prove the nonexistence of supersymmetry-invariant deformations that retract to Gardner's formulas for the Korteweg-de Vries (KdV) with equation under the component reduction. At the same time, we propose a two-step scheme for the recursive production of the integrals of motion for the N=2, a=4-SKdV. First, we find a new Gardner's deformation of the Kaup-Boussinesq equation, which is contained in the bosonic limit of the superhierarchy. This yields the recurrence relation between the Hamiltonians of the limit, whence we determine the bosonic super-Hamiltonians of the full N=2, a=4-SKdV hierarchy. Our method is applicable toward the solution of Gardner's deformation problems for other supersymmetric KdV-type systems.

  17. Numerical study of blow-up and dispersive shocks in solutions to generalized Korteweg-de Vries equations

    NASA Astrophysics Data System (ADS)

    Klein, C.; Peter, R.

    2015-06-01

    We present a detailed numerical study of solutions to general Korteweg-de Vries equations with critical and supercritical nonlinearity, both in the context of dispersive shocks and blow-up. We study the stability of solitons and show that they are unstable against being radiated away and blow-up. In the L2 critical case, the blow-up mechanism by Martel, Merle and Raphaël can be numerically identified. In the limit of small dispersion, it is shown that a dispersive shock always appears before an eventual blow-up. In the latter case, always the first soliton to appear will blow up. It is shown that the same type of blow-up as for the perturbations of the soliton can be observed which indicates that the theory by Martel, Merle and Raphaël is also applicable to initial data with a mass much larger than the soliton mass. We study the scaling of the blow-up time t∗ in dependence of the small dispersion parameter ɛ and find an exponential dependence t∗(ɛ) and that there is a minimal blow-up time t0∗ greater than the critical time of the corresponding Hopf solution for ɛ → 0. To study the cases with blow-up in detail, we apply the first dynamic rescaling for generalized Korteweg-de Vries equations. This allows to identify the type of the singularity.

  18. Spontaneous soliton generation in the higher order Korteweg-de Vries equations on the half-line.

    PubMed

    Burde, G I

    2012-03-01

    Some new effects in the soliton dynamics governed by higher order Korteweg-de Vries (KdV) equations are discussed based on the exact explicit solutions of the equations on the positive half-line. The solutions describe the process of generation of a soliton that occurs without boundary forcing and on the steady state background: the boundary conditions remain constant and the initial distribution is a steady state solution of the problem. The time moment when the soliton generation starts is not determined by the parameters present in the problem formulation, the additional parameters imbedded into the solution are needed to determine that moment. The equations found capable of describing those effects are the integrable Sawada-Kotera equation and the KdV-Kaup-Kupershmidt (KdV-KK) equation which, albeit not proven to be integrable, possesses multi-soliton solutions. PMID:22463014

  19. Quasi-periodic wave solutions and asymptotic properties to an extended Korteweg-de Vries equation from fluid dynamics

    NASA Astrophysics Data System (ADS)

    Xu, Mei-Juan; Tian, Shou-Fu; Tu, Jian-Min; Ma, Pan-Li; Zhang, Tian-Tian

    2016-01-01

    In this paper, an extended Korteweg-de Vries (eKdV) equation is investigated, which can be used to describe many nonlinear phenomena in fluid dynamics and plasma physics. With the aid of the generalized Bell’s polynomials, the Hirota’s bilinear equation to the eKdV equation is succinctly constructed. Based on that, its solition solutions are directly obtained. By virtue of the Riemann theta function, a straightforward way is presented to explicitly construct Riemann theta function periodic wave solutions of the eKdV equation. Finally, the asymptotic behaviors of the Riemann theta function periodic waves are presented, which yields a relationship between the periodic waves and solition solutions by considering a limiting procedure.

  20. Explicit solutions from eigenfunction symmetry of the Korteweg-de Vries equation.

    PubMed

    Hu, Xiao-Rui; Lou, Sen-Yue; Chen, Yong

    2012-05-01

    In nonlinear science, it is very difficult to find exact interaction solutions among solitons and other kinds of complicated waves such as cnoidal waves and Painlevé waves. Actually, even if for the most well-known prototypical models such as the Kortewet-de Vries (KdV) equation and the Kadomtsev-Petviashvili (KP) equation, this kind of problem has not yet been solved. In this paper, the explicit analytic interaction solutions between solitary waves and cnoidal waves are obtained through the localization procedure of nonlocal symmetries which are related to Darboux transformation for the well-known KdV equation. The same approach also yields some other types of interaction solutions among different types of solutions such as solitary waves, rational solutions, Bessel function solutions, and/or general Painlevé II solutions. PMID:23004895

  1. Quasi-periodic wave solutions and asymptotic properties for a fifth-order Korteweg-de Vries type equation

    NASA Astrophysics Data System (ADS)

    Qin, Chun-Yan; Tian, Shou-Fu; Wang, Xiu-Bin; Zhang, Tian-Tian

    2016-07-01

    Under investigation in this paper is a fifth-order Korteweg-de Vries type (fKdV-type) equation with time-dependent coefficients, which can be used to describe many nonlinear phenomena in fluid mechanics, ocean dynamics and plasma physics. The binary Bell polynomials are employed to find its Hirota’s bilinear formalism with an extra auxiliary variable, based on which its N-soliton solutions can be also directly derived. Furthermore, by considering multi-dimensional Riemann theta function, a lucid and straightforward generalization of the Hirota-Riemann method is presented to explicitly construct the multiperiodic wave solutions of the equation. Finally, the asymptotic properties of these periodic wave solutions are strictly analyzed to reveal the relationships between periodic wave solutions and soliton solutions.

  2. (3 + 1)-dimensional cylindrical Korteweg-de Vries equation for nonextensive dust acoustic waves: Symbolic computation and exact solutions

    SciTech Connect

    Guo Shimin; Wang Hongli; Mei Liquan

    2012-06-15

    By combining the effects of bounded cylindrical geometry, azimuthal and axial perturbations, the nonlinear dust acoustic waves (DAWs) in an unmagnetized plasma consisting of negatively charged dust grains, nonextensive ions, and nonextensive electrons are studied in this paper. Using the reductive perturbation method, a (3 + 1)-dimensional variable-coefficient cylindrical Korteweg-de Vries (KdV) equation describing the nonlinear propagation of DAWs is derived. Via the homogeneous balance principle, improved F-expansion technique and symbolic computation, the exact traveling and solitary wave solutions of the KdV equation are presented in terms of Jacobi elliptic functions. Moreover, the effects of the plasma parameters on the solitary wave structures are discussed in detail. The obtained results could help in providing a good fit between theoretical analysis and real applications in space physics and future laboratory plasma experiments where long-range interactions are present.

  3. Soliton solutions for a (3 + 1)-dimensional modified Korteweg-de Vries-Zakharov-Kuznetsov equation in a plasma

    NASA Astrophysics Data System (ADS)

    Sun, Yan; Tian, Bo; Zhen, Hui-Ling; Wu, Xiao-Yu; Xie, Xi-Yang

    2016-07-01

    Under investigation in this paper is a (3 + 1)-dimensional modified Korteweg-de Vries-Zakharov-Kuznetsov (KdV-ZK) equation, which describes the nonlinear behaviors of ion-acoustic waves in a magnetized plasma where the cooler ions are treated as a fluid with adiabatic pressure and the hot isothermal electrons are described by a Boltzmann distribution. With the Hirota method and symbolic computation, we obtain the one-, two- and three-soliton solutions for such an equation. We graphically study the solitons related with the coefficient of the cubic nonlinearity M. Amplitude of the one soliton increases with increasing M, but the width of one soliton keeps unchanged as M increases. The two solitons and three solitons are parallel, and the amplitudes of the solitons increase with increasing M, but the widths of the solitons are unchanged. It is shown that the interactions between the two solitons and among the three solitons are elastic.

  4. Solitonic propagation and interaction for a generalized variable-coefficient forced Korteweg-de Vries equation in fluids.

    PubMed

    Yu, Xin; Gao, Yi-Tian; Sun, Zhi-Yuan; Liu, Ying

    2011-05-01

    Under investigation is a generalized variable-coefficient forced Korteweg-de Vries equation in fluids and other fields. From the bilinear form of such equation, the N-soliton solution and a type of analytic solution are constructed with symbolic computation. Analytic analysis indicates that: (1) dispersive and dissipative coefficients affect the solitonic velocity; (2) external-force term affects the solitonic velocity and background; (3) line-damping coefficient and some parameters affect the solitonic velocity, background, and amplitude. Solitonic propagation and interaction can be regarded as the combination of the effects of various variable coefficients. According to a constraint among the nonlinear, dispersive, and line-damping coefficients in this paper, the possible applications of our results in the real world are also discussed in three aspects, i.e., solution with the constraint, solution without the constraint, and approximate solution. PMID:21728676

  5. Phase Transitions and the Korteweg-De Vries Equation in the Density Difference Lattice Hydrodynamic Model of Traffic Flow

    NASA Astrophysics Data System (ADS)

    Tian, Jun-Fang; Yuan, Zhen-Zhou; Jia, Bin; Fan, Hong-Qiang

    2013-03-01

    We investigate the phase transitions and the Korteweg-de Vries (KdV) equation in the density difference lattice hydrodynamic (DDLM) model, which shows a close connection with the gas-kinetic-based model and the microscopic car following model. The KdV equation near the neutral stability line is derived and the corresponding soliton solution describing the density waves is obtained. Numerical simulations are conducted in two aspects. On the one hand, under periodic conditions perturbations are applied to demonstrate the nonlinear analysis result. On the other hand, the open boundary condition with random fluctuations is designed to explore the empirical congested traffic patterns. The phase transitions among the free traffic (FT), widening synchronized flow pattern (WSP), moving localized cluster (MLC), oscillatory congested traffic (OCT) and homogeneous congested traffic (HCT) occur by varying the amplitude of the fluctuations. To our knowledge, it is the first research showing that the lattice hydrodynamic model could reproduce so many congested traffic patterns.

  6. Nonlinear Korteweg-de Vries equation for soliton propagation in relativistic electron-positron-ion plasma with thermal ions

    NASA Astrophysics Data System (ADS)

    Saeed, R.; Shah, Asif; Noaman-Ul-Haq, Muhammad

    2010-10-01

    The nonlinear propagation of ion-acoustic solitons in relativistic electron-positron-ion plasma comprising of Boltzmannian electrons, positrons, and relativistic thermal ions has been examined. The Korteweg-de Vries equation has been derived by reductive perturbation technique. The effect of various plasma parameters on amplitude and structure of solitary wave is investigated. The pert graphical view of the results has been presented for illustration. It is observed that increase in the relativistic streaming factor causes the soliton amplitude to thrive and its width shrinks. The soliton amplitude and width decline as the ion to electron temperature ratio is increased. The increase in positron concentration results in reduction of soliton amplitude. The soliton amplitude enhances as the electron to positron temperature ratio is increased. Our results may have relevance in the understanding of astrophysical plasmas.

  7. Solitary waves propagation described by Korteweg-de Vries equation in the granular chain with initial prestress

    NASA Astrophysics Data System (ADS)

    Yang, Yang Yang; Liu, Shi Wei; Yang, Qiong; Zhang, Zhen Bin; Duan, Wen Shan; Yang, Lei

    2016-07-01

    The paper work relates to Nesterenko's problem to further study the solitary wave when the strong external force acts on the granular chain. We also study the problem under the long-wavelength approximation and find that such kind of solitary wave in system with the initial prestress can be described by the Korteweg-de Vries (KdV) equation. It is found that the results of analytical and numerical are in an excellent agreement. Furthermore, we study the scattering of the KdV solitary wave in different granular materials both in theoretical and numerical methods. It is found that the numbers and the amplitudes of both the reflected and the transmitted waves depend not only on the amplitude of the incident solitary wave but also on the variations of both sides of the discontinuity such as the mass, Young's modulus or radius of the grains.

  8. Nonlinear Korteweg-de Vries equation for soliton propagation in relativistic electron-positron-ion plasma with thermal ions

    SciTech Connect

    Saeed, R.; Shah, Asif; Noaman-ul-Haq, Muhammad

    2010-10-15

    The nonlinear propagation of ion-acoustic solitons in relativistic electron-positron-ion plasma comprising of Boltzmannian electrons, positrons, and relativistic thermal ions has been examined. The Korteweg-de Vries equation has been derived by reductive perturbation technique. The effect of various plasma parameters on amplitude and structure of solitary wave is investigated. The pert graphical view of the results has been presented for illustration. It is observed that increase in the relativistic streaming factor causes the soliton amplitude to thrive and its width shrinks. The soliton amplitude and width decline as the ion to electron temperature ratio is increased. The increase in positron concentration results in reduction of soliton amplitude. The soliton amplitude enhances as the electron to positron temperature ratio is increased. Our results may have relevance in the understanding of astrophysical plasmas.

  9. The Hamiltonian structure of a coupled system derived from a supersymmetric breaking of super Korteweg-de Vries equations

    NASA Astrophysics Data System (ADS)

    Restuccia, A.; Sotomayor, A.

    2013-11-01

    A supersymmetric breaking procedure for N = 1 super Korteweg-de Vries (KdV), using a Clifford algebra, is implemented. Dirac's method for the determination of constraints is used to obtain the Hamiltonian structure, via a Lagrangian, for the resulting solitonic system of coupled KdV type system. It is shown that the Hamiltonian obtained by this procedure is bounded from below and in that sense represents a model which is physically admissible.

  10. The Hamiltonian structure of a coupled system derived from a supersymmetric breaking of super Korteweg-de Vries equations

    SciTech Connect

    Restuccia, A.; Sotomayor, A.

    2013-11-15

    A supersymmetric breaking procedure for N= 1 super Korteweg-de Vries (KdV), using a Clifford algebra, is implemented. Dirac's method for the determination of constraints is used to obtain the Hamiltonian structure, via a Lagrangian, for the resulting solitonic system of coupled KdV type system. It is shown that the Hamiltonian obtained by this procedure is bounded from below and in that sense represents a model which is physically admissible.

  11. Travelling Wave Solutions for the Burgers Equation and the Korteweg-de Vries Equation with Variable Coefficients Using the Generalized (Ǵ/G)-Expansion Method

    NASA Astrophysics Data System (ADS)

    Zayed, Elsayed M. E.; Abdelaziz, Mahmoud A. M.

    2010-12-01

    In this article, a generalized (Ǵ/G)-expansion method is used to find exact travelling wave solutions of the Burgers equation and the Korteweg-de Vries (KdV) equation with variable coefficients. As a result, hyperbolic, trigonometric, and rational function solutions with parameters are obtained. When these parameters are taking special values, the solitary wave solutions are derived from the hyperbolic function solution. It is shown that the proposed method is direct, effective, and can be applied to many other nonlinear evolution equations in mathematical physics.

  12. Nonlinear structures of the Korteweg-de Vries and modified Korteweg-de Vries equations in non-Maxwellian electron-positron-ion plasma: Solitons collision and rogue waves

    SciTech Connect

    El-Tantawy, S. A.; Moslem, W. M.

    2014-05-15

    Solitons (small-amplitude long-lived waves) collision and rogue waves (large-amplitude short-lived waves) in non-Maxwellian electron-positron-ion plasma have been investigated. For the solitons collision, the extended Poincaré-Lighthill-Kuo perturbation method is used to derive the coupled Korteweg-de Vries (KdV) equations with the quadratic nonlinearities and their corresponding phase shifts. The calculations reveal that both positive and negative polarity solitons can propagate in the present model. At critical value of plasma parameters, the coefficients of the quadratic nonlinearities disappear. Therefore, the coupled modified KdV (mKdV) equations with cubic nonlinearities and their corresponding phase shifts have been derived. The effects of the electron-to-positron temperature ratio, the ion-to-electron temperature ratio, the positron-to-ion concentration, and the nonextensive parameter on the colliding solitons profiles and their corresponding phase shifts are examined. Moreover, generation of ion-acoustic rogue waves from small-amplitude initial perturbations in plasmas is studied in the framework of the mKdV equation. The properties of the ion-acoustic rogue waves are examined within a nonlinear Schrödinger equation (NLSE) that has been derived from the mKdV equation. The dependence of the rogue wave profile on the relevant physical parameters has been investigated. Furthermore, it is found that the NLSE that has been derived from the KdV equation cannot support the propagation of rogue waves.

  13. Initial conditions and Korteweg-de Vries solitons

    NASA Technical Reports Server (NTRS)

    Weidman, P. D.; Redekopp, L. G.

    1982-01-01

    The effects of rectangular initial data on the evolution of solitons governed by the Korteweg-de Vries equation is studied. Both isolated and separated disturbances are considered, providing some general insight into how the nature of the initial condition influences the appearance of solitons in the asymptotic state. The analytic approach is based on the inverse scattering transform which relates the initial condition to Schroedinger's equation. The results are used to model the initial shallow-water disturbances, and the results can be summarized by stating that the number of evolved solitons depends on the strength of each rectangular disturbance, the relative amplitudes of the rectangular disturbances, and the relative proximity of the disturbances.

  14. Compactons in PT-symmetric generalized Korteweg-de Vries equations

    SciTech Connect

    Saxena, Avadh B; Mihaila, Bogdan; Bender, Carl M; Cooper, Fred; Khare, Avinash

    2008-01-01

    In an earlier paper Cooper, Shepard, and Sodano introduced a generalized KdV equation that can exhibit the kinds of compacton solitary waves that were first seen in equations studied by Rosenau and Hyman. This paper considers the PT-symmetric extensions of the equations examined by Cooper, Shepard, and Sodano. From the scaling properties of the PT-symmetric equations a general theorem relating the energy, momentum, and velocity of any solitary-wave solution of the generalized KdV equation is derived, and it is shown that the velocity of the solitons is determined by their amplitude, width, and momentum.

  15. Asymptotic behavior of solutions of the Korteweg-de Vries equation

    SciTech Connect

    Buslaev, V.S.

    1986-09-01

    For the KdV equation a complete asymptotic expansion of the ''dispersive tail'' for large times is described, and generalized wave operators are introduced. The asymptotics for large times of the spectral Schrodinger equation with a potential of the type of a solution of the KdV equation is studied. It is shown that the KdV equation is connected in a specific manner with the structure of the asymptotics of solutions of the spectral equation. As a corollary, known explicit formulas for the leading terms of the asymptotics of solutions of the KdV equation in terms of spectral data corresponding to the initial conditions are obtained. A plan for justifying the results listed is outlined.

  16. Asymptotic behavior of solutions of the Korteweg-de Vries equation for large times

    SciTech Connect

    Buslaev, V.S.; Sukhanov, V.V.

    1986-09-10

    For the KdV equation a complete asymptotic expansion of the dispersive tail for large times is described, and generalized wave operators are introduced. The asymptotics for large times of the spectral Schroedinger equation with a potential of the type of a solution of the KdV equation is studied. It is shown that the KdV equation is connected in a specific manner with the structure of the asymptotics of solutions of the spectral equation. As a corollary, known explicit formulas for the leading terms of the asymptotics of solutions of the KdV equation in terms of spectral data corresponding to the initial conditions are obtained. A plan for justifying the results listed is outlined.

  17. Korteweg-de Vries-Kuramoto-Sivashinsky filters in biomedical image processing

    NASA Astrophysics Data System (ADS)

    Arango, Juan C.

    2015-09-01

    The Kuramoto- Sivashinsky operator is applied to the two-dimensional solution of the Korteweg-de Vries equation and the resulting filter is applied via convolution to image processing. The full procedure is implemented using an algorithm: prototyped with the Maple package named Image Tools. Some experiments were performed using biomedical images, infrared images obtained with smartphones and images generated by photon diffusion. The results from these experiments show that the Kuramoto-Sivashinsky-Korteweg-de Vries Filters are excellent tools for enhancement of images with interesting applications in image processing at general and biomedical image processing in particular. It is expected that the incorporation of the Kuramoto-Sivashinsky-Korteweg-de Vries Filters in standard programs for image processing will led to important improvements in various fields of optical engineering.

  18. Long-time asymptotic behavior of the solutions of the Korteweg-De Vries equations

    SciTech Connect

    Buslaev, V.S.; Sukhanov, V.V.

    1987-05-20

    The complete asymptotic expansion of the dispersion tail in the long-time limit is described for the KdV equation and generalized wave operators are introduced. The long-time asymptotic behavior of the Schroedinger spectral equation is studied assuming a potential of the type of the KdV solution. It is shown that the KdV equation is specifically related with the asymptotic structure of the solutions of the spectral equation. As a corollary, they derive the well-known explicit formulas for the leading asymptotic terms of the KdV solutions in terms of the spectral values corresponding to the initial conditions. A sketch of a proof for the various results is suggested.

  19. Conservation laws, Korteweg--de Vries and sine-Gordon systems, and the role of supersymmetry

    SciTech Connect

    Bagchi, B.; Lahiri, A.; Roy, P.K.

    1989-02-15

    It is shown that the eigenvalue problem of the L operator for the sine-Gordon equation can be put in a supersymmetric form. We comment on the connection between the conserved quantities of the Korteweg--de Vries and sine-Gordon systems.

  20. Stability analysis solutions for nonlinear three-dimensional modified Korteweg-de Vries-Zakharov-Kuznetsov equation in a magnetized electron-positron plasma

    NASA Astrophysics Data System (ADS)

    Seadawy, Aly R.

    2016-08-01

    The nonlinear three-dimensional modified Korteweg-de Vries-Zakharov-Kuznetsov ​(mKdV-ZK) equation governs the behavior of weakly nonlinear ion-acoustic waves in magnetized electron-positron plasma which consists of equal hot and cool components of each species. By using the reductive perturbation procedure leads to a mKdV-ZK equation governing the oblique propagation of nonlinear electrostatic modes. The stability of solitary traveling wave solutions of the mKdV-ZK equation to three-dimensional long-wavelength perturbations is investigated. We found the electrostatic field potential and electric field in form traveling wave solutions for three-dimensional mKdV-ZK equation. The solutions for the mKdV-ZK equation are obtained precisely and efficiency of the method can be demonstrated.

  1. Extended modified Korteweg - de Vries equation for internal gravity waves in a symmetric three-layer fluid

    NASA Astrophysics Data System (ADS)

    Polukhina, Oxana; Kurkin, Andrey; Vladykina, Ekaterina

    2010-05-01

    Three-layer stratification is proved to be a proper approximation of sea water density and background current profiles in some basins in the World Ocean with specific hydrological conditions. Such a medium is interesting from the point of view of internal gravity wave dynamics, because, in the symmetric about mid-depth case (equal thicknesses of the lower and the upper layers, equal small density jumps on the interfaces), it leads to disappearing of quadratic nonlinearity when described in the framework of weakly nonlinear evolutionary models, which are derived through the asymptotic expansion in small parameters of nonlinearity and dispersion. In this situation the nonlinear transformation of the internal wave disturbances, as is customary, is determined by the influence of the next-order - cubic - nonlinear term in asymptotic series, and for three-layer fluid model the cubic nonlinearity coefficient can have either sign depending on the layer depths (in contrast to traditional two-layer approximation, for which cubic nonlinearity is always negative). Appropriate nonlinear evolutionary equation is modified Korteweg - de Vries equation (mKdV). It is well-known integrable equation of KdV-type, providing solitary wave and breather solutions for positive cubic nonlinearity. The property of sign change for cubic nonlinear coefficient in the mKdV for internal gravity waves in symmetric three-layer fluid requires taking into account next-order nonlinear term (or terms), therefore higher-order extensions of mKdV equation are necessary to provide improved description of internal wave processes. In the present study we derive nonlinear evolution equations for both interfaces in symmetric three-layer fluid (under Boussinesq approximation) up to the fourth order in small parameters of nonlinearity (epsilon) and dispersion (?). Applying mKdV-scaling for ratio of these parameters (? = epsilon2) we obtain high-order mKdV equations for interfaces (they have different signs of

  2. Symmetry breaking in linearly coupled Korteweg-de Vries systems.

    PubMed

    Espinosa-Cerón, A; Malomed, B A; Fujioka, J; Rodríguez, R F

    2012-09-01

    We consider solitons in a system of linearly coupled Korteweg-de Vries (KdV) equations, which model two-layer settings in various physical media. We demonstrate that traveling symmetric solitons with identical components are stable at velocities lower than a certain threshold value. Above the threshold, which is found exactly, the symmetric modes are unstable against spontaneous symmetry breaking, which gives rise to stable asymmetric solitons. The shape of the asymmetric solitons is found by means of a variational approximation and in the numerical form. Simulations of the evolution of an unstable symmetric soliton sometimes produce its breakup into two different asymmetric modes. Collisions between moving stable solitons, symmetric and asymmetric ones, are studied numerically, featuring noteworthy features. In particular, collisions between asymmetric solitons with identical polarities are always elastic, while in the case of opposite polarities the collision leads to a switch of the polarities of both solitons. Three-soliton collisions are studied too, featuring quite complex interaction scenarios. PMID:23020484

  3. An extension of the steepest descent method for Riemann-Hilbert problems: the small dispersion limit of the Korteweg-de Vries (KdV) equation.

    PubMed

    Deift, P; Venakides, S; Zhou, X

    1998-01-20

    This paper extends the steepest descent method for Riemann-Hilbert problems introduced by Deift and Zhou in a critical new way. We present, in particular, an algorithm, to obtain the support of the Riemann-Hilbert problem for leading asymptotics. Applying this extended method to small dispersion KdV (Korteweg-de Vries) equation, we (i) recover the variational formulation of P. D. Lax and C. D. Levermore [(1979) Proc. Natl. Acad. Sci. USA76, 3602-3606] for the weak limit of the solution, (ii) derive, without using an ansatz, the hyperelliptic asymptotic solution of S. Venakides that describes the oscillations; and (iii) are now able to compute the phase shifts, integrating the modulation equations exactly. The procedure of this paper is a version of fully nonlinear geometrical optics for integrable systems. With some additional analysis the theory can provide rigorous error estimates between the solution and its computed asymptotic expression. PMID:11038618

  4. Effect of trapped electron on the dust ion acoustic waves in dusty plasma using time fractional modified Korteweg-de Vries equation

    SciTech Connect

    Nazari-Golshan, A.; Nourazar, S. S.

    2013-10-15

    The time fractional modified Korteweg-de Vries (TFMKdV) equation is solved to study the nonlinear propagation of small but finite amplitude dust ion-acoustic (DIA) solitary waves in un-magnetized dusty plasma with trapped electrons. The plasma is composed of a cold ion fluid, stationary dust grains, and hot electrons obeying a trapped electron distribution. The TFMKdV equation is derived by using the semi-inverse and Agrawal's methods and then solved by the Laplace Adomian decomposition method. Our results show that the amplitude of the DIA solitary waves increases with the increase of time fractional order β, the wave velocity v{sub 0}, and the population of the background free electrons λ. However, it is vice-versa for the deviation from isothermality parameter b, which is in agreement with the result obtained previously.

  5. Bell-Polynomial Approach and Soliton Solutions for Some Higher-Order Korteweg-de Vries Equations in Fluid Mechanics, Plasma Physics and Lattice Dynamics

    NASA Astrophysics Data System (ADS)

    Li, He; Gao, Yi-Tian; Liu, Li-Cai

    2015-12-01

    The Korteweg-de Vries (KdV)-type equations have been seen in fluid mechanics, plasma physics and lattice dynamics, etc. This paper will address the bilinearization problem for some higher-order KdV equations. Based on the relationship between the bilinear method and Bell-polynomial scheme, with introducing an auxiliary independent variable, we will present the general bilinear forms. By virtue of the symbolic computation, one- and two-soliton solutions are derived. Supported by the National Natural Science Foundation of China under Grant No. 11272023, the Open Fund of State Key Laboratory of Information Photonics and Optical Communications (Beijing University of Posts and Telecommunications), and by the Fundamental Research Funds for the Central Universities of China under Grant No. 2011BUPTYB02

  6. Characterizing traveling-wave collisions in granular chains starting from integrable limits: the case of the Korteweg-de Vries equation and the Toda lattice.

    PubMed

    Shen, Y; Kevrekidis, P G; Sen, S; Hoffman, A

    2014-08-01

    Our aim in the present work is to develop approximations for the collisional dynamics of traveling waves in the context of granular chains in the presence of precompression. To that effect, we aim to quantify approximations of the relevant Hertzian FPU-type lattice through both the Korteweg-de Vries (KdV) equation and the Toda lattice. Using the availability in such settings of both one-soliton and two-soliton solutions in explicit analytical form, we initialize such coherent structures in the granular chain and observe the proximity of the resulting evolution to the underlying integrable (KdV or Toda) model. While the KdV offers the possibility to accurately capture collisions of solitary waves propagating in the same direction, the Toda lattice enables capturing both copropagating and counterpropagating soliton collisions. The error in the approximation is quantified numerically and connections to bounds established in the mathematical literature are also given. PMID:25215797

  7. A Korteweg-de Vries Burgers-like equation for weakly nonlinear dust ion-acoustic waves in a charge-varying dusty plasma with nonthermal electrons

    SciTech Connect

    Berbri, Abderrezak; Tribeche, Mouloud

    2009-05-15

    A weakly nonlinear analysis is carried out to derive a Korteweg-de Vries Burgers-like equation for small but finite amplitude dust ion-acoustic (DIA) waves in a charge varying dusty plasma with non thermally distributed electrons. The correct expression for the nonthermal electron charging current is used. Interestingly, it may be noted that due to electron nonthermality and finite equilibrium ion streaming velocity, the present dusty plasma model can admit compressive as well as rarefactive DIA solitary waves. Furthermore, there may exist DIA shocks which have either monotonic or oscillatory behavior and the properties of which depend sensitively on the number of fast nonthermal electrons. Our results should be useful to understand the properties of localized DIA waves that may occur in space dusty plasmas.

  8. Generalized Korteweg-de Vries equation induced from position-dependent effective mass quantum models and mass-deformed soliton solution through inverse scattering transform

    SciTech Connect

    Ganguly, A. E-mail: aganguly@maths.iitkgp.ernet.in; Das, A.

    2014-11-15

    We consider one-dimensional stationary position-dependent effective mass quantum model and derive a generalized Korteweg-de Vries (KdV) equation in (1+1) dimension through Lax pair formulation, one being the effective mass Schrödinger operator and the other being the time-evolution of wave functions. We obtain an infinite number of conserved quantities for the generated nonlinear equation and explicitly show that the new generalized KdV equation is an integrable system. Inverse scattering transform method is applied to obtain general solution of the nonlinear equation, and then N-soliton solution is derived for reflectionless potentials. Finally, a special choice has been made for the variable mass function to get mass-deformed soliton solution. The influence of position and time-dependence of mass and also of the different representations of kinetic energy operator on the nature of such solitons is investigated in detail. The remarkable features of such solitons are demonstrated in several interesting figures and are contrasted with the conventional KdV-soliton associated with constant-mass quantum model.

  9. Nonlinear Korteweg-de Vries-Burger equation for ion acoustic shock waves in a weakly relativistic electron-positron-ion plasma with thermal ions

    NASA Astrophysics Data System (ADS)

    Saeed, R.; Shah, Asif

    2010-03-01

    The nonlinear propagation of ion acoustic waves in electron-positron-ion plasma comprising of Boltzmannian electrons, positrons, and relativistic thermal ions has been examined. The Korteweg-de Vries-Burger equation has been derived by reductive perturbation technique, and its shock like solution is determined analytically through tangent hyperbolic method. The effect of various plasma parameters on strength and structure of shock wave is investigated. The pert graphical view of the results has been presented for illustration. It is observed that strength and steepness of the shock wave enervate with an increase in the ion temperature, relativistic streaming factor, positron concentrations, electron temperature and they accrue with an increase in coefficient of kinematic viscosity. The convective, dispersive, and dissipative properties of the plasma are also discussed. It is determined that the electron temperature has remarkable influence on the propagation and structure of nonlinear wave in such relativistic plasmas. The numerical analysis has been done based on the typical numerical data from a pulsar magnetosphere.

  10. Nonlinear Korteweg-de Vries-Burger equation for ion acoustic shock waves in a weakly relativistic electron-positron-ion plasma with thermal ions

    SciTech Connect

    Saeed, R.; Shah, Asif

    2010-03-15

    The nonlinear propagation of ion acoustic waves in electron-positron-ion plasma comprising of Boltzmannian electrons, positrons, and relativistic thermal ions has been examined. The Korteweg-de Vries-Burger equation has been derived by reductive perturbation technique, and its shock like solution is determined analytically through tangent hyperbolic method. The effect of various plasma parameters on strength and structure of shock wave is investigated. The pert graphical view of the results has been presented for illustration. It is observed that strength and steepness of the shock wave enervate with an increase in the ion temperature, relativistic streaming factor, positron concentrations, electron temperature and they accrue with an increase in coefficient of kinematic viscosity. The convective, dispersive, and dissipative properties of the plasma are also discussed. It is determined that the electron temperature has remarkable influence on the propagation and structure of nonlinear wave in such relativistic plasmas. The numerical analysis has been done based on the typical numerical data from a pulsar magnetosphere.

  11. Soliton collisions and integrable aspects of the fifth-order Korteweg-de Vries equation for shallow water with surface tension

    NASA Astrophysics Data System (ADS)

    Sun, Wen-Rong; Shan, Wen-Rui; Jiang, Yan; Wang, Pan; Tian, Bo

    2015-02-01

    The fifth-order Korteweg-de Vries (KdV) equation works as a model for the shallow water waves with surface tension. Through symbolic computation, binary Bell-polynomial approach and auxiliary independent variable, the bilinear forms, N-soliton solutions, two different Bell-polynomial-type Bäcklund transformations, Lax pair and infinite conservation laws are obtained. Characteristic-line method is applied to discuss the effects of linear wave speed c as well as length scales τ and γ on the soliton amplitudes and velocities. Increase of τ, c and γ can lead to the increase of the soliton velocity. Soliton amplitude increases with the increase of τ. The larger-amplitude soliton is seen to move faster and then to overtake the smaller one. After the collision, the solitons keep their original shapes and velocities invariant except for the phase shift. Graphic analysis on the two and three-soliton solutions indicates that the overtaking collisions between/among the solitons are all elastic.

  12. Modulated elliptic wave and asymptotic solitons in a shock problem to the modified Korteweg-de Vries equation

    NASA Astrophysics Data System (ADS)

    Kotlyarov, Vladimir; Minakov, Alexander

    2015-07-01

    We study the long-time asymptotic behavior of the Cauchy problem for the modified Korteweg—de Vries equation with an initial function of the step type. This function rapidly tends to zero as x\\to +∞ and to some positive constant c as x\\to -∞ . In 1989 Khruslov and Kotlyarov have found (Khruslov and Kotlyarov 1989 Inverse Problems 5 1075-88) that for a large time the solution breaks up into a train of asymptotic solitons located in the domain 4{c}2t-{C}N{ln}t\\lt x≤slant 4{c}2t ({C}N is a constant). The number N of these solitons grows unboundedly as t\\to ∞ . In 2010 Kotlyarov and Minakov have studied temporary asymptotics of the solution of the Cauchy problem on the whole line (Kotlyarov and Minakov 2010 J. Math. Phys. 51 093506) and have found that in the domain -6{c}2t\\lt x\\lt 4{c}2t this solution is described by a modulated elliptic wave. We consider here the modulated elliptic wave in the domain 4{c}2t-{C}N{ln}t\\lt x\\lt 4{c}2t. Our main result shows that the modulated elliptic wave also breaks up into solitons, which are similar to the asymptotic solitons in Khruslov and Kotlyarov (1989 Inverse Problems 5 1075-88), but differ from them in phase. It means that the modulated elliptic wave does not represent the asymptotics of the solution in the domain 4{c}2t-{C}N{ln}t\\lt x\\lt 4{c}2t. The correct asymptotic behavior of the solution is given by the train of asymptotic solitons given in Khruslov and Kotlyarov (1989 Inverse Problems 5 1075-88). However, in the asymptotic regime as t\\to ∞ in the region 4{c}2t-\\displaystyle \\frac{N+1/4}{c}{ln}t\\lt x\\lt 4{c}2t-\\displaystyle \\frac{N-3/4}{c}{ln}t we can watch precisely a pair of solitons with numbers N. One of them is the asymptotic soliton while the other soliton is generated from the elliptic wave. Their phases become closer to each other for a large N, i.e. these solitons are also close to each other. This result gives the answer on a very important question about matching of the asymptotic

  13. Korteweg-de Vries solitons on electrified liquid jets.

    PubMed

    Wang, Qiming; Papageorgiou, Demetrios T; Vanden-Broeck, Jean-Marc

    2015-06-01

    The propagation of axisymmetric waves on the surface of a liquid jet under the action of a radial electric field is considered. The jet is assumed to be inviscid and perfectly conducting, and a field is set up by placing the jet concentrically inside a perfectly cylindrical tube whose wall is maintained at a constant potential. A nontrivial interaction arises between the hydrodynamics and the electric field in the annulus, resulting in the formation of electrocapillary waves. The main objective of the present study is to describe nonlinear aspects of such axisymmetric waves in the weakly nonlinear regime, which is valid for long waves relative to the undisturbed jet radius. This is found to be possible if two conditions hold: the outer electrode radius is not too small, and the applied electric field is sufficiently strong. Under these conditions long waves are shown to be dispersive and a weakly nonlinear theory can be developed to describe the evolution of the disturbances. The canonical system that arises is the Kortweg-de Vries equation with coefficients that vary as the electric field and the electrode radius are varied. Interestingly, the coefficient of the highest-order third derivative term does not change sign and remains strictly positive, whereas the coefficient α of the nonlinear term can change sign for certain values of the parameters. This finding implies that solitary electrocapillary waves are possible; there are waves of elevation for α>0 and of depression for α<0. Regions in parameter space are identified where such waves are found. PMID:26172797

  14. Korteweg-de Vries solitons on electrified liquid jets

    NASA Astrophysics Data System (ADS)

    Wang, Qiming; Papageorgiou, Demetrios T.; Vanden-Broeck, Jean-Marc

    2015-06-01

    The propagation of axisymmetric waves on the surface of a liquid jet under the action of a radial electric field is considered. The jet is assumed to be inviscid and perfectly conducting, and a field is set up by placing the jet concentrically inside a perfectly cylindrical tube whose wall is maintained at a constant potential. A nontrivial interaction arises between the hydrodynamics and the electric field in the annulus, resulting in the formation of electrocapillary waves. The main objective of the present study is to describe nonlinear aspects of such axisymmetric waves in the weakly nonlinear regime, which is valid for long waves relative to the undisturbed jet radius. This is found to be possible if two conditions hold: the outer electrode radius is not too small, and the applied electric field is sufficiently strong. Under these conditions long waves are shown to be dispersive and a weakly nonlinear theory can be developed to describe the evolution of the disturbances. The canonical system that arises is the Kortweg-de Vries equation with coefficients that vary as the electric field and the electrode radius are varied. Interestingly, the coefficient of the highest-order third derivative term does not change sign and remains strictly positive, whereas the coefficient α of the nonlinear term can change sign for certain values of the parameters. This finding implies that solitary electrocapillary waves are possible; there are waves of elevation for α >0 and of depression for α <0 . Regions in parameter space are identified where such waves are found.

  15. Electrostatic Korteweg-deVries solitary waves in a plasma with Kappa-distributed electrons

    SciTech Connect

    Choi, C.-R.; Min, K.-W.; Rhee, T.-N.

    2011-09-15

    The Korteweg-deVries (KdV) equation that describes the evolution of nonlinear ion-acoustic solitary waves in plasmas with Kappa-distributed electrons is derived by using a reductive perturbation method in the small amplitude limit. We identified a dip-type (negative) electrostatic KdV solitary wave, in addition to the hump-type solution reported previously. The two types of solitary waves occupy different domains on the {kappa} (Kappa index)-V (propagation velocity) plane, separated by a curve corresponding to singular solutions with infinite amplitudes. For a given Kappa value, the dip-type solitary wave propagates faster than the hump-type. It was also found that the hump-type solitary waves cannot propagate faster than V = 1.32.

  16. Anomalous autoresonance threshold for chirped-driven Korteweg-de-Vries waves.

    PubMed

    Friedland, L; Shagalov, A G; Batalov, S V

    2015-10-01

    Large amplitude traveling waves of the Korteweg-de-Vries (KdV) equation can be excited and controlled by a chirped frequency driving perturbation. The process involves capturing the wave into autoresonance (a continuous nonlinear synchronization) with the drive by passage through the linear resonance in the problem. The transition to autoresonance has a sharp threshold on the driving amplitude. In all previously studied autoresonant problems the threshold was found via a weakly nonlinear theory and scaled as α(3/4),α being the driving frequency chirp rate. It is shown that this scaling is violated in a long wavelength KdV limit because of the increased role of the nonlinearity in the problem. A fully nonlinear theory describing the phenomenon and applicable to all wavelengths is developed. PMID:26565321

  17. Travelling wave solutions of a coupled Korteweg-de Vries-Burgers system

    NASA Astrophysics Data System (ADS)

    Motsepa, Tanki; Khalique, Chaudry Masood

    2016-02-01

    In this paper we study a coupled Korteweg-de Vries-Burgers system which arises in mathematical physics and has a wide range of scientific applications. We obtain new travelling wave solutions of this system by employing the (G'/G)-expansion method. The solutions that will be obtained are going to be expressed in two different forms, viz., hyperbolic functions and trigonometric functions.

  18. Static algebraic solitons in Korteweg-de Vries type systems and the Hirota transformation.

    PubMed

    Burde, G I

    2011-08-01

    Some effects in the soliton dynamics governed by higher-order Korteweg-de Vries (KdV) type equations are discussed. This is done based on the exact explicit solutions of the equations derived in the paper. It is shown that some higher order KdV equations possessing multisoliton solutions also admit steady state solutions in terms of algebraic functions describing localized patterns. Solutions including both those static patterns and propagating KdV-like solitons are combinations of algebraic and hyperbolic functions. It is shown that the localized structures behave like static solitons upon collisions with regular moving solitons, with their shape remaining unchanged after the collision and only the position shifted. These phenomena are not revealed in common multisoliton solutions derived using inverse scattering or Hirota's method. The solutions of the higher-order KdV type equations were obtained using a method devised for obtaining soliton solutions of nonlinear evolution equations. This method can be combined with Hirota's method with a modified representation of the solution which allows the results to be extended to multisoliton solutions. The prospects for applying the methods to soliton equations not of KdV type are discussed. PMID:21929136

  19. Integrability, analyticity, isochrony, equilibria, small oscillations, and Diophantine relations: Results from the stationary Korteweg-de Vries hierarchy

    NASA Astrophysics Data System (ADS)

    Bruschi, M.; Calogero, F.; Droghei, R.

    2009-12-01

    The isochronous variant is exhibited of the dynamical system corresponding to the Mth ordinary differential equation of the stationary Korteweg-de Vries (KdV) hierarchy. New Diophantine relations are thereby obtained, in the guise of matrices of arbitrary order having integer eigenvalues or equivalently of polynomials of arbitrary degree having integer zeros. Generalizations of these formulas to relations among rational functions are also obtained. The basic idea to arrive at such relations is not new, but the specific application reported in this paper is new, and it is likely to open the way to several analogous new findings.

  20. Modified Korteweg-de Vries soliton reflection in a magnetized plasma with dust grains and trapped electrons

    SciTech Connect

    Kumar, Ravinder; Malik, Hitendra K.

    2013-03-15

    This article aims at studying the reflection of solitons in an inhomogeneous magnetized warm plasma having dust grains with positive or negative charge and trapped electrons (low temperature nonisothermal electrons). In order to study the soliton reflection, a coupled modified Korteweg-de Vries equation is derived and solved along with the use of incident soliton solution. The expressions for the reflected soliton amplitude, width, and reflection coefficient are obtained, and examined under different parameter regimes. The combined effect of the dust grain density with their charge polarity and trapping of the electrons is largely studied on the soliton reflection characteristics under the influence of magnetic field.

  1. Hybrid (Vlasov-Fluid) simulation of ion-acoustic soliton chain formation and validity of Korteweg de-Vries model

    SciTech Connect

    Aminmansoor, F.; Abbasi, H.

    2015-08-15

    The present paper is devoted to simulation of nonlinear disintegration of a localized perturbation into ion-acoustic solitons train in a plasma with hot electrons and cold ions. A Gaussian initial perturbation is used to model the localized perturbation. For this purpose, first, we reduce fluid system of equations to a Korteweg de-Vries equation by the following well-known assumptions. (i) On the ion-acoustic evolution time-scale, the electron velocity distribution function (EVDF) is assumed to be stationary. (ii) The calculation is restricted to small amplitude cases. Next, in order to generalize the model to finite amplitudes cases, the evolution of EVDF is included. To this end, a hybrid code is designed to simulate the case, in which electrons dynamics is governed by Vlasov equation, while cold ions dynamics is, like before, studied by the fluid equations. A comparison between the two models shows that although the fluid model is capable of demonstrating the general features of the process, to have a better insight into the relevant physics resulting from the evolution of EVDF, the use of kinetic treatment is of great importance.

  2. Korteweg-deVries-Burgers (KdVB) equation in a five component cometary plasma with kappa described electrons and ions

    NASA Astrophysics Data System (ADS)

    Michael, Manesh; Willington, Neethu T.; Jayakumar, Neethu; Sebastian, Sijo; Sreekala, G.; Venugopal, Chandu

    2016-07-01

    We investigate the existence of ion-acoustic shock waves in a five component cometary plasma consisting of positively and negatively charged oxygen ions, kappa described hydrogen ions, hot solar electrons, and slightly colder cometary electrons. The KdVB equation has been derived for the system, and its solution plotted for different kappa values, oxygen ion densities, as well as the temperature ratios for the ions. It is found that the amplitude of the shock wave decreases with increasing kappa values. The strength of the shock profile decreases with increasing temperatures of the positively charged oxygen ions and densities of negatively charged oxygen ions.

  3. Symbolic computation of conservation laws and exact solutions of a coupled variable-coefficient modified Korteweg-de Vries system

    NASA Astrophysics Data System (ADS)

    Adem, Abdullahi Rashid; Khalique, Chaudry Masood

    2016-04-01

    In this paper we study a generalized coupled variable-coefficient modified Korteweg-de Vries (CVCmKdV) system that models a two-layer fluid, which is applied to investigate the atmospheric and oceanic phenomena such as the atmospheric blockings, interactions between the atmosphere and ocean, oceanic circulations and hurricanes. The conservation laws of the CVCmKdV system are derived using the multiplier approach and a new conservation theorem. In addition to this, a similarity reduction and exact solutions with the aid of symbolic computation are computed.

  4. Duality relation among the Hamiltonian structures of a parametric coupled Korteweg-de Vries system

    NASA Astrophysics Data System (ADS)

    Restuccia, Alvaro; Sotomayor, Adrián

    2016-03-01

    We obtain the full Hamiltonian structure for a parametric coupled KdV system. The coupled system arises from four different real basic lagrangians. The associated Hamiltonian functionals and the corresponding Poisson structures follow from the geometry of a constrained phase space by using the Dirac approach for constrained systems. The overall algebraic structure for the system is given in terms of two pencils of Poisson structures with associated Hamiltonians depending on the parameter of the Poisson pencils. The algebraic construction we present admits the most general space of observables related to the coupled system. We then construct two master lagrangians for the coupled system whose field equations are the ɛ-parametric Gardner equations obtained from the coupled KdV system through a Gardner transformation. In the weak limit ɛ → 0 the lagrangians reduce to the ones of the coupled KdV system while, after a suitable redefinition of the fields, in the strong limit ɛ → ∞ we obtain the lagrangians of the coupled modified KdV system. The Hamiltonian structures of the coupled KdV system follow from the Hamiltonian structures of the master system by taking the two limits ɛ → 0 and ɛ → ∞.

  5. Nonlocal symmetries of the Hirota-Satsuma coupled Korteweg-de Vries system and their applications: Exact interaction solutions and integrable hierarchy

    SciTech Connect

    Chen, Junchao; Xin, Xiangpeng; Chen, Yong

    2014-05-15

    The nonlocal symmetry is derived from the known Darboux transformation (DT) of the Hirota-Satsuma coupled Korteweg-de Vries (HS-cKdV) system, and infinitely many nonlocal symmetries are given by introducing the internal parameters. By extending the HS-cKdV system to an auxiliary system with five dependent variables, the prolongation is found to localize the so-called seed nonlocal symmetry related to the DT. By applying the general Lie point symmetry method to this enlarged system, we obtain two main results: a new type of finite symmetry transformation is derived, which is different from the initial DT and can generate new solutions from old ones; some novel exact interaction solutions among solitons and other complicated waves including periodic cnoidal waves and Painlevé waves are computed through similarity reductions. In addition, two kinds of new integrable models are proposed from the obtained nonlocal symmetry: the negative HS-cKdV hierarchy by introducing the internal parameters; the integrable models both in lower and higher dimensions by restricting the symmetry constraints.

  6. Complex and singular solutions of KdV and MKdV equations

    NASA Technical Reports Server (NTRS)

    Buti, B.; Rao, N. N.; Khadkikar, S. B.

    1986-01-01

    The Korteweg-de Vries (KdV) and the modified Korteweg-de Vries (MKdV) equations are shown to have, besides the regular real solutions, exact regular complex as well as singular solutions. The singular solution for the KdV is real but for the MKdV it is pure imaginary. Implications of the complex solutions are discussed.

  7. Deriving average soliton equations with a perturbative method

    SciTech Connect

    Ballantyne, G.J.; Gough, P.T.; Taylor, D.P. )

    1995-01-01

    The method of multiple scales is applied to periodically amplified, lossy media described by either the nonlinear Schroedinger (NLS) equation or the Korteweg--de Vries (KdV) equation. An existing result for the NLS equation, derived in the context of nonlinear optical communications, is confirmed. The method is then applied to the KdV equation and the result is confirmed numerically.

  8. Evolution equations: Frobenius integrability, conservation laws and travelling waves

    NASA Astrophysics Data System (ADS)

    Prince, Geoff; Tehseen, Naghmana

    2015-10-01

    We give new results concerning the Frobenius integrability and solution of evolution equations admitting travelling wave solutions. In particular, we give a powerful result which explains the extraordinary integrability of some of these equations. We also discuss ‘local’ conservations laws for evolution equations in general and demonstrate all the results for the Korteweg-de Vries equation.

  9. The KdV equation under periodic boundary conditions and its perturbations

    NASA Astrophysics Data System (ADS)

    Guan, Huang; Kuksin, Sergei

    2014-09-01

    In this paper we discuss properties of the Korteweg-de Vries (KdV) equation under periodic boundary conditions, especially those which are important for studying perturbations of the equation. We then review what is known about the long-time behaviour of solutions for perturbed KdV equations.

  10. Differential geometry techniques for sets of nonlinear partial differential equations

    NASA Technical Reports Server (NTRS)

    Estabrook, Frank B.

    1990-01-01

    An attempt is made to show that the Cartan theory of partial differential equations can be a useful technique for applied mathematics. Techniques for finding consistent subfamilies of solutions that are generically rich and well-posed and for introducing potentials or other usefully consistent auxiliary fields are introduced. An extended sample calculation involving the Korteweg-de Vries equation is given.

  11. Role of de Vries in the recovery of Mendel's work. I. Was de Vries really an independent discoverer of Mendel?

    PubMed

    Corcos, A; Monaghan, F

    1985-01-01

    Recently, doubt has been cast on the view that de Vries developed the idea of disjunction independently of Mendel. Arguments are based on de Vries' own writings that showed the F2 data of his numerous crosses are reported as 3:1 ratios only after 1900. They also show that his theory of inheritance becomes quasi Mendelian only after 1900. The authors of this review paper cannot but agree with de Vries' critics that he did not develop his law of disjunction independently of Mendel. They also raise some questions that, hopefully, will lead to a reanalysis of de Vries' theory of inheritance in 1900. PMID:3889132

  12. Solitons and nonlinear wave equations

    SciTech Connect

    Dodd, Roger K.; Eilbeck, J. Chris; Gibbon, John D.; Morris, Hedley C.

    1982-01-01

    A discussion of the theory and applications of classical solitons is presented with a brief treatment of quantum mechanical effects which occur in particle physics and quantum field theory. The subjects addressed include: solitary waves and solitons, scattering transforms, the Schroedinger equation and the Korteweg-de Vries equation, and the inverse method for the isospectral Schroedinger equation and the general solution of the solvable nonlinear equations. Also considered are: isolation of the Korteweg-de Vries equation in some physical examples, the Zakharov-Shabat/AKNS inverse method, kinks and the sine-Gordon equation, the nonlinear Schroedinger equation and wave resonance interactions, amplitude equations in unstable systems, and numerical studies of solitons. 45 references.

  13. Local well-posedness for the fifth-order KdV equations on T

    NASA Astrophysics Data System (ADS)

    Kwak, Chulkwang

    2016-05-01

    This paper is a continuation of the paper Low regularity Cauchy problem for the fifth-order modified KdV equations on T[7]. In this paper, we consider the fifth-order equation in the Korteweg-de Vries (KdV) hierarchy as following:

  14. Existence and stability of alternative ion-acoustic solitary wave solution of the combined MKdV-KdV-ZK equation in a magnetized nonthermal plasma consisting of warm adiabatic ions

    SciTech Connect

    Das, Jayasree; Bandyopadhyay, Anup; Das, K. P.

    2007-09-15

    The purpose of this paper is to present the recent work of Das et al. [J. Plasma Phys. 72, 587 (2006)] on the existence and stability of the alternative solitary wave solution of fixed width of the combined MKdV-KdV-ZK (Modified Korteweg-de Vries-Korteweg-de Vries-Zakharov-Kuznetsov) equation for the ion-acoustic wave in a magnetized nonthermal plasma consisting of warm adiabatic ions in a more generalized form. Here we derive the alternative solitary wave solution of variable width instead of fixed width of the combined MKdV-KdV-ZK equation along with the condition for its existence and find that this solution assumes the sech profile of the MKdV-ZK (Modified Korteweg-de Vries-Zakharov-Kuznetsov) equation, when the coefficient of the nonlinear term of the KdV-ZK (Korteweg-de Vries-Zakharov-Kuznetsov) equation tends to zero. The three-dimensional stability analysis of the alternative solitary wave solution of variable width of the combined MKdV-KdV-ZK equation shows that the instability condition and the first order growth rate of instability are exactly the same as those of the solitary wave solution (the sech profile) of the MKdV-ZK equation, when the coefficient of the nonlinear term of the KdV-ZK equation tends to zero.

  15. N-fold Darboux transformation and double-Wronskian-typed solitonic structures for a variable-coefficient modified Kortweg-de Vries equation

    SciTech Connect

    Wang, Lei; Gao, Yi-Tian; State Key Laboratory of Software Development Environment, Beijing University of Aeronautics and Astronautics, Beijing 100191 ; Qi, Feng-Hua

    2012-08-15

    Under investigation in this paper is a variable-coefficient modified Kortweg-de Vries (vc-mKdV) model describing certain situations from the fluid mechanics, ocean dynamics and plasma physics. N-fold Darboux transformation (DT) of a variable-coefficient Ablowitz-Kaup-Newell-Segur spectral problem is constructed via a gauge transformation. Multi-solitonic solutions in terms of the double Wronskian for the vc-mKdV model are derived by the reduction of the N-fold DT. Three types of the solitonic interactions are discussed through figures: (1) Overtaking collision; (2) Head-on collision; (3) Parallel solitons. Nonlinear, dispersive and dissipative terms have the effects on the velocities of the solitonic waves while the amplitudes of the waves depend on the perturbation term. - Highlights: Black-Right-Pointing-Pointer N-fold DT is firstly applied to a vc-AKNS spectral problem. Black-Right-Pointing-Pointer Seeking a double Wronskian solution is changed into solving two systems. Black-Right-Pointing-Pointer Effects of the variable coefficients on the multi-solitonic waves are discussed in detail. Black-Right-Pointing-Pointer This work solves the problem from Yi Zhang [Ann. Phys. 323 (2008) 3059].

  16. Integrability of the Kruskal--Zabusky Discrete Equation by Multiscale Expansion

    SciTech Connect

    Levi, Decio; Scimiterna, Christian

    2010-03-08

    In 1965 Kruskal and Zabusky in a very famous article in Physical Review Letters introduced the notion of 'soliton' to describe the interaction of solitary waves solutions of the Korteweg de Vries equation (KdV). To do so they introduced a discrete approximation to the KdV, the Kruskal-Zabusky equation (KZ). Here we analyze the KZ equation using the multiscale expansion and show that the equation is only A{sub 2} integrable.

  17. Linear superposition in nonlinear equations.

    PubMed

    Khare, Avinash; Sukhatme, Uday

    2002-06-17

    Several nonlinear systems such as the Korteweg-de Vries (KdV) and modified KdV equations and lambda phi(4) theory possess periodic traveling wave solutions involving Jacobi elliptic functions. We show that suitable linear combinations of these known periodic solutions yield many additional solutions with different periods and velocities. This linear superposition procedure works by virtue of some remarkable new identities involving elliptic functions. PMID:12059300

  18. Complex solitary waves and soliton trains in KdV and mKdV equations

    NASA Astrophysics Data System (ADS)

    Modak, Subhrajit; Singh, Akhil Pratap; Panigrahi, Prasanta Kumar

    2016-06-01

    We demonstrate the existence of complex solitary wave and periodic solutions of the Korteweg-de Vries (KdV) and modified Korteweg-de Vries (mKdV) equations. The solutions of the KdV (mKdV) equation appear in complex-conjugate pairs and are even (odd) under the simultaneous actions of parity (𝓟) and time-reversal (𝓣) operations. The corresponding localized solitons are hydrodynamic analogs of Bloch soliton in magnetic system, with asymptotically vanishing intensity. The 𝓟𝓣-odd complex soliton solution is shown to be iso-spectrally connected to the fundamental sech2 solution through supersymmetry. Physically, these complex solutions are analogous to the experimentally observed grey solitons of non-liner Schödinger equation, governing the dynamics of shallow water waves and hence may also find physical verification.

  19. Fast neural solution of a nonlinear wave equation

    NASA Technical Reports Server (NTRS)

    Toomarian, Nikzad; Barhen, Jacob

    1992-01-01

    A neural algorithm for rapidly simulating a certain class of nonlinear wave phenomena using analog VLSI neural hardware is presented and applied to the Korteweg-de Vries partial differential equation. The corresponding neural architecture is obtained from a pseudospectral representation of the spatial dependence, along with a leap-frog scheme for the temporal evolution. Numerical simulations demonstrated the robustness of the proposed approach.

  20. Two-component coupled KdV equations and its connection with the generalized Harry Dym equations

    SciTech Connect

    Popowicz, Ziemowit

    2014-01-15

    It is shown that three different Lax operators in the Dym hierarchy produce three generalized coupled Harry Dym equations. These equations transform, via the reciprocal link, to the coupled two-component Korteweg de Vries (KdV) system. The first equation gives us known integrable two-component KdV system, while the second reduces to the known symmetrical two-component KdV equation. The last one reduces to the Drienfeld-Sokolov equation. This approach gives us new Lax representation for these equations.

  1. The Sturm-Liouville Hierarchy of Evolution Equations and Limits of Algebro-Geometric Initial Data

    NASA Astrophysics Data System (ADS)

    Johnson, Russell; Zampogni, Luca

    2014-03-01

    The Sturm-Liouville hierarchy of evolution equations was introduced in [Adv. Nonlinear Stud. 11 (2011), 555-591] and includes the Korteweg-de Vries and the Camassa-Holm hierarchies. We discuss some solutions of this hierarchy which are obtained as limits of algebro-geometric solutions. The initial data of our solutions are (generalized) reflectionless Sturm-Liouville potentials [Stoch. Dyn. 8 (2008), 413-449].

  2. Nonvanishing boundary condition for the mKdV hierarchy and the Gardner equation

    NASA Astrophysics Data System (ADS)

    Gomes, J. F.; França, Guilherme S.; Zimerman, A. H.

    2012-01-01

    A Kac-Moody algebra construction for the integrable hierarchy containing the Gardner equation is proposed. Solutions are systematically constructed by employing the dressing method and deformed vertex operators, which take into account the nonvanishing boundary value problem for the modified Korteweg-de Vries (mKdV) hierarchy. Explicit examples are given and besides the usual KdV-like solitons, our solutions contemplate the large amplitude table-top solitons, kinks, dark solitons, breathers and wobbles.

  3. Method of Multiple Scales and Travelling Wave Solutions for (2+1)-Dimensional KdV Type Nonlinear Evolution Equations

    NASA Astrophysics Data System (ADS)

    Ayhan, Burcu; Özer, M. Naci; Bekir, Ahmet

    2016-08-01

    In this article, we applied the method of multiple scales for Korteweg-de Vries (KdV) type equations and we derived nonlinear Schrödinger (NLS) type equations. So we get a relation between KdV type equations and NLS type equations. In addition, exact solutions were found for KdV type equations. The ( G'} over G )-expansion methods and the ( {G'} over G, {1 over G}} )-expansion methods were proposed to establish new exact solutions for KdV type differential equations. We obtained periodic and hyperbolic function solutions for these equations. These methods are very effective for getting travelling wave solutions of nonlinear evolution equations (NEEs).

  4. A note on improved F-expansion method combined with Riccati equation applied to nonlinear evolution equations

    PubMed Central

    Islam, Md. Shafiqul; Khan, Kamruzzaman; Akbar, M. Ali; Mastroberardino, Antonio

    2014-01-01

    The purpose of this article is to present an analytical method, namely the improved F-expansion method combined with the Riccati equation, for finding exact solutions of nonlinear evolution equations. The present method is capable of calculating all branches of solutions simultaneously, even if multiple solutions are very close and thus difficult to distinguish with numerical techniques. To verify the computational efficiency, we consider the modified Benjamin–Bona–Mahony equation and the modified Korteweg-de Vries equation. Our results reveal that the method is a very effective and straightforward way of formulating the exact travelling wave solutions of nonlinear wave equations arising in mathematical physics and engineering. PMID:26064530

  5. Deriving the New Traveling Wave Solutions for the Nonlinear Dispersive Equation, KdV-ZK Equation and Complex Coupled KdV System Using Extended Simplest Equation Method

    NASA Astrophysics Data System (ADS)

    Mohammed, K. Elboree

    2015-10-01

    In this paper, we investigate the traveling wave solutions for the nonlinear dispersive equation, Korteweg-de Vries Zakharov-Kuznetsov (KdV-ZK) equation and complex coupled KdV system by using extended simplest equation method, and then derive the hyperbolic function solutions include soliton solutions, trigonometric function solutions include periodic solutions with special values for double parameters and rational solutions. The properties of such solutions are shown by figures. The results show that this method is an effective and a powerful tool for handling the solutions of nonlinear partial differential equations (NLEEs) in mathematical physics.

  6. Solitons induced by boundary conditions from the Boussinesq equation

    NASA Technical Reports Server (NTRS)

    Chou, Ru Ling; Chu, C. K.

    1990-01-01

    The behavior of solitons induced by boundary excitation is investigated at various time-dependent conditions and different unperturbed water depths, using the Korteweg-de Vries (KdV) equation. Then, solitons induced from Boussinesq equations under similar conditions were studied, making it possible to remove the restriction in the KdV equation and to treat soliton head-on collisions (as well as overtaking collisions) and reflections. It is found that the results obtained from the KdV and the Boussinesq equations are in good agreement.

  7. An integrable shallow water equation with linear and nonlinear dispersion.

    PubMed

    Dullin, H R; Gottwald, G A; Holm, D D

    2001-11-01

    We use asymptotic analysis and a near-identity normal form transformation from water wave theory to derive a 1+1 unidirectional nonlinear wave equation that combines the linear dispersion of the Korteweg-deVries (KdV) equation with the nonlinear/nonlocal dispersion of the Camassa-Holm (CH) equation. This equation is one order more accurate in asymptotic approximation beyond KdV, yet it still preserves complete integrability via the inverse scattering transform method. Its traveling wave solutions contain both the KdV solitons and the CH peakons as limiting cases. PMID:11690414

  8. An h-adaptive local discontinuous Galerkin method for the Navier-Stokes-Korteweg equations

    NASA Astrophysics Data System (ADS)

    Tian, Lulu; Xu, Yan; Kuerten, J. G. M.; van der Vegt, J. J. W.

    2016-08-01

    In this article, we develop a mesh adaptation algorithm for a local discontinuous Galerkin (LDG) discretization of the (non)-isothermal Navier-Stokes-Korteweg (NSK) equations modeling liquid-vapor flows with phase change. This work is a continuation of our previous research, where we proposed LDG discretizations for the (non)-isothermal NSK equations with a time-implicit Runge-Kutta method. To save computing time and to capture the thin interfaces more accurately, we extend the LDG discretization with a mesh adaptation method. Given the current adapted mesh, a criterion for selecting candidate elements for refinement and coarsening is adopted based on the locally largest value of the density gradient. A strategy to refine and coarsen the candidate elements is then provided. We emphasize that the adaptive LDG discretization is relatively simple and does not require additional stabilization. The use of a locally refined mesh in combination with an implicit Runge-Kutta time method is, however, non-trivial, but results in an efficient time integration method for the NSK equations. Computations, including cases with solid wall boundaries, are provided to demonstrate the accuracy, efficiency and capabilities of the adaptive LDG discretizations.

  9. Multi-Soliton Solutions of the Generalized Sawada-Kotera Equation

    NASA Astrophysics Data System (ADS)

    Zuo, Da-Wei; Mo, Hui-Xia; Zhou, Hui-Ping

    2016-04-01

    Korteweg-de Vries (KdV)-type equations can describe the nonlinear phenomena in shallow water waves, stratified internal waves, and ion-acoustic waves in plasmas. In this article, the two-dimensional generalization of the Sawada-Kotera equation, one of the KdV-type equations, is discussed by virtue of the Bell polynomials and Hirota method. The results show that there exist multi-soliton solutions for such an equation. Relations between the direction of the soliton propagation and coordinate axes are shown. Elastic interaction with the multi-soliton solutions are analysed.

  10. Modulational instability in nonlinear nonlocal equations of regularized long wave type

    NASA Astrophysics Data System (ADS)

    Hur, Vera Mikyoung; Pandey, Ashish Kumar

    2016-06-01

    We study the stability and instability of periodic traveling waves in the vicinity of the origin in the spectral plane, for equations of Benjamin-Bona-Mahony (BBM) and regularized Boussinesq types permitting nonlocal dispersion. We extend recent results for equations of Korteweg-de Vries type and derive modulational instability indices as functions of the wave number of the underlying wave. We show that a sufficiently small, periodic traveling wave of the BBM equation is spectrally unstable to long wavelength perturbations if the wave number is greater than a critical value and a sufficiently small, periodic traveling wave of the regularized Boussinesq equation is stable to square integrable perturbations.

  11. Soliton solutions of the KdV equation with higher-order corrections

    NASA Astrophysics Data System (ADS)

    Wazwaz, Abdul-Majid

    2010-10-01

    In this work, the Korteweg-de Vries (KdV) equation with higher-order corrections is examined. We studied the KdV equation with first-order correction and that with second-order correction that include the terms of the fifth-order Lax, Sawada-Kotera and Caudrey-Dodd-Gibbon equations. The simplified form of the bilinear method was used to show the integrability of the first-order models and therefore to obtain multiple soliton solutions for each one. The obstacles to integrability of some of the models with second-order corrections are examined as well.

  12. Complex PT-symmetric nonlinear Schrödinger equation and Burgers equation.

    PubMed

    Yan, Zhenya

    2013-04-28

    The complex -symmetric nonlinear wave models have drawn much attention in recent years since the complex -symmetric extensions of the Korteweg-de Vries (KdV) equation were presented in 2007. In this review, we focus on the study of the complex -symmetric nonlinear Schrödinger equation and Burgers equation. First of all, we briefly introduce the basic property of complex symmetry. We then report on exact solutions of one- and two-dimensional nonlinear Schrödinger equations (known as the Gross-Pitaevskii equation in Bose-Einstein condensates) with several complex -symmetric potentials. Finally, some complex -symmetric extension principles are used to generate some complex -symmetric nonlinear wave equations starting from both -symmetric (e.g. the KdV equation) and non- -symmetric (e.g. the Burgers equation) nonlinear wave equations. In particular, we discuss exact solutions of some representative ones of the complex -symmetric Burgers equation in detail. PMID:23509385

  13. Undular bore theory for the Gardner equation.

    PubMed

    Kamchatnov, A M; Kuo, Y-H; Lin, T-C; Horng, T-L; Gou, S-C; Clift, R; El, G A; Grimshaw, R H J

    2012-09-01

    We develop modulation theory for undular bores (dispersive shock waves) in the framework of the Gardner, or extended Korteweg-de Vries (KdV), equation, which is a generic mathematical model for weakly nonlinear and weakly dispersive wave propagation, when effects of higher order nonlinearity become important. Using a reduced version of the finite-gap integration method we derive the Gardner-Whitham modulation system in a Riemann invariant form and show that it can be mapped onto the well-known modulation system for the Korteweg-de Vries equation. The transformation between the two counterpart modulation systems is, however, not invertible. As a result, the study of the resolution of an initial discontinuity for the Gardner equation reveals a rich phenomenology of solutions which, along with the KdV-type simple undular bores, include nonlinear trigonometric bores, solibores, rarefaction waves, and composite solutions representing various combinations of the above structures. We construct full parametric maps of such solutions for both signs of the cubic nonlinear term in the Gardner equation. Our classification is supported by numerical simulations. PMID:23031043

  14. Linking Literacy, Technology, and the Environment: An Interview with Joan Goble and Rene de Vries.

    ERIC Educational Resources Information Center

    Strangman, Nicole

    2003-01-01

    Interviews Joan Goble, a third-grade teacher in Indiana, and Rene de Vries, a sixth-grade teacher in The Netherlands. Explains that the two teachers created and managed three Internet projects discussing endangered species and the environment. Notes that through these projects, students can experience the double satisfaction of educating others…

  15. Solitons, Bäcklund transformations, Lax pair and conservation laws for the nonautonomous mKdV-sinh-Gordon equation with time-dependent coefficients

    NASA Astrophysics Data System (ADS)

    Liu, Lei; Tian, Bo; Sun, Wen-Rong; Wang, Yu-Feng; Wang, Yun-Po

    2016-01-01

    The transition phenomenon of few-cycle-pulse optical solitons from a pure modified Korteweg-de Vries (mKdV) to a pure sine-Gordon regime can be described by the nonautonomous mKdV-sinh-Gordon equation with time-dependent coefficients. Based on the Bell polynomials, Hirota method and symbolic computation, bilinear forms and soliton solutions for this equation are obtained. Bäcklund transformations (BTs) in both the binary Bell polynomial and bilinear forms are obtained. By virtue of the BTs and Ablowitz-Kaup-Newell-Segur system, Lax pair and infinitely many conservation laws for this equation are derived as well.

  16. The Linear KdV Equation with an Interface

    NASA Astrophysics Data System (ADS)

    Deconinck, Bernard; Sheils, Natalie E.; Smith, David A.

    2016-07-01

    The interface problem for the linear Korteweg-de Vries (KdV) equation in one-dimensional piecewise homogeneous domains is examined by constructing an explicit solution in each domain. The location of the interface is known and a number of compatibility conditions at the boundary are imposed. We provide an explicit characterization of sufficient interface conditions for the construction of a solution using Fokas's Unified Transform Method. The problem and the method considered here extend that of earlier papers to problems with more than two spatial derivatives.

  17. Absent bystanders and cognitive dissonance: a comment on Timmins & de Vries.

    PubMed

    Paley, John

    2015-04-01

    Timmins & de Vries are more sympathetic to my editorial than other critics, but they take issue with the details. They doubt whether the bystander phenomenon applies to Mid Staffs nurses; they believe that cognitive dissonance is a better explanation of why nurses fail to behave compassionately; and they think that I am 'perhaps a bit rash' to conclude that 'teaching compassion may be fruitless'. In this comment, I discuss all three points. I suggest that the bystander phenomenon is irrelevant; that Timmins & de Vries give an incomplete account of cognitive dissonance; and that it isn't rash to propose that educating nurses 'for compassion' is a red herring. Additionally, I comment on the idea that I wish to mount a 'defence of healthcare staff'. PMID:25549986

  18. On the discrete and continuous Miura chain associated with the sixth Painlevé equation

    NASA Astrophysics Data System (ADS)

    Nijhoff, Frank; Joshi, Nalini; Hone, Andrew

    2000-01-01

    A Miura chain is a (closed) sequence of differential (or difference) equations that are related by Miura or Bäcklund transformations. We describe such a chain for the sixth Painlevé equation (P VI), containing, apart from P VI itself, a Schwarzian version as well as a second-order second-degree ordinary differential equation (ODE). As a byproduct we derive an auto-Bäcklund transformation, relating two copies of P VI with different parameters. We also establish the analogous ordinary difference equations in the discrete counterpart of the chain. Such difference equations govern iterations of solutions of P VI under Bäcklund transformations. Both discrete and continuous equations constitute a larger system which include partial difference equations, differential-difference equations and partial differential equations, all associated with the lattice Korteweg-de Vries equation subject to similarity constraints.

  19. Averaging principle for the KdV equation with a small initial value

    NASA Astrophysics Data System (ADS)

    Yuan, Xiaoping; Zhang, Jing

    2016-02-01

    The averaging principle with a small initial value is constructed for a Hamiltonian perturbed Korteweg-de Vries (KdV) equation under periodic boundary condition where the positive integer n 0 is not divisible by three and K 1 and K 2 are real analytic functions. More precisely, any action I with the small initial value \\parallel I(0){{\\parallel}{{\\tilde{\\mathop{\\ell} }s}}}≤slant \\varepsilon evolves slowly over a long time interval: where s is the index of some space.

  20. Bifurcation and chaos in a perturbed soliton equation with higher-order nonlinearity

    NASA Astrophysics Data System (ADS)

    Yu, Jun; Zhang, Rongbo; Jin, Guojuan

    2011-12-01

    The influence of a soliton system under external perturbation is considered. We take the compound Korteweg-de Vries-Burgers-type equation with nonlinear terms of any order as an example, and investigate numerically the chaotic behavior of the system with periodic forcing. It is shown that dynamical chaos can occur when we appropriately choose system parameters. Abundant bifurcation structures and different routes to chaos, such as period doubling, intermittent bifurcation and crisis, are found by applying bifurcation diagrams, Poincaré maps and phase portraits. To characterize the chaotic behavior of this system, a spectrum of Lyapunov exponents and Lyapunov dimensions of attractors are also employed.

  1. Why the Rediscoverer Ended up on the Sidelines: Hugo De Vries's Theory of Inheritance and the Mendelian Laws

    NASA Astrophysics Data System (ADS)

    Stamhuis, Ida H.

    2015-01-01

    Eleven years before the `rediscovery' in 1900 of Mendel's work, Hugo De Vries published his theory of heredity. He expected his theory to become a big success, but it was not well-received. To find supporting evidence for this theory De Vries started an extensive research program. Because of the parallels of his ideas with the Mendelian laws and because of his use of statistics, he became one of the rediscoverers. However, the Mendelian laws, which soon became the foundation of a new discipline of genetics, presented a problem. De Vries was the only one of the early Mendelians who had developed his own theory of heredity. His theory could not be brought in line with the Mendelian laws. But because his original theory was still very dear to him, something important was at stake and he was unwilling to adapt his ideas to the new situation. He belittled the importance of the Mendelian laws and ended up on the sidelines.

  2. Why the Rediscoverer Ended up on the Sidelines: Hugo De Vries's Theory of Inheritance and the Mendelian Laws

    ERIC Educational Resources Information Center

    Stamhuis, Ida H.

    2015-01-01

    Eleven years before the "rediscovery" in 1900 of Mendel's work, Hugo De Vries published his theory of heredity. He expected his theory to become a big success, but it was not well-received. To find supporting evidence for this theory De Vries started an extensive research program. Because of the parallels of his ideas with the…

  3. Anomalous temperature dependence of layer spacing of de Vries liquid crystals: Compensation model

    NASA Astrophysics Data System (ADS)

    Merkel, K.; Kocot, A.; Vij, J. K.; Stevenson, P. J.; Panov, A.; Rodriguez, D.

    2016-06-01

    Smectic liquid crystals that exhibit temperature independent layer thickness offer technological advantages for their use in displays and photonic devices. The dependence of the layer spacing in SmA and SmC phases of de Vries liquid crystals is found to exhibit distinct features. On entering the SmC phase, the layer thickness initially decreases below SmA to SmC (TA-C) transition temperature but increases anomalously with reducing temperature despite the molecular tilt increasing. This anomalous observation is being explained quantitatively. Results of IR spectroscopy show that layer shrinkage is caused by tilt of the mesogen's rigid core, whereas the expansion is caused by the chains getting more ordered with reducing temperature. This mutual compensation arising from molecular fragments contributing to the layer thickness differs from the previous models. The orientational order parameter of the rigid core of the mesogen provides direct evidence for de Vries cone model in the SmA phase for the two compounds investigated.

  4. The reactions on Hugo de Vries's Intracellular pangenesis: the discussion with August Weismann.

    PubMed

    Stamhuis, Ida H

    2003-01-01

    In 1889 Hugo de Vries published Intracellular Pangenesis in which he formulated his ideas on heredity. The expectations of the impression these ideas would make did not come true and publication was negated or reviewed critically. From the reactions of his Dutch colleagues and the discussion with the famous German zoologist August Weissmann we conclude that the assertion that each cell contains all hereditary material was controversial and even more the claim that characters are inherited independently of each other. De Vries felt that he had to convince his colleagues of the validity of his theory by providing experimental evidence. He established an important research program which resulted in the rediscovery of Mendal's laws and the publication of The Mutation Theory. This article also illustrates some phenomena that go beyond an interesting episode in the development of theories of heredity. It shows that criticism from colleagues can move a researcher so deeply that he feels compelled to set up an extensive research program. Moreover it illustrates that it is not unusual that a creative scientist is only partially willing to take criticism on his theories into account. Last but not least it demonstrates that common opinion on the validity of specific arguments may change in the course of time. PMID:12778942

  5. Hugo De Vries: from the theory of intracellular pangenesis to the rediscovery of Mendel.

    PubMed

    Lenay, C

    2000-12-01

    On the basis of the article by the Dutch botanist Hugo De Vries 'On the law of separation of hybrids' published in the Reports of the Académie des Sciences in 1900, and the beginning of the controversy about priority with Carl Correns and Erich von Tschermak, I consider the question of the posthumous influence of the Mendel paper. I examine the construction of the new theoretical framework which enabled its reading in 1900 as a clear and acceptable presentation of the rules of the transmission of hereditary characters. In particular, I analyse the introduction of the idea of determinants of organic characters, understood as separable material elements which can be distributed randomly in descendants. Starting from the question of heredity, such as it was defined by Darwin in 1868, and after its critical developments by August Weismann, Hugo De Vries was able to suggest such an idea in his Intracellular Pangenesis. He then laid out a programme of research which helps us to understand the 'rediscovery' published in 1900. PMID:11147091

  6. On the asymptotic solutions of the KdV equation with higher-order corrections

    NASA Astrophysics Data System (ADS)

    Burde, Georgy I.

    2005-07-01

    A method for construction of new integrable PDEs, whose properties are related to an asymptotic perturbation expansion with the leading-order term given by an integrable equation, is developed. A new integrable equation is constructed by applying the properly defined Lie-Bäcklund group of transformations to the leading-order equation. The integrable equations related to the Korteweg-de Vries (KdV) equation with higher-order corrections are used to investigate the limits of applicability of the so-called asymptotic integrability concept. It is found that the solutions of the higher-order KdV equations obtained by a near identity transform from the normal form solitary waves cannot, in principle, describe some intrinsic features of the high-order KdV solitons.

  7. Multi-soliton rational solutions for some nonlinear evolution equations

    NASA Astrophysics Data System (ADS)

    Osman, Mohamed S.

    2016-01-01

    The Korteweg-de Vries equation (KdV) and the (2+ 1)-dimensional Nizhnik-Novikov-Veselov system (NNV) are presented. Multi-soliton rational solutions of these equations are obtained via the generalized unified method. The analysis emphasizes the power of this method and its capability of handling completely (or partially) integrable equations. Compared with Hirota's method and the inverse scattering method, the proposed method gives more general exact multi-wave solutions without much additional effort. The results show that, by virtue of symbolic computation, the generalized unified method may provide us with a straightforward and effective mathematical tool for seeking multi-soliton rational solutions for solving many nonlinear evolution equations arising in different branches of sciences.

  8. The zero dispersion limits of nonlinear wave equations

    SciTech Connect

    Tso, T.

    1992-01-01

    In chapter 2 the author uses functional analytic methods and conservation laws to solve the initial-value problem for the Korteweg-de Vries equation, the Benjamin-Bona-Mahony equation, and the nonlinear Schroedinger equation for initial data that satisfy some suitable conditions. In chapter 3 the energy estimates are used to show that the strong convergence of the family of the solutions of the KdV equation obtained in chapter 2 in H[sup 3](R) as [epsilon] [yields] 0; also, it is shown that the strong L[sup 2](R)-limit of the solutions of the BBM equation as [epsilon] [yields] 0 before a critical time. In chapter 4 the author uses the Whitham modulation theory and averaging method to find the 2[pi]-periodic solutions and the modulation equations of the KdV equation, the BBM equation, the Klein-Gordon equation, the NLS equation, the mKdV equation, and the P-system. It is shown that the modulation equations of the KdV equation, the K-G equation, the NLS equation, and the mKdV equation are hyperbolic but those of the BBM equation and the P-system are not hyperbolic. Also, the relations are studied of the KdV equation and the mKdV equation. Finally, the author studies the complex mKdV equation to compare with the NLS equation, and then study the complex gKdV equation.

  9. Darboux Transformations and N-soliton Solutions of Two (2+1)-Dimensional Nonlinear Equations

    NASA Astrophysics Data System (ADS)

    Wang, Xin; Chen, Yong

    2014-04-01

    Two Darboux transformations of the (2+1)-dimensional Caudrey-Dodd-Gibbon-Kotera-Sawaka (CDGKS) equation and (2+1)-dimensional modified Korteweg-de Vries (mKdV) equation are constructed through the Darboux matrix method, respectively. N-soliton solutions of these two equations are presented by applying the Darboux transformations N times. The right-going bright single-soliton solution and interactions of two and three-soliton overtaking collisions of the (2+1)-dimensional CDGKS equation are studied. By choosing different seed solutions, the right-going bright and left-going dark single-soliton solutions, the interactions of two and three-soliton overtaking collisions, and kink soliton solutions of the (2+1)-dimensional mKdV equation are investigated. The results can be used to illustrate the interactions of water waves in shallow water.

  10. Experimental study of de Vries properties in antiferroelectric smectic liquid crystals.

    PubMed

    Sandhya, K L; Panarin, Yu P; Panov, V P; Vij, J K; Dabrowski, R

    2008-12-01

    Results of the experimental study on different antiferroelectric liquid crystal (AFLC) materials are presented using a number of techniques such as the optical birefringence, electro-optics and the measurements of optical thickness of free-standing films. Despite differences in the molecular structures of the various AFLC materials studied, these are found to exhibit a de Vries type of smecticA (SmA) properties in a temperature range higher than SmC. This correlation leads to the conclusion that these two classes of liquid crystals are related to each other. Furthermore, we suggest that these arise from the same physical mechanism, namely the existence of the weak synclinic (or reduced anticlinic) correlations between the neighbouring molecular tilt directions. PMID:19104855

  11. Evolution of higher order nonlinear equation for the dust ion-acoustic waves in nonextensive plasma

    SciTech Connect

    Yasmin, S.; Asaduzzaman, M.; Mamun, A. A.

    2012-10-15

    There are three different types of nonlinear equations, namely, Korteweg-de Vries (K-dV), modified K-dV (mK-dV), and mixed modified K-dV (mixed mK-dV) equations, for the nonlinear propagation of the dust ion-acoustic (DIA) waves. The effects of electron nonextensivity on DIA solitary waves propagating in a dusty plasma (containing negatively charged stationary dust, inertial ions, and nonextensive q distributed electrons) are examined by solving these nonlinear equations. The basic features of mixed mK-dV (higher order nonlinear equation) solitons are found to exist beyond the K-dV limit. The properties of mK-dV solitons are compared with those of mixed mK-dV solitons. It is found that both positive and negative solitons are obtained depending on the q (nonextensive parameter).

  12. Higher order nonlinear equations for the dust-acoustic waves in a dusty plasma with two temperature-ions and nonextensive electrons

    SciTech Connect

    Emamuddin, M.; Yasmin, S.; Mamun, A. A.

    2013-04-15

    The nonlinear propagation of dust-acoustic waves in a dusty plasma whose constituents are negatively charged dust, Maxwellian ions with two distinct temperatures, and electrons following q-nonextensive distribution, is investigated by deriving a number of nonlinear equations, namely, the Korteweg-de-Vries (K-dV), the modified Korteweg-de-Vries (mK-dV), and the Gardner equations. The basic characteristics of the hump (positive potential) and dip (negative potential) shaped dust-acoustic (DA) Gardner solitons are found to exist beyond the K-dV limit. The effects of two temperature ions and electron nonextensivity on the basic features of DA K-dV, mK-dV, and Gardner solitons are also examined. It has been observed that the DA Gardner solitons exhibit negative (positive) solitons for qq{sub c}) (where q{sub c} is the critical value of the nonextensive parameter q). The implications of our results in understanding the localized nonlinear electrostatic perturbations existing in stellar polytropes, quark-gluon plasma, protoneutron stars, etc. (where ions with different temperatures and nonextensive electrons exist) are also briefly addressed.

  13. Systematics of strongly self-dominant higher-order differential equations based on the Painlevé analysis of their singularities

    NASA Astrophysics Data System (ADS)

    King, R. B.

    1986-04-01

    This paper presents a simple way of classifying higher-order differential equations based on the requirements of the Painlevé property, i.e., the presence of no movable critical points. The fundamental building blocks for such equations may be generated by strongly self-dominant differential equations of the type (∂/∂x)nu =(∂/∂xm)[u(m-n+p)/p] in which m and n are positive integers and p is a negative integer. Such differential equations having both a constant degree d and a constant value of the difference n-m form a Painlevé chain; however, only three of the many possible Painlevé chains can have the Painlevé property. Among the three Painlevé chains that can have the Painlevé property, one contains the Burgers' equation; another contains the dominant terms of the first Painlevé transcendent, the isospectral Korteweg-de Vries equation, and the isospectral Boussinesq equation; and the third contains the dominant terms of the second Painlevé transcendent and the isospectral modified (cubic) Korteweg-de Vries equation. Differential equations of the same order and having the same value of the quotient (n-m)/(d-1) can be mixed to generate a new hybrid differential equation. In such cases a hybrid can have the Painlevé property even if only one of its components has the Painlevé property. Such hybridization processes can be used to generate the various fifth-order evolution equations of interest, namely the Caudrey-Dodd-Gibbon, Kuperschmidt, and Morris equations.

  14. De Vries-Weber gain control and dark adaptation in human vision

    NASA Astrophysics Data System (ADS)

    Bouman, Maarten A.

    2002-02-01

    Thresholds for seeing light from a stimulus are determined by a mechanism that pairs subliminal excitations from both halves of a twin unit. Such excitations stem from a package of k>=1 receptor responses. A half-unit contains one red or one green cone and P rods. The receptor's ``Weber machine'' controls the receptor's gain. Each half of a twin unit contains a ``de Vries machine,'' which controls the half's k number. In the dark the receptor's dark noise events reset its Weber machine and the receptor's relation to its de Vries machine. A pairing product for light perception also represents a direction event. The local time signs of the two subliminal excitations are crucial for the polarity, size, and pace of the direction event. In relation to the time when and the area in which the stimulus is presented, these signs have average latency periods that depend on intensity and average locations that depend on movement. Polarity depends on which of the two subliminal excitations happens to arrive first at the twin's pairing facility. The intra- and inter-twin pairings in a persepton for the perceptions of light, edge and movement and the probability summation of the pairing products of the mutually independent three sets of twins of the retrinet improve intensity discrimination. Cross-pairings of intra-receptor pairings in red and green cones of a trion for yellow improve visual discrimination further. Discrimination of stimuli that exploit the model's entire summation mechanisms and pairing facilities represents ``what the perfect human eye sees best.'' For the model this threshold of modulation in quantum absorption is the ideal limit that is prescribed by statistical physics. The lateral and meta interaction in a twin unit enhance the contrast of an edge and of a temporal transient. The precision of the local time sign of a half's stimulation determines the spatiotemporal hyperfunctions for location and speed. The model's design for the perfect retinal mosaic

  15. Double criticality and the two-way Boussinesq equation in stratified shallow water hydrodynamics

    NASA Astrophysics Data System (ADS)

    Bridges, Thomas J.; Ratliff, Daniel J.

    2016-06-01

    Double criticality and its nonlinear implications are considered for stratified N-layer shallow water flows with N = 1, 2, 3. Double criticality arises when the linearization of the steady problem about a uniform flow has a double zero eigenvalue. We find that there are two types of double criticality: non-semisimple (one eigenvector and one generalized eigenvector) and semi-simple (two independent eigenvectors). Using a multiple scales argument, dictated by the type of singularity, it is shown that the weakly nonlinear problem near double criticality is governed by a two-way Boussinesq equation (non-semisimple case) and a coupled Korteweg-de Vries equation (semisimple case). Parameter values and reduced equations are constructed for the examples of two-layer and three-layer stratified shallow water hydrodynamics.

  16. Origin of weak layer contraction in de Vries smectic liquid crystals

    NASA Astrophysics Data System (ADS)

    Agra-Kooijman, Dena M.; Yoon, HyungGuen; Dey, Sonal; Kumar, Satyendra

    2014-03-01

    Structural investigations of the de Vries smectic-A (SmA) and smectic-C (SmC) phases of four mesogens containing a trisiloxane end segment reveal a linear molecular conformation in the SmA phase and a bent conformation resembling a hockey stick in the SmC phase. The siloxane and the hydrocarbon parts of the molecule tilt at different angles relative to the smectic layer normal and are oriented along different directions. For the compounds investigated, the shape of orientational distribution function (ODF) is found to be sugarloaf shaped and not the widely expected volcano like with positive orientational order parameters: ⟨P2⟩ = 0.53-0.78, ⟨P4⟩ = 0.14-0.45, and ⟨P6⟩˜0.10. The increase in the effective molecular length, and consequently in the smectic layer spacing caused by reduced fluctuations and the corresponding narrowing of the ODF, counteracts the effect of molecular tilt and significantly reduces the SmC layer contraction. Maximum tilt of the hydrocarbon part of the molecule lies between approximately 18° and 25° and between 6° and 12° for the siloxane part. The critical exponent of the tilt order parameter, β˜0.25, is in agreement with tricritical behavior at the SmA-SmC transition for two compounds and has lower value for first-order transition in the other compounds with finite enthalpy of transition.

  17. Functional entropy variables: A new methodology for deriving thermodynamically consistent algorithms for complex fluids, with particular reference to the isothermal Navier–Stokes–Korteweg equations

    SciTech Connect

    Liu, Ju; Gomez, Hector; Landis, Chad M.

    2013-09-01

    We propose a new methodology for the numerical solution of the isothermal Navier–Stokes–Korteweg equations. Our methodology is based on a semi-discrete Galerkin method invoking functional entropy variables, a generalization of classical entropy variables, and a new time integration scheme. We show that the resulting fully discrete scheme is unconditionally stable-in-energy, second-order time-accurate, and mass-conservative. We utilize isogeometric analysis for spatial discretization and verify the aforementioned properties by adopting the method of manufactured solutions and comparing coarse mesh solutions with overkill solutions. Various problems are simulated to show the capability of the method. Our methodology provides a means of constructing unconditionally stable numerical schemes for nonlinear non-convex hyperbolic systems of conservation laws.

  18. A Haar wavelet collocation method for coupled nonlinear Schrödinger-KdV equations

    NASA Astrophysics Data System (ADS)

    Oruç, Ömer; Esen, Alaattin; Bulut, Fatih

    2016-04-01

    In this paper, to obtain accurate numerical solutions of coupled nonlinear Schrödinger-Korteweg-de Vries (KdV) equations a Haar wavelet collocation method is proposed. An explicit time stepping scheme is used for discretization of time derivatives and nonlinear terms that appeared in the equations are linearized by a linearization technique and space derivatives are discretized by Haar wavelets. In order to test the accuracy and reliability of the proposed method L2, L∞ error norms and conserved quantities are used. Also obtained results are compared with previous ones obtained by finite element method, Crank-Nicolson method and radial basis function meshless methods. Error analysis of Haar wavelets is also given.

  19. Origin of weak layer contraction in de Vries smectic liquid crystals.

    PubMed

    Agra-Kooijman, Dena M; Yoon, HyungGuen; Dey, Sonal; Kumar, Satyendra

    2014-03-01

    Structural investigations of the de Vries smectic-A (SmA) and smectic-C (SmC) phases of four mesogens containing a trisiloxane end segment reveal a linear molecular conformation in the SmA phase and a bent conformation resembling a hockey stick in the SmC phase. The siloxane and the hydrocarbon parts of the molecule tilt at different angles relative to the smectic layer normal and are oriented along different directions. For the compounds investigated, the shape of orientational distribution function (ODF) is found to be sugarloaf shaped and not the widely expected volcano like with positive orientational order parameters: ⟨P2⟩ = 0.53-0.78, ⟨P4⟩ = 0.14-0.45, and ⟨P6⟩∼0.10. The increase in the effective molecular length, and consequently in the smectic layer spacing caused by reduced fluctuations and the corresponding narrowing of the ODF, counteracts the effect of molecular tilt and significantly reduces the SmC layer contraction. Maximum tilt of the hydrocarbon part of the molecule lies between approximately 18° and 25° and between 6° and 12° for the siloxane part. The critical exponent of the tilt order parameter, β∼0.25, is in agreement with tricritical behavior at the SmA-SmC transition for two compounds and has lower value for first-order transition in the other compounds with finite enthalpy of transition. PMID:24730863

  20. Direct Observation of Diffuse Cone Behavior in de Vries Smectic-A and -C Phases of Organosiloxane Mesogens

    NASA Astrophysics Data System (ADS)

    Yoon, Hyungguen; Agra-Kooijman, Dena M.; Ayub, Khurshid; Lemieux, Robert P.; Kumar, Satyendra

    2011-02-01

    Simultaneous and direct x-ray measurements of the smectic layer spacing, molecular tilt, and orientational order in the de Vries smectic A (SmA) and C (SmC) phases of two organosiloxane mesogens reveal that (i) the SmC (tilt) order parameter exponent β=0.26±0.01 for 2nd order SmA-SmC transition—in excellent agreement with the tricritical behavior, (ii) the siloxane and hydrocarbon parts of the molecules are segregated and oriented parallel to the director with very different degree of orientational order, and (iii) thermal evolution of the effective molecular length is different in the two phases.

  1. Extended Painlevé Expansion, Nonstandard Truncation and Special Reductions of Nonlinear Evolution Equations

    NASA Astrophysics Data System (ADS)

    Lou, Sen-yue

    1998-05-01

    To study a nonlinear partial differential equation (PDE), the Painleve expansion developed by Weiss, Tabor and Carnevale (WTC) is one of the most powerful methods. In this paper, using any singular manifold, the expansion series in the usual Painleve analysis is shown to be resummable in some different ways. A simple nonstandard truncated expansion with a quite universal reduction function is used for many nonlinear integrable and nonintegrable PDEs such as the Burgers, Korteweg de-Vries (KdV), Kadomtsev-Petviashvli (KP), Caudrey-Dodd-Gibbon-Sawada-Kortera (CDGSK), Nonlinear Schrödinger (NLS), Davey-Stewartson (DS), Broer-Kaup (BK), KdV-Burgers (KdVB), λf4 , sine-Gordon (sG) etc.

  2. Higher Painlevé transcendents as special solutions of some nonlinear integrable hierarchies

    NASA Astrophysics Data System (ADS)

    Kudryashov, Nikolay A.

    2014-02-01

    It is well known that the self-similar solutions of the Korteweg-de Vries equation and the modified Korteweg-de Vries equation are expressed via the solutions of the first and second Painlevé equations. In this paper we solve this problem for all equations from the Korteveg-de Vries, modified Korteweg-de Vries, Kaup-Kupershmidt, Caudrey-Dodd-Gibbon and Fordy-Gibbons hierarchies. We show that the self-similar solutions of equations corresponding to hierarchies mentioned above can be found by means of the general solutions of higher-order Painlevé hierarchies introduced more than ten years ago.

  3. Diffuse cone behavior and microscopic structure of the de Vries smectic-A and smectic-C phases

    NASA Astrophysics Data System (ADS)

    Yoon, HyunGuen; Agra-Kooijman, Dena M.; Ayub, Khurshid; Lemieux, Robert P.; Kumar, Satyendra

    2011-10-01

    Direct synchrotron x-ray scattering measurements of the orientational order parameter, S, corresponding to the siloxane and hydrocarbon parts of the molecule, smectic layer spacing, and director tilt angle with respect to the smectic-C (SmC) layer normal in the de Vries smectics-A (SmA) and SmC phases of two organosiloxane mesogens are reported. The results reveal that (i) the SmC (tilt) order parameter exponent β = 0.26 +/- 0.01 for 2nd order SmA-SmC transition in excellent agreement with the tricritical behavior, (ii) the siloxane and hydrocarbon parts of the molecules are segregated and oriented parallel to the director with different degree of orientational order, and (iii) thermal evolution of the effective molecular length is different in the two phases contrary to the conventional wisdom.

  4. Conservation laws and symmetries of Hunter-Saxton equation: revisited

    NASA Astrophysics Data System (ADS)

    Tian, Kai; Liu, Q. P.

    2016-03-01

    Through a reciprocal transformation {{T}0} induced by the conservation law {{\\partial}t}≤ft(ux2\\right)={{\\partial}x}≤ft(2uux2\\right) , the Hunter-Saxton (HS) equation {{u}xt}=2u{{u}2x}+ux2 is shown to possess conserved densities involving arbitrary smooth functions, which have their roots in infinitesimal symmetries of {{w}t}={{w}2} , the counterpart of the HS equation under {{T}0} . Hierarchies of commuting symmetries of the HS equation are studied under appropriate changes of variables initiated by {{T}0} , and two of these are linearized while the other is identical to the hierarchy of commuting symmetries admitted by the potential modified Korteweg-de Vries equation. A fifth order symmetry of the HS equation is endowed with a sixth order hereditary recursion operator, which is proved to have a bi-Hamiltonian factorization, by its connection with the Fordy-Gibbons equation. These results reveal the origin for the rich and remarkable structures of the HS equation and partially answer the questions raised by Wang (2010 Nonlinearity 23 2009).

  5. X-ray diffraction study of ferroelectric and antiferroelectric liquid crystal mixtures exhibiting de Vries SmA∗-SmC∗ transitions.

    PubMed

    Manna, U; Richardson, R M; Fukuda, Atsuo; Vij, J K

    2010-05-01

    In this Rapid Communication, results on smectic layer thickness, using synchrotron radiation x-ray diffraction, for different mixtures of ferroelectric and antiferroelectric liquid crystals are given. We find that with an increased ferroelectric component in the mixtures, the layer shrinkage at the de Vries SmA∗-SmC∗ transition increases. This observation can be used to explain our previously observed behaviors [U. Manna, J.-K. Song, Yu. P. Panarin, A. Fukuda, and J. K. Vij, Phys. Rev. E 77, 041707 (2008)] that the soft-mode dielectric strength decreases, the Landau coefficient increases, and the Curie-Weiss temperature range decreases with increased ferroelectric component in the mixture exhibiting de Vries SmA∗-SmC∗ transition. PMID:20866175

  6. On the Origin of the "Giant" Electroclinic Effect in a "De Vries"-Type Ferroelectric Liquid Crystal Material for Chirality Sensing Applications

    SciTech Connect

    Kapernaum, N.; Walba, D; Korblova, E; Zhu, C; Jones, C; Shen, Y; Clark, N; Giesselmann, F

    2009-01-01

    W415 is a chiral smectic compound with a remarkably weak temperature dependence of its giant electroclinic effect in the liquid crystalline smectic A* phase. Furthermore it possesses a high spontaneous polarization in the smectic C* phase. The origin of this striking electroclinic effect is the co-occurrence of a de Vries-type ordering with a weak first-order tilting transition (see the synchroton X-ray scattering profiles).

  7. The classical Korteweg capillarity system: geometry and invariant transformations

    NASA Astrophysics Data System (ADS)

    Rogers, C.; Schief, W. K.

    2014-08-01

    A class of invariant transformations is presented for the classical Korteweg capillarity system. The invariance is an extension of a kind originally introduced in an anisentropic gasdynamics context. In a particular instance, application of the invariant transformation leads to a deformed one-parameter class of Kármán-Tsien-type capillarity laws associated with a deformation of an integrable nonlinear Schrödinger-type equation which incorporates a de Broglie-Bohm potential. The latter and another integrable case associated with the classical Boussinesq equation may be linked to the motion of curves in Euclidean and projective space so that both the invariant transformation and the Galilean invariance of the capillarity system may be interpreted in a geometric and soliton-theoretic manner. The work is set in the broader context of other connections of invariant transformations in gasdynamics with soliton theory.

  8. Modulational Instability and Rogue Waves in Shallow Water Models

    NASA Astrophysics Data System (ADS)

    Grimshaw, R.; Chow, K. W.; Chan, H. N.

    It is now well known that the focussing nonlinear Schrödinger equation allows plane waves to be modulationally unstable, and at the same time supports breather solutions which are often invoked as models for rogue waves. This suggests a direct connection between modulation instability and the existence of rogue waves. In this chapter we review this connection for a suite of long wave models, such as the Korteweg-de Vries equation, the extended Korteweg-de Vries (Gardner) equation, often used to describe surface and internal waves in shallow water, a Boussinesq equation and, also a coupled set of Korteweg-de Vries equations.

  9. On the orbital stability of Gaussian solitary waves in the log-KdV equation

    NASA Astrophysics Data System (ADS)

    Carles, Rémi; Pelinovsky, Dmitry

    2014-12-01

    We consider the logarithmic Korteweg-de Vries (log-KdV) equation, which models solitary waves in anharmonic chains with Hertzian interaction forces. By using an approximating sequence of global solutions of the regularized generalized KdV equation in H^1({R}) with conserved L2 norm and energy, we construct a weak global solution of the log-KdV equation in a subset of H^1({R}) . This construction yields conditional orbital stability of Gaussian solitary waves of the log-KdV equation, provided that uniqueness and continuous dependence of the constructed solution holds. Furthermore, we study the linearized log-KdV equation at the Gaussian solitary wave and prove that the associated linearized operator has a purely discrete spectrum consisting of simple purely imaginary eigenvalues in addition to the double zero eigenvalue. The eigenfunctions, however, do not decay like Gaussian functions but have algebraic decay. Using numerical approximations, we show that the Gaussian initial data do not spread out but produce visible radiation at the left slope of the Gaussian-like pulse in the time evolution of the linearized log-KdV equation.

  10. Rogue waves in electronegative space plasmas: The link between the family of the KdV equations and the nonlinear Schrödinger equation

    NASA Astrophysics Data System (ADS)

    El-Tantawy, S. A.

    2016-05-01

    We examine the likelihood of the ion-acoustic rogue waves propagation in a non-Maxwellian electronegative plasma in the framework of the family of the Korteweg-de Vries (KdV) equations (KdV/modified KdV/Extended KdV equation). For this purpose, we use the reductive perturbation technique to carry out this study. It is known that the family of the KdV equations have solutions of distinct structures such as solitons, shocks, kinks, cnoidal waves, etc. However, the dynamics of the nonlinear rogue waves is governed by the nonlinear Schrödinger equation (NLSE). Thus, the family of the KdV equations is transformed to their corresponding NLSE developing a weakly nonlinear wave packets. We show the possible region for the existence of the rogue waves and define it precisely for typical parameters of space plasmas. We investigate numerically the effects of relevant physical parameters, namely, the negative ion relative concentration, the nonthermal parameter, and the mass ratio on the propagation of the rogue waves profile. The present study should be helpful in understanding the salient features of the nonlinear structures such as, ion-acoustic solitary waves, shock waves, and rogue waves in space and in laboratory plasma where two distinct groups of ions, i.e. positive and negative ions, and non-Maxwellian (nonthermal) electrons are present.

  11. Phase space lattices and integrable nonlinear wave equations

    NASA Astrophysics Data System (ADS)

    Tracy, Eugene; Zobin, Nahum

    2003-10-01

    Nonlinear wave equations in fluids and plasmas that are integrable by Inverse Scattering Theory (IST), such as the Korteweg-deVries and nonlinear Schrodinger equations, are known to be infinite-dimensional Hamiltonian systems [1]. These are of interest physically because they predict new phenomena not present in linear wave theories, such as solitons and rogue waves. The IST method provides solutions of these equations in terms of a special class of functions called Riemann theta functions. The usual approach to the theory of theta functions tends to obscure the underlying phase space structure. A theory due to Mumford and Igusa [2], however shows that the theta functions arise naturally in the study of phase space lattices. We will describe this theory, as well as potential applications to nonlinear signal processing and the statistical theory of nonlinear waves. 1] , S. Novikov, S. V. Manakov, L. P. Pitaevskii and V. E. Zakharov, Theory of solitons: the inverse scattering method (Consultants Bureau, New York, 1984). 2] D. Mumford, Tata lectures on theta, Vols. I-III (Birkhauser); J. Igusa, Theta functions (Springer-Verlag, New York, 1972).

  12. Wave-packet formation at the zero-dispersion point in the Gardner-Ostrovsky equation.

    PubMed

    Whitfield, A J; Johnson, E R

    2015-05-01

    The long-time effect of weak rotation on an internal solitary wave is the decay into inertia-gravity waves and the eventual emergence of a coherent, steadily propagating, nonlinear wave packet. There is currently no entirely satisfactory explanation as to why these wave packets form. Here the initial value problem is considered within the context of the Gardner-Ostrovsky, or rotation-modified extended Korteweg-de Vries, equation. The linear Gardner-Ostrovsky equation has maximum group velocity at a critical wave number, often called the zero-dispersion point. It is found here that a nonlinear splitting of the wave-number spectrum at the zero-dispersion point, where energy is shifted into the modulationally unstable regime of the Gardner-Ostrovsky equation, is responsible for the wave-packet formation. Numerical comparisons of the decay of a solitary wave in the Gardner-Ostrovsky equation and a derived nonlinear Schrödinger equation at the zero-dispersion point are used to confirm the spectral splitting. PMID:26066112

  13. INVITED ARTICLE: The second Painlevé equation, its hierarchy and associated special polynomials

    NASA Astrophysics Data System (ADS)

    Clarkson, Peter A.; Mansfield, Elizabeth L.

    2003-05-01

    In this paper we are concerned with hierarchies of rational solutions and associated polynomials for the second Painlevé equation (PII) and the equations in the PII hierarchy which is derived from the modified Korteweg-de Vries hierarchy. These rational solutions of PII are expressible as the logarithmic derivative of special polynomials, the Yablonskii-Vorob'ev polynomials. The structure of the roots of these Yablonskii-Vorob'ev polynomials is studied and it is shown that these have a highly regular triangular structure. Further, the properties of the Yablonskii-Vorob'ev polynomials are compared and contrasted with those of classical orthogonal polynomials. We derive the special polynomials for the second and third equations of the PII hierarchy and give a representation of the associated rational solutions in the form of determinants through Schur functions. Additionally the analogous special polynomials associated with rational solutions and representation in the form of determinants are conjectured for higher equations in the PII hierarchy. The roots of these special polynomials associated with rational solutions for the equations of the PII hierarchy also have a highly regular structure.

  14. Inverse scattering transform for the KPI equation on the background of a one-line soliton*Inverse scattering transform for the KPI equation on the background of a one-line soliton

    NASA Astrophysics Data System (ADS)

    Fokas, A. S.; Pogrebkov, A. K.

    2003-03-01

    We study the initial value problem of the Kadomtsev-Petviashvili I (KPI) equation with initial data u(x1,x2,0) = u1(x1)+u2(x1,x2), where u1(x1) is the one-soliton solution of the Korteweg-de Vries equation evaluated at zero time and u2(x1,x2) decays sufficiently rapidly on the (x1,x2)-plane. This involves the analysis of the nonstationary Schrödinger equation (with time replaced by x2) with potential u(x1,x2,0). We introduce an appropriate sectionally analytic eigenfunction in the complex k-plane where k is the spectral parameter. This eigenfunction has the novelty that in addition to the usual jump across the real k-axis, it also has a jump across a segment of the imaginary k-axis. We show that this eigenfunction can be reconstructed through a linear integral equation uniquely defined in terms of appropriate scattering data. In turn, these scattering data are uniquely constructed in terms of u1(x1) and u2(x1,x2). This result implies that the solution of the KPI equation can be obtained through the above linear integral equation where the scattering data have a simple t-dependence.

  15. 17q21.31 microdeletion syndrome: Description of a case further contributing to the delineation of Koolen-de Vries syndrome.

    PubMed

    Bernardo, Pia; Madia, Francesca; Santulli, Lia; Del Gaudio, Luigi; Caccavale, Carmela; Zara, Federico; Traverso, Monica; Cirillo, Mario; Striano, Salvatore; Coppola, Antonietta

    2016-08-01

    The widespread use of Array Comparative Genomic Hybridization (aCGH) technology has enabled the identification of several syndromes associated with copy number variants (CNVs) including the 17q21.31 microdeletion. The 17q21.31 microdeletion syndrome, also known as Koolen-de Vries syndrome, was first described in 2006 in individuals with intellectual disabilities and organ abnormalities. We report the clinical, instrumental, cytogenetic and molecular investigations of a boy admitted for epilepsy and intellectual disabilities. We carried out detailed analysis of the clinical phenotype of this patient and investigated the genetic basis by using aCGH. We identified a de novo microdeletion on chromosome 17q21.31, compatible with Koolen-de Vries syndrome. Our case shares some of the typical characteristics of the syndrome already described by other authors: delayed psychomotor development, primarily affecting the expressive language, dysmorphic facial features, and epilepsy. However the clinical outcome was not severe as the intellectual disabilities were moderate with good adaptive and functional behaviour. Epilepsy was easily controlled by a single drug, and he never needed surgery for organ abnormalities. PMID:26897099

  16. A complete list of conservation laws for non-integrable compacton equations of K(m, m) type

    NASA Astrophysics Data System (ADS)

    Vodová, Jiřina

    2013-03-01

    In 1993, P Rosenau and J M Hyman introduced and studied Korteweg-de-Vries-like equations with nonlinear dispersion admitting compacton solutions, u_t+D_x^3(u^n)+D_x(u^m)=0 , m, n > 1, which are known as the K(m, n) equations. In this paper we consider a slightly generalized version of the K(m, n) equations for m = n, namely, u_t=aD_x^3(u^m)+bD_x(u^m) , where m, a, b are arbitrary real numbers. We describe all generalized symmetries and conservation laws thereof for m ≠ -2, -1/2, 0, 1; for these four exceptional values of m the equation in question is either completely integrable (m = -2, -1/2) or linear (m = 0, 1). It turns out that for m ≠ -2, -1/2, 0, 1 there are only three symmetries corresponding to x- and t-translations and scaling of t and u, and four non-trivial conservation laws, one of which expresses the conservation of energy, and the other three are associated with the Casimir functionals of the Hamiltonian operator \\mathfrak{D}=aD_x^3+bD_x admitted by our equation. Our result provides inter alia a rigorous proof of the fact that the K (2, 2) equation has just four conservation laws from the paper of P Rosenau and J M Hyman.

  17. Bernoulli, Euler, Riccati and Solitons

    SciTech Connect

    Rzadkowski, Grzegorz

    2009-09-09

    In this paper we present a theorem showing the reason of the connection between Bernoulli numbers and solitons, the solutions of the Korteweg-de Vries equation. The theorem involves Eulerian numbers and Riccati's differential equation.

  18. Orientational order parameters of a de Vries-type ferroelectric liquid crystal obtained by polarized Raman spectroscopy and x-ray diffraction.

    PubMed

    Sanchez-Castillo, A; Osipov, M A; Jagiella, S; Nguyen, Z H; Kašpar, M; Hamplovă, V; Maclennan, J; Giesselmann, F

    2012-06-01

    The orientational order parameters (P{2}) and (P{4}) of the ferroelectric, de Vries-type liquid crystal 9HL have been determined in the SmA and SmC phases by means of polarized Raman spectroscopy, and in the SmA phase using x-ray diffraction. Quantum density functional theory predicts Raman spectra for 9HL that are in good agreement with the observations and indicates that the strong Raman band probed in the experiment corresponds to the uniaxial, coupled vibration of the three phenyl rings along the molecular long axis. The magnitudes of the orientational order parameters obtained in the Raman and x-ray experiments differ dramatically from each other, a discrepancy that is resolved by considering that the two techniques probe the orientational distributions of different molecular axes. We have developed a systematic procedure in which we calculate the angle between these axes and rescale the orientational order parameters obtained from x-ray scattering with results that are then in good agreement with the Raman data. At least in the case of 9HL, the results obtained by both techniques support a "sugar loaf" orientational distribution in the SmA phase with no qualitative difference to conventional smectics A. The role of individual molecular fragments in promoting de Vries-type behavior is considered. PMID:23005110

  19. Some Remarks on the Riccati Equation Expansion Method for Variable Separation of Nonlinear Models

    NASA Astrophysics Data System (ADS)

    Zhang, Yu-Peng; Dai, Chao-Qing

    2015-10-01

    Based on the Riccati equation expansion method, 11 kinds of variable separation solutions with different forms of (2+1)-dimensional modified Korteweg-de Vries equation are obtained. The following two remarks on the Riccati equation expansion method for variable separation are made: (i) a remark on the equivalence of different solutions constructed by the Riccati equation expansion method. From analysis, we find that these seemly independent solutions with different forms actually depend on each other, and they can transform from one to another via some relations. We should avoid arbitrarily asserting so-called "new" solutions; (ii) a remark on the construction of localised excitation based on variable separation solutions. For two or multi-component systems, we must be careful with excitation structures constructed by all components for the same model lest the appearance of some un-physical structures. We hope that these results are helpful to deeply study exact solutions of nonlinear models in physical, engineering and biophysical contexts.

  20. Stable and unstable vector dark solitons of coupled nonlinear Schroedinger equations: Application to two-component Bose-Einstein condensates

    SciTech Connect

    Brazhnyi, V.A.; Konotop, V.V.

    2005-08-01

    The dynamics of vector dark solitons in two-component Bose-Einstein condensates is studied within the framework of coupled one-dimensional nonlinear Schroedinger (NLS) equations. We consider the small-amplitude limit in which the coupled NLS equations are reduced to coupled Korteweg-de Vries (KdV) equations. For a specific choice of the parameters the obtained coupled KdV equations are exactly integrable. We find that there exist two branches of (slow and fast) dark solitons corresponding to the two branches of the sound waves. Slow solitons, corresponding to the lower branch of the acoustic wave, appear to be unstable and transform during the evolution into stable fast solitons (corresponding to the upper branch of the dispersion law). Vector dark solitons of arbitrary depths are studied numerically. It is shown that effectively different parabolic traps, to which the two components are subjected, cause an instability of the solitons, leading to a splitting of their components and subsequent decay. A simple phenomenological theory, describing the oscillations of vector dark solitons in a magnetic trap, is proposed.

  1. Analytical integrability and physical solutions of d-KdV equation

    SciTech Connect

    Karmakar, P.K.; Dwivedi, C.B.

    2006-03-15

    A new idea of electron inertia-induced ion sound wave excitation for transonic plasma equilibrium has already been reported. In such unstable plasma equilibrium, a linear source driven Korteweg-de Vries (d-KdV) equation describes the nonlinear ion sound wave propagation behavior. By numerical techniques, two distinct classes of solution (soliton and oscillatory shocklike structures) are obtained. Present contribution deals with the systematic methodological efforts to find out its (d-KdV) analytical solutions. As a first step, we apply the Painleve method to test whether the derived d-KdV equation is analytically integrable or not. We find that the derived d-KdV equation is indeed analytically integrable since it satisfies Painleve property. Hirota's bilinearization method and the modified sine-Gordon method (also termed as sine-cosine method) are used to derive the analytical results. Perturbative technique is also applied to find out quasistationary solutions. A few graphical plots are provided to offer a glimpse of the structural profiles obtained by different methods applied. It is conjectured that these solutions may open a new scope of acoustic spectroscopy in plasma hydrodynamics.

  2. Symplectically invariant soliton equations from non-stretching geometric curve flows

    NASA Astrophysics Data System (ADS)

    Anco, Stephen C.; Asadi, Esmaeel

    2012-11-01

    Bi-Hamiltonian hierarchies of symplectically invariant soliton equations are derived from geometric non-stretching flows of curves in the Riemannian symmetric spaces Sp(n + 1)/Sp(1) × Sp(n) and SU(2n)/Sp(n). The derivation uses Hasimoto variables defined by a moving parallel frame along the curves. As main results, two new multi-component versions of the sine-Gordon equation and the modified Korteweg-de Vries (mKdV) equation exhibiting Sp(1) × Sp(n - 1) invariance are obtained along with their bi-Hamiltonian integrability structure consisting of a hierarchy of symmetries and conservation laws generated by a hereditary recursion operator. The corresponding geometric curve flows in both Sp(n + 1)/Sp(1) × Sp(n) and SU(2n)/Sp(n) are shown to be described by a non-stretching wave map and a mKdV analogue of a non-stretching Schrödinger map.

  3. Stable and unstable vector dark solitons of coupled nonlinear Schrödinger equations: application to two-component Bose-Einstein condensates.

    PubMed

    Brazhnyi, V A; Konotop, V V

    2005-08-01

    The dynamics of vector dark solitons in two-component Bose-Einstein condensates is studied within the framework of coupled one-dimensional nonlinear Schrödinger (NLS) equations. We consider the small-amplitude limit in which the coupled NLS equations are reduced to coupled Korteweg-de Vries (KdV) equations. For a specific choice of the parameters the obtained coupled KdV equations are exactly integrable. We find that there exist two branches of (slow and fast) dark solitons corresponding to the two branches of the sound waves. Slow solitons, corresponding to the lower branch of the acoustic wave, appear to be unstable and transform during the evolution into stable fast solitons (corresponding to the upper branch of the dispersion law). Vector dark solitons of arbitrary depths are studied numerically. It is shown that effectively different parabolic traps, to which the two components are subjected, cause an instability of the solitons, leading to a splitting of their components and subsequent decay. A simple phenomenological theory, describing the oscillations of vector dark solitons in a magnetic trap, is proposed. PMID:16196744

  4. Numerical and perturbative computations of solitary waves of the Benjamin-Ono equation with higher order nonlinearity using Christov rational basis functions

    NASA Astrophysics Data System (ADS)

    Boyd, John P.; Xu, Zhengjie

    2012-02-01

    Computation of solitons of the cubically-nonlinear Benjamin-Ono equation is challenging. First, the equation contains the Hilbert transform, a nonlocal integral operator. Second, its solitary waves decay only as O(1/∣ x∣ 2). To solve the integro-differential equation for waves traveling at a phase speed c, we introduced the artificial homotopy H( uXX) - c u + (1 - δ) u2 + δu3 = 0, δ ∈ [0, 1] and solved it in two ways. The first was continuation in the homotopy parameter δ, marching from the known Benjamin-Ono soliton for δ = 0 to the cubically-nonlinear soliton at δ = 1. The second strategy was to bypass continuation by numerically computing perturbation series in δ and forming Padé approximants to obtain a very accurate approximation at δ = 1. To further minimize computations, we derived an elementary theorem to reduce the two-parameter soliton family to a parameter-free function, the soliton symmetric about the origin with unit phase speed. Solitons for higher order Benjamin-Ono equations are also computed and compared to their Korteweg-deVries counterparts. All computations applied the pseudospectral method with a basis of rational orthogonal functions invented by Christov, which are eigenfunctions of the Hilbert transform.

  5. Some exact solutions to the Lighthill-Whitham-Richards-Payne traffic flow equations

    NASA Astrophysics Data System (ADS)

    Rowlands, G.; Infeld, E.; Skorupski, A. A.

    2013-09-01

    We find a class of exact solutions to the Lighthill-Whitham-Richards-Payne (LWRP) traffic flow equations. Using two consecutive Lagrangian transformations, a linearization is achieved. Next, depending on the initial density, we either apply (again two) Lambert functions and obtain exact formulae for the dependence of the car density and velocity on x, t, or else, failing that, the same result in a parametric representation. The calculation always involves two possible factorizations of a consistency condition. Both must be considered. In physical terms, the lineup usually separates into two offshoots at different velocities. Each velocity soon becomes uniform. This outcome in many ways resembles the two soliton solution to the Korteweg-de Vries equation. We check general conservation requirements. Although traffic flow research has developed tremendously since LWRP, this calculation, being exact, may open the door to solving similar problems, such as gas dynamics or water flow in rivers. With this possibility in mind, we outline the procedure in some detail at the end.

  6. Dust acoustic shock waves in two temperatures charged dusty grains

    SciTech Connect

    El-Shewy, E. K.; Abdelwahed, H. G.; Elmessary, M. A.

    2011-11-15

    The reductive perturbation method has been used to derive the Korteweg-de Vries-Burger equation and modified Korteweg-de Vries-Burger for dust acoustic shock waves in a homogeneous unmagnetized plasma having electrons, singly charged ions, hot and cold dust species with Boltzmann distributions for electrons and ions in the presence of the cold (hot) dust viscosity coefficients. The behavior of the shock waves in the dusty plasma has been investigated.

  7. The Koolen-de Vries syndrome: a phenotypic comparison of patients with a 17q21.31 microdeletion versus a KANSL1 sequence variant.

    PubMed

    Koolen, David A; Pfundt, Rolph; Linda, Katrin; Beunders, Gea; Veenstra-Knol, Hermine E; Conta, Jessie H; Fortuna, Ana Maria; Gillessen-Kaesbach, Gabriele; Dugan, Sarah; Halbach, Sara; Abdul-Rahman, Omar A; Winesett, Heather M; Chung, Wendy K; Dalton, Marguerite; Dimova, Petia S; Mattina, Teresa; Prescott, Katrina; Zhang, Hui Z; Saal, Howard M; Hehir-Kwa, Jayne Y; Willemsen, Marjolein H; Ockeloen, Charlotte W; Jongmans, Marjolijn C; Van der Aa, Nathalie; Failla, Pinella; Barone, Concetta; Avola, Emanuela; Brooks, Alice S; Kant, Sarina G; Gerkes, Erica H; Firth, Helen V; Õunap, Katrin; Bird, Lynne M; Masser-Frye, Diane; Friedman, Jennifer R; Sokunbi, Modupe A; Dixit, Abhijit; Splitt, Miranda; Kukolich, Mary K; McGaughran, Julie; Coe, Bradley P; Flórez, Jesús; Nadif Kasri, Nael; Brunner, Han G; Thompson, Elizabeth M; Gecz, Jozef; Romano, Corrado; Eichler, Evan E; de Vries, Bert Ba

    2016-05-01

    The Koolen-de Vries syndrome (KdVS; OMIM #610443), also known as the 17q21.31 microdeletion syndrome, is a clinically heterogeneous disorder characterised by (neonatal) hypotonia, developmental delay, moderate intellectual disability, and characteristic facial dysmorphism. Expressive language development is particularly impaired compared with receptive language or motor skills. Other frequently reported features include social and friendly behaviour, epilepsy, musculoskeletal anomalies, congenital heart defects, urogenital malformations, and ectodermal anomalies. The syndrome is caused by a truncating variant in the KAT8 regulatory NSL complex unit 1 (KANSL1) gene or by a 17q21.31 microdeletion encompassing KANSL1. Herein we describe a novel cohort of 45 individuals with KdVS of whom 33 have a 17q21.31 microdeletion and 12 a single-nucleotide variant (SNV) in KANSL1 (19 males, 26 females; age range 7 months to 50 years). We provide guidance about the potential pitfalls in the laboratory testing and emphasise the challenges of KANSL1 variant calling and DNA copy number analysis in the complex 17q21.31 region. Moreover, we present detailed phenotypic information, including neuropsychological features, that contribute to the broad phenotypic spectrum of the syndrome. Comparison of the phenotype of both the microdeletion and SNV patients does not show differences of clinical importance, stressing that haploinsufficiency of KANSL1 is sufficient to cause the full KdVS phenotype. PMID:26306646

  8. Finite-gap solutions of 2+1 dimensional integrable nonlinear evolution equations generated by the Neumann systems

    NASA Astrophysics Data System (ADS)

    Chen, Jinbing

    2010-08-01

    Each soliton equation in the Korteweg-de Vries (KdV) hierarchy, the 2+1 dimensional breaking soliton equation, and the 2+1 dimensional Caudrey-Dodd-Gibbon-Kotera-Sawada (CDGKS) equation are reduced to two or three Neumann systems on the tangent bundle TSN -1 of the unit sphere SN -1. The Lax-Moser matrix for the Neumann systems of degree N -1 is deduced in view of the Mckean-Trubowitz identity and a bilinear generating function, whose favorite characteristic accounts for the problem of the genus of Riemann surface matching to the number of elliptic variables. From the Lax-Moser matrix, the constrained Hamiltonians in the sense of Dirac-Poisson bracket for all the Neumann systems are written down in a uniform recursively determined by integrals of motion. The involution of integrals of motion and constrained Hamiltonians is completed on TSN -1 by using a Lax equation and their functional independence is displayed over a dense open subset of TSN -1 by a direct calculation, which contribute to the Liouville integrability of a family of Neumann systems in a new systematical way. We also construct the hyperelliptic curve of Riemann surface and the Abel map straightening out the restricted Neumann flows that naturally leads to the Jacobi inversion problem on the Jacobian with the aid of the holomorphic differentials, from which some finite-gap solutions expressed by Riemann theta functions for the 2+1 dimensional breaking soliton equation, the 2+1 dimensional CDGKS equation, the KdV, and the fifth-order KdV equations are presented by means of the Riemann theorem.

  9. Exact kink solitons in the presence of diffusion, dispersion, and polynomial nonlinearity

    NASA Astrophysics Data System (ADS)

    Raposo, E. P.; Bazeia, D.

    1999-03-01

    We describe exact travelling-wave kink soliton solutions in some classes of nonlinear partial differential equations, such as generalized Korteweg-de Vries-Burgers, Korteweg-de Vries-Huxley, and Korteweg-de Vries-Burgers-Huxley equations, as well as equations in the generic form ut + P( u) ux + vuxx - δuxxx = A( u), with polynomial functions P( u) and A( u) of u = u( x, t), whose generality allows the identification with a number of relevant equations in physics. We focus on the analysis of the role of diffusion, dispersion, nonlinear effects, and parity of the polynomials to the properties of the solutions, particularly their velocity of propagation. In addition, we show that, for some appropriate choices, these equations can be mapped onto equations of motion of relativistic (1 + 1)-dimensional φ4 and φ6 field theories of real scalar fields. Systems of two coupled nonlinear equations are also considered.

  10. Higher Order Corrections for Shallow-Water Solitary Waves: Elementary Derivation and Experiments

    ERIC Educational Resources Information Center

    Halasz, Gabor B.

    2009-01-01

    We present an elementary method to obtain the equations of the shallow-water solitary waves in different orders of approximation. The first two of these equations are solved to get the shapes and propagation velocities of the corresponding solitary waves. The first-order equation is shown to be equivalent to the Korteweg-de Vries (KdV) equation,…

  11. Parametric study of a Schamel equation for low-frequency dust acoustic waves in dusty electronegative plasmas

    NASA Astrophysics Data System (ADS)

    Sabetkar, Akbar; Dorranian, Davoud

    2015-08-01

    In this paper, our attention is first concentrated on obliquely propagating properties of low-frequency (ω ≪ ωcd) "fast" and "slow" dust acoustic waves, in the linear regime, in dusty electronegative plasmas with Maxwellian electrons, kappa distributed positive ions, negative ions (following the combination of kappa-Schamel distribution), and negatively charged dust particles. So, an explicit expression for dispersion relation is derived by linearizing a set of dust-fluid equations. The results show that wave frequency ω in long and short-wavelengths limit is conspicuously affected by physical parameters, namely, positive to negative temperature ion ratio (βp), trapping parameter of negative ions (μ), magnitude of the magnetic field B0 (via ωcd), superthermal index ( κn,κp ), and positive ion to dust density ratio (δp). The signature of the penultimate parameter (i.e., κn) on wave frequency reveals that the frequency gap between the modes reduces (escalates) for k kc r ), where kcr is critical wave number. Alternatively, for weakly nonlinear analysis, reductive perturbation theory has been used to construct 1D and 3D Schamel Korteweg-de Vries (S-KdV) equations, whose nonlinearity coefficient prescribes only compressive soliton for all parameter values of interest. The survey manifests that deviation of ions from Maxwellian behavior leads intrinsic properties of solitary waves to be evolved in opposite trend. Additionally, at lower proportion of trapped negative ions, solitary wave amplitude mitigates, whilst the trapping parameter has no effect on both spatial width and the linear wave. The results are discussed in the context of the Earth's mesosphere of dusty electronegative plasma.

  12. Reductions of lattice mKdV to q-PVI

    NASA Astrophysics Data System (ADS)

    Ormerod, Christopher M.

    2012-10-01

    This Letter presents a reduction of the lattice modified Korteweg-de Vries equation that gives rise to a q-analogue of the sixth Painlevé equation via a new approach to reductions. This new approach also allows us to give the first ultradiscrete Lax representation of an ultradiscrete analogue of the sixth Painlevé equation.

  13. Solitons in nucleon-nucleus collisions

    SciTech Connect

    Fogaca, D.A.; Navarra, F.S.

    2004-12-02

    Under certain conditions, the equations of non-relativistic hydrodynamics may provide a Korteweg-de Vries equation (KdV) which gives a soliton solution. We show that this solution and its properties are related to the microscopic features of the nuclear matter equation of state.

  14. Quantum positron acoustic waves

    SciTech Connect

    Metref, Hassina; Tribeche, Mouloud

    2014-12-15

    Nonlinear quantum positron-acoustic (QPA) waves are investigated for the first time, within the theoretical framework of the quantum hydrodynamic model. In the small but finite amplitude limit, both deformed Korteweg-de Vries and generalized Korteweg-de Vries equations governing, respectively, the dynamics of QPA solitary waves and double-layers are derived. Moreover, a full finite amplitude analysis is undertaken, and a numerical integration of the obtained highly nonlinear equations is carried out. The results complement our previously published results on this problem.

  15. Optical and x-ray evidence of the ``de Vries'' Sm-A*-Sm-C* transition in a non-layer-shrinkage ferroelectric liquid crystal with very weak interlayer tilt correlation

    NASA Astrophysics Data System (ADS)

    Lagerwall, Jan P.; Giesselmann, Frank; Radcliffe, Marc D.

    2002-09-01

    A non-layer-shrinkage fluorinated ferroelectric liquid crystal compound, 8422[2F3], has been characterized by means of optical, x-ray, and calorimetric methods. The orientational distribution within macroscopic volumes, determined through wide-angle x-ray scattering and birefringence measurements, was found to be identical in the Sm-A* and helical Sm-C* phases. Together with the absence of layer shrinkage, this constitutes strong evidence that the second-order Sm-A*-Sm-C* transition in this material is well described by the diffuse cone model of de Vries. The absolute values of the layer spacing show that the molecules aggregate to antiparallel pairs. The molecular interaction across the layer boundaries will then occur only between fluorine atoms, leading to unusually weak interlayer tilt direction correlation. This explains the experimental observations of a very easily disturbed Sm-C* helix and a peculiar surface-stabilized texture. Tilt angle and birefringence values as a function of field and temperature have been evaluated in the Sm-A* and Sm-C* phases and the results corroborate the conclusions from the x-ray investigations.

  16. Optical and x-ray evidence of the "de Vries" Sm-A*-Sm-C* transition in a non-layer-shrinkage ferroelectric liquid crystal with very weak interlayer tilt correlation.

    PubMed

    Lagerwall, Jan P F; Giesselmann, Frank; Radcliffe, Marc D

    2002-09-01

    A non-layer-shrinkage fluorinated ferroelectric liquid crystal compound, 8422[2F3], has been characterized by means of optical, x-ray, and calorimetric methods. The orientational distribution within macroscopic volumes, determined through wide-angle x-ray scattering and birefringence measurements, was found to be identical in the Sm-A* and helical Sm-C* phases. Together with the absence of layer shrinkage, this constitutes strong evidence that the second-order Sm-A*-Sm-C* transition in this material is well described by the diffuse cone model of de Vries. The absolute values of the layer spacing show that the molecules aggregate to antiparallel pairs. The molecular interaction across the layer boundaries will then occur only between fluorine atoms, leading to unusually weak interlayer tilt direction correlation. This explains the experimental observations of a very easily disturbed Sm-C* helix and a peculiar surface-stabilized texture. Tilt angle and birefringence values as a function of field and temperature have been evaluated in the Sm-A* and Sm-C* phases and the results corroborate the conclusions from the x-ray investigations. PMID:12366132

  17. Pseudopotentials of Estabrook and Wahlquist, the geometry of solitons, and the theory of connections

    NASA Technical Reports Server (NTRS)

    Hermann, R.

    1976-01-01

    The prolongation structure of Wahlquist and Estabrook is interpreted as a connection. In this way, some geometric insight might be provided for the description of those nonlinear partial differential equations which admit soliton solutions. A new geometric property - linked to the existence of an SL(2,R) connection - is proved for the solutions of the Korteweg-de Vries equation.

  18. Linear stability analysis of Korteweg stresses effect on miscible viscous fingering in porous media

    NASA Astrophysics Data System (ADS)

    Pramanik, Satyajit; Mishra, Manoranjan

    2013-07-01

    Viscous fingering (VF) is an interfacial hydrodynamic instability phenomenon observed when a fluid of lower viscosity displaces a higher viscous one in a porous media. In miscible viscous fingering, the concentration gradient of the undergoing fluids is an important factor, as the viscosity of the fluids are driven by concentration. Diffusion takes place when two miscible fluids are brought in contact with each other. However, if the diffusion rate is slow enough, the concentration gradient of the two fluids remains very large during some time. Such steep concentration gradient, which mimics a surface tension type force, called the effective interfacial tension, appears in various cases such as aqua-organic, polymer-monomer miscible systems, etc. Such interfacial tension effects on miscible VF is modeled using a stress term called Korteweg stress in the Darcy's equation by coupling with the convection-diffusion equation of the concentration. The effect of the Korteweg stresses at the onset of the instability has been analyzed through a linear stability analysis using a self-similar Quasi-steady-state-approximation (SS-QSSA) in which a self-similar diffusive base state profile is considered. The quasi-steady-state analyses available in literature are compared with the present SS-QSSA method and found that the latter captures appropriately the unconditional stability criterion at an earlier diffusive time as well as in long wave approximation. The effects of various governing parameters such as log-mobility ratio, Korteweg parameters, disturbances' wave number, etc., on the onset of the instability are discussed for, (i) the two semi-infinite miscible fluid zones and (ii) VF of the miscible slice cases. The stabilizing property of the Korteweg stresses effect is observed for both of the above mentioned cases. Critical miscible slice lengths are computed to have the onset of the instability for different governing parameters with or without Korteweg stresses. These

  19. Thermal Creep of a Rarefied Gas on the Basis of Non-linear Korteweg-Theory

    NASA Astrophysics Data System (ADS)

    Kim, Yong-Jung; Lee, Min-Gi; Slemrod, Marshall

    2015-02-01

    The study of thermal transpiration, more commonly called thermal creep, is accomplished by use of Korteweg's theory of capillarity. Incorporation of this theory into the balance laws of continuum mechanics allows resolution of boundary value problems via solutions to systems of ordinary differential equations. The problem was originally considered by Maxwell in his classic 1879 paper M axwell (Phil Trans Roy Soc (London) 170:231-256, 1879). In that paper Maxwell derived what is now called the Burnett higher order contribution to the Cauchy stress, but was not able to solve his newly derived system of partial differential equations. In this paper the authors note that a more appropriate higher order contribution to the Cauchy stress follows from Korteweg's 1901 theory K orteweg (Arch Neerl Sci Exactes Nat Ser II 6:1-24, 1901). The appropriateness of Korteweg's theory is based on the exact summation of the Chapman-Enskog expansion given by Gorban and Karlin. The resulting balance laws are solved exactly, qualitatively, and numerically and the results are qualitatively similar to the numerical and exact results given by Aoki et al., Loyalka et al., and Struchtrup et al.

  20. Nongauge bright soliton of the nonlinear Schrödinger (NLS) equation and a family of generalized NLS equations

    NASA Astrophysics Data System (ADS)

    Reyes, M. A.; Gutiérrez-Ruiz, D.; Mancas, S. C.; Rosu, H. C.

    2016-01-01

    We present an approach to the bright soliton solution of the nonlinear Schrödinger (NLS) equation from the standpoint of introducing a constant potential term in the equation. We discuss a “nongauge” bright soliton for which both the envelope and the phase depend only on the traveling variable. We also construct a family of generalized NLS equations with solitonic sechp solutions in the traveling variable and find an exact equivalence with other nonlinear equations, such as the Korteveg-de Vries (KdV) and Benjamin-Bona-Mahony (BBM) equations when p = 2.

  1. Modified ion-acoustic solitary waves in plasmas with field-aligned shear flows

    SciTech Connect

    Saleem, H.; Haque, Q.

    2015-08-15

    The nonlinear dynamics of ion-acoustic waves is investigated in a plasma having field-aligned shear flow. A Korteweg-deVries-type nonlinear equation for a modified ion-acoustic wave is obtained which admits a single pulse soliton solution. The theoretical result has been applied to solar wind plasma at 1 AU for illustration.

  2. On soliton amplification

    NASA Technical Reports Server (NTRS)

    Leibovich, S.; Randall, J. D.

    1979-01-01

    The paper considers a modified Korteweg-de Vries equation that permits wave amplification or damping. A 'terminal similarity' solution is identified for large times in amplified systems. Numerical results are given which confirm that the terminal similarity solution is a valid local approximation for mu t sufficiently large and positive, even though the approximation is not uniformly valid in space.

  3. Conduction-only transport phenomena in compressible bivelocity fluids: Diffuse interfaces and Korteweg stresses

    NASA Astrophysics Data System (ADS)

    Brenner, Howard

    2014-04-01

    "Diffuse interface" theories for single-component fluids—dating back to van der Waals, Korteweg, Cahn-Hilliard, and many others—are currently based upon an ad hoc combination of thermodynamic principles (built largely upon Helmholtz's free-energy potential) and so-called "nonclassical" continuum-thermomechanical principles (built largely upon Newtonian mechanics), with the latter originating with the pioneering work of Dunn and Serrin [Arch. Ration. Mech. Anal. 88, 95 (1985)]. By introducing into the equation governing the transport of energy the notion of an interstitial work-flux contribution, above and beyond the usual Fourier heat-flux contribution, namely, jq=-k∇T, to the energy flux, Dunn and Serrin provided a rational continuum-thermomechanical basis for the presence of Korteweg stresses in the equation governing the transport of linear momentum in compressible fluids. Nevertheless, by their failing to recognize the existence and fundamental need for an independent volume transport equation [Brenner, Physica A 349, 11 (2005), 10.1016/j.physa.2004.10.033]—especially for the roles played therein by the diffuse volume flux jv and the rate of production of volume πv at a point of the fluid continuum—we argue that diffuse interface theories for fluids stand today as being both ad hoc and incomplete owing to their failure to recognize the need for an independent volume transport equation for the case of compressible fluids. In contrast, we point out that bivelocity hydrodynamics, as it already exists [Brenner, Phys. Rev. E 86, 016307 (2012), 10.1103/PhysRevE.86.016307], provides a rational, non-ad hoc, and comprehensive theory of diffuse interfaces, not only for single-component fluids, but also for certain classes of crystalline solids [Danielewski and Wierzba, J. Phase Equilib. Diffus. 26, 573 (2005), 10.1007/s11669-005-0002-y]. Furthermore, we provide not only what we believe to be the correct constitutive equation for the Korteweg stress in the

  4. Solving Differential Equations in R: Package deSolve

    EPA Science Inventory

    In this paper we present the R package deSolve to solve initial value problems (IVP) written as ordinary differential equations (ODE), differential algebraic equations (DAE) of index 0 or 1 and partial differential equations (PDE), the latter solved using the method of lines appr...

  5. Phase-modulated solitary waves controlled by a boundary condition at the bottom.

    PubMed

    Mukherjee, Abhik; Janaki, M S

    2014-06-01

    A forced Korteweg-de Vries (KdV) equation is derived to describe weakly nonlinear, shallow-water surface wave propagation over nontrivial bottom boundary condition. We show that different functional forms of bottom boundary conditions self-consistently produce different forced KdV equations as the evolution equations for the free surface. Solitary wave solutions have been analytically obtained where phase gets modulated controlled by bottom boundary condition, whereas amplitude remains constant. PMID:25019847

  6. Dressed soliton in quantum dusty pair-ion plasma

    SciTech Connect

    Chatterjee, Prasanta; Muniandy, S. V.; Wong, C. S.; Roy, Kaushik

    2009-11-15

    Nonlinear propagation of a quantum ion-acoustic dressed soliton is studied in a dusty pair-ion plasma. The Korteweg-de Vries (KdV) equation is derived using reductive perturbation technique. A higher order inhomogeneous differential equation is obtained for the higher order correction. The expression for a dressed soliton is calculated using a renormalization method. The expressions for higher order correction are determined using a series solution technique developed by Chatterjee et al. [Phys. Plasmas 16, 072102 (2009)].

  7. Dust-ion-acoustic solitary structure with opposite polarity ions and non-thermal electrons

    NASA Astrophysics Data System (ADS)

    Haider, M. M.

    2016-02-01

    The propagation of dust-ion-acoustic solitary waves in magnetized plasmas containing opposite polarity ions, opposite polarity dusts and non-thermal electrons has been studied. The fluid equations in the system are reduced to a Korteweg-de Vries equation in the limit of small amplitude perturbation. The effect of non-thermal electrons and the opposite polarity of ions and dusts in the solitary waves are presented graphically and numerically.

  8. Formation of quasiparallel Alfven solitons

    NASA Technical Reports Server (NTRS)

    Hamilton, R. L.; Kennel, C. F.; Mjolhus, E.

    1992-01-01

    The formation of quasi-parallel Alfven solitons is investigated through the inverse scattering transformation (IST) for the derivative nonlinear Schroedinger (DNLS) equation. The DNLS has a rich complement of soliton solutions consisting of a two-parameter soliton family and a one-parameter bright/dark soliton family. In this paper, the physical roles and origins of these soliton families are inferred through an analytic study of the scattering data generated by the IST for a set of initial profiles. The DNLS equation has as limiting forms the nonlinear Schroedinger (NLS), Korteweg-de-Vries (KdV) and modified Korteweg-de-Vries (MKdV) equations. Each of these limits is briefly reviewed in the physical context of quasi-parallel Alfven waves. The existence of these limiting forms serves as a natural framework for discussing the formation of Alfven solitons.

  9. Linear and nonlinear coupled drift and ion acoustic waves in collisional pair ion-electron magnetoplasma

    SciTech Connect

    Mushtaq, A.; Saeed, R.; Haque, Q.

    2011-04-15

    Linear and nonlinear coupled electrostatic drift and ion acoustic waves are studied in inhomogeneous, collisional pair ion-electron plasma. The Korteweg-de Vries-Burgers (KdVB) equation for a medium where both dispersion and dissipation are present is derived. An attempt is made to obtain exact solution of KdVB equation by using modified tanh-coth method for arbitrary velocity of nonlinear drift wave. Another exact solution for KdVB is obtained, which gives a structure of shock wave. Korteweg-de Vries (KdV) and Burgers equations are derived in limiting cases with solitary and monotonic shock solutions, respectively. Effects of species density, magnetic field, obliqueness, and the acoustic to drift velocity ratio on the solitary and shock solutions are investigated. The results discussed are useful in understanding of low frequency electrostatic waves at laboratory pair ion plasmas.

  10. Automating prescription map building for VRI systems using plant feedback

    Technology Transfer Automated Retrieval System (TEKTRAN)

    Prescription maps for commercial variable rate irrigation (VRI) equipment direct the irrigation rates for each sprinkler zone on a sprinkler lateral as the lateral moves across the field. Typically, these maps are manually uploaded at the beginning of the irrigation season; and the maps are based on...

  11. Wheeler-DeWitt Equation with Variable Constants

    NASA Astrophysics Data System (ADS)

    Belinchón, José Antonio; Dolgov, A.

    In this paper we study how all the physical ``constants'' vary in the framework described by a model in which we have taken into account the generalize conservation principle for its stress-energy tensor. This possibility enable us to take into account the adiabatic matter creation in order to get rid of the entropy problem. We try to generalize this situation by contemplating multi-fluid components. To validate all the obtained results we explore the possibility of considering the variation of the ``constants'' in the quantum cosmological scenario described by the Wheeler-DeWitt equation. For this purpose we explore the Wheeler-DeWitt equation in different contexts but from a dimensional point of view. We end by presenting the Wheeler-DeWitt equation in the case of considering all the constants varying. The quantum potential is obtained and the tunneling probability is studied.

  12. Dust ion-acoustic solitary waves in a dusty plasma with nonextensive electrons

    NASA Astrophysics Data System (ADS)

    Bacha, Mustapha; Tribeche, Mouloud; Shukla, Padma Kant

    2012-05-01

    The dust-modified ion-acoustic waves of Shukla and Silin are revisited within the theoretical framework of the Tsallis statistical mechanics. Nonextensivity may originate from correlation or long-range plasma interactions. Interestingly, we find that owing to electron nonextensivity, dust ion-acoustic (DIA) solitary waves may exhibit either compression or rarefaction. Our analysis is then extended to include self-consistent dust charge fluctuation. In this connection, the correct nonextensive electron charging current is rederived. The Korteweg-de Vries equation, as well as the Korteweg-de Vries-Burgers equation, is obtained, making use of the reductive perturbation method. The DIA waves are then analyzed for parameters corresponding to space dusty plasma situations.

  13. Magnetoacoustic solitons in quantum plasma

    SciTech Connect

    Hussain, S.; Mahmood, S.

    2011-08-15

    Nonlinear magnetoacoustic waves in collisionless homogenous, magnetized quantum plasma is studied. Two fluid quantum magneto-hydrodynamic model (QMHD) is employed and reductive perturbation method is used to derive Korteweg de Vries (KdV) equation for magnetoacoustic waves. The effects of plasma density and magnetic field intensity are investigated on magnetoacoustic solitary structures in quantum plasma. The numerical results are also presented, which are applicable to explain some aspects of the propagation of nonlinear magnetoacosutic wave in dense astrophysical plasma situations.

  14. Nonplanar ion-acoustic solitary waves with superthermal electrons in warm plasma

    SciTech Connect

    Eslami, Parvin; Mottaghizadeh, Marzieh; Pakzad, Hamid Reza

    2011-07-15

    In this paper, we consider an unmagnetized plasma consisting of warm adiabatic ions, superthermal electrons, and thermal positrons. Nonlinear cylindrical and spherical modified Korteweg-de Vries (KdV) equations are derived for ion acoustic waves by using reductive perturbation technique. It is observed that an increasing positron concentration decreases the amplitude of the waves. Furthermore, the effects of the superthermal parameter (k) on the ion acoustic waves are found.

  15. Cylindrical and spherical ion acoustic waves in a plasma with nonthermal electrons and warm ions

    SciTech Connect

    Sahu, Biswajit; Roychoudhury, Rajkumar

    2005-05-15

    Using the reductive perturbation technique, nonlinear cylindrical and spherical Korteweg-de Vries (KdV) and modified KdV equations are derived for ion acoustic waves in an unmagnetized plasma consisting of warm adiabatic ions and nonthermal electrons. The effects of nonthermally distributed electrons on cylindrical and spherical ion acoustic waves are investigated. It is found that the nonthermality has a very significant effect on the nature of ion acoustic waves.

  16. Evolution of solitons over a randomly rough seabed.

    PubMed

    Mei, Chiang C; Li, Yile

    2004-01-01

    For long waves propagating over a randomly uneven seabed, we derive a modified Korteweg-de Vries (KdV) equation including new terms representing the effects of disorder on amplitude attenuation and wave phase. Analytical and numerical results are described for the evolution of a soliton entering a semi-infinite region of disorder, and the fission of new solitons after passing over a finite region of disorder. PMID:15324164

  17. The effects of drivers’ aggressive characteristics on traffic stability from a new car-following model

    NASA Astrophysics Data System (ADS)

    Peng, Guanghan; Qing, Li

    2016-06-01

    In this paper, a new car-following model is proposed by considering the drivers’ aggressive characteristics. The stable condition and the modified Korteweg-de Vries (mKdV) equation are obtained by the linear stability analysis and nonlinear analysis, which show that the drivers’ aggressive characteristics can improve the stability of traffic flow. Furthermore, the numerical results show that the drivers’ aggressive characteristics increase the stable region of traffic flow and can reproduce the evolution and propagation of small perturbation.

  18. Time evolution of nonplanar dust ion-acoustic solitary waves in a charge varying dusty plasma with superthermal electrons

    NASA Astrophysics Data System (ADS)

    Mayout, Saliha; Sahu, Biswajit; Tribeche, Mouloud

    2015-12-01

    A theoretical study on the nonlinear propagation of nonplanar (cylindrical and spherical) dust ion-acoustic solitary waves (DIASW) is carried out in a dusty plasma, whose constituents are inertial ions, superthermal electrons, and charge fluctuating stationary dust particles. Using the reductive perturbation theory, a modified Korteweg-de Vries equation is derived. It is shown that the propagation characteristics of the cylindrical and spherical DIA solitary waves significantly differ from those of their one-dimensional counterpart.

  19. Dynamics of a dust crystal with positive and negative dust

    SciTech Connect

    Kourakis, Ioannis; Shukla, Padma Kant; Morfill, Gregor

    2005-10-31

    A dust crystal consisting of charged dust grains of alternating charge sign (.../+/-/+/-/+/...) and mass is considered. Considering the equations of longitudinal motion, a linear dispersion relation is derived from first principles, and then analyzed. Two modes are obtained, including an acoustic mode and an inverse-dispersive optic-like one. The nonlinear aspects of longitudinal dust grain motion are also briefly addressed, via a Boussineq and Korteweg- de Vries description.

  20. On certain families of rational functions arising in dynamics

    NASA Technical Reports Server (NTRS)

    Byrnes, C. I.

    1979-01-01

    It is noted that linear systems, depending on parameters, can occur in diverse situations including families of rational solutions to the Korteweg-de Vries equation or to the finite Toda lattice. The inverse scattering method used by Moser (1975) to obtain canonical coordinates for the finite homogeneous Toda lattice can be used for the synthesis of RC networks. It is concluded that the multivariable RC setting is ideal for the analysis of the periodic Toda lattice.

  1. Time evolution of nonplanar dust ion-acoustic solitary waves in a charge varying dusty plasma with superthermal electrons

    SciTech Connect

    Mayout, Saliha; Tribeche, Mouloud; Sahu, Biswajit

    2015-12-15

    A theoretical study on the nonlinear propagation of nonplanar (cylindrical and spherical) dust ion-acoustic solitary waves (DIASW) is carried out in a dusty plasma, whose constituents are inertial ions, superthermal electrons, and charge fluctuating stationary dust particles. Using the reductive perturbation theory, a modified Korteweg-de Vries equation is derived. It is shown that the propagation characteristics of the cylindrical and spherical DIA solitary waves significantly differ from those of their one-dimensional counterpart.

  2. Voice recognition interfaces (VRI) optimize the utilization of theatre staff and time during laparoscopic cholecystectomy.

    PubMed

    El-Shallaly, G E H; Mohammed, B; Muhtaseb, M S; Hamouda, A H; Nassar, A H M

    2005-01-01

    During laparoscopy, members of staff spend time setting up and de-activating the light source, camera and insufflator. Voice Recognition Interface (VRI) devices, such as HERMES (Stryker Europe, Montreux, Switzerland), enable the surgeon to perform and control these and other functions. They recognize the surgeon's voice and adjust the instruments in response to programmed verbal commands. The aim of this study was to evaluate HERMES with regards to the utilization of time and theatre staff during laparoscopic cholecystectomy. A total of 100 patients were randomized to either HERMES-assisted or standard laparoscopic cholecystectomy. Three time variables were measured for performing three VRI tasks: (1) The initial setting up of the light source and camera, (2) the activation of the insufflator, and (3) the deactivation of the insufflator and light source at the end of the operation. The mean (and standard deviation) of the time in seconds required for setting up the light source and camera was 27.6 (26.9) in non-HERMES operations and 11.7 (4.7) in HERMES-assisted cases (p<0.001). Insufflation time was 19.8 (13.3) vs. 6.7 (2.5) (p<0.001), and switch-off time was 19.5 (11.8) vs. 11.8 (5.7) (p<0.001). HERMES optimized the operating time and the utilization of theatre staff during laparoscopic cholecystectomy. PMID:16754183

  3. Evaluation of Vibration Response Imaging (VRI) Technique and Difference in VRI Indices Among Non-Smokers, Active Smokers, and Passive Smokers

    PubMed Central

    Jiang, Hongying; Chen, Jichao; Cao, Jinying; Mu, Lan; Hu, Zhenyu; He, Jian

    2015-01-01

    Background Vibration response imaging (VRI) is a new technology for lung imaging. Active smokers and non-smokers show differences in VRI findings, but no data are available for passive smokers. The aim of this study was to evaluate the use of VRI and to assess the differences in VRI findings among non-smokers, active smokers, and passive smokers. Material/Methods Healthy subjects (n=165: 63 non-smokers, 56 active smokers, and 46 passive smokers) with normal lung function were enrolled. Medical history, physical examination, lung function test, and VRI were performed for all subjects. Correlation between smoking index and VRI scores (VRIS) were performed. Results VRI images showed progressive and regressive stages representing the inspiratory and expiratory phases bilaterally in a vertical and synchronized manner in non-smokers. Vibration energy curves with low expiratory phase and plateau were present in 6.35% and 3.17%, respectively, of healthy non-smokers, 41.07% and 28.60% of smokers, and 39.13% and 30.43% of passive smokers, respectively. The massive energy peak in the non-smokers, smokers, and passive-smokers was 1.77±0.27, 1.57±0.29, and 1.66±0.33, respectively (all P<0.001). A weak but positive correlation was observed between VRIS and smoking index. Conclusions VRI can intuitively show the differences between non-smokers and smokers. VRI revealed that passive smoking can also harm the lungs. VRI could be used to visually persuade smokers to give up smoking. PMID:26212715

  4. Planar and nonplanar ion acoustic shock waves in relativistic degenerate astrophysical electron-positron-ion plasmas

    SciTech Connect

    Ata-ur-Rahman,; Qamar, A.; Ali, S.; Mirza, Arshad M.

    2013-04-15

    We have studied the propagation of ion acoustic shock waves involving planar and non-planar geometries in an unmagnetized plasma, whose constituents are non-degenerate ultra-cold ions, relativistically degenerate electrons, and positrons. By using the reductive perturbation technique, Korteweg-deVries Burger and modified Korteweg-deVries Burger equations are derived. It is shown that only compressive shock waves can propagate in such a plasma system. The effects of geometry, the ion kinematic viscosity, and the positron concentration are examined on the ion acoustic shock potential and electric field profiles. It is found that the properties of ion acoustic shock waves in a non-planar geometry significantly differ from those in planar geometry. The present study has relevance to the dense plasmas, produced in laboratory (e.g., super-intense laser-dense matter experiments) and in dense astrophysical objects.

  5. An extended optimal velocity difference model in a cooperative driving system

    NASA Astrophysics Data System (ADS)

    Cao, Jinliang; Shi, Zhongke; Zhou, Jie

    2015-10-01

    An extended optimal velocity (OV) difference model is proposed in a cooperative driving system by considering multiple OV differences. The stability condition of the proposed model is obtained by applying the linear stability theory. The results show that the increase in number of cars that precede and their OV differences lead to the more stable traffic flow. The Burgers, Korteweg-de Vries (KdV) and modified Korteweg-de Vries (mKdV) equations are derived to describe the density waves in the stable, metastable and unstable regions, respectively. To verify these theoretical results, the numerical simulation is carried out. The theoretical and numerical results show that the stabilization of traffic flow is enhanced by considering multiple OV differences. The traffic jams can be suppressed by taking more information of cars ahead.

  6. Nonlinear, dispersive, elliptically polarized Alfven wavaes

    NASA Technical Reports Server (NTRS)

    Kennel, C. F.; Buti, B.; Hada, T.; Pellat, R.

    1988-01-01

    The derivative nonlinear Schroedinger (DNLS) equation is derived by an efficient means that employs Lagrangian variables. An expression for the stationary wave solutions of the DNLS that contains vanishing and nonvanishing and modulated and nonmodulated boundary conditions as subcases is then obtained. The solitary wave solutions for elliptically polarized quasiparallel Alfven waves in the magnetohydrodynamic limit (nonvanishing, unmodulated boundary conditions) are obtained. These converge to the Korteweg-de Vries and the modified Korteweg-de Vries solitons obtained previously for oblique propagation, but are more general. It is shown that there are no envelope solitary waves if the point at infinity is unstable to the modulational instability. The periodic solutions of the DNLS are characterized.

  7. Capillary solitons on a levitated medium.

    PubMed

    Perrard, S; Deike, L; Duchêne, C; Pham, C-T

    2015-07-01

    A water cylinder deposited on a heated channel levitates on its own generated vapor film owing to the Leidenfrost effect. This experimental setup permits the study of the one-dimensional propagation of surface waves in a free-to-move liquid system. We report the observation of gravity-capillary waves under a dramatic reduction of gravity (up to a factor 30), leading to capillary waves at the centimeter scale. The generated nonlinear structures propagate without deformation and undergo mutual collisions and reflections at the boundaries of the domain. They are identified as Korteweg-de Vries solitons with negative amplitude and subsonic velocity. The typical width and amplitude-dependent velocities are in excellent agreement with theoretical predictions based on a generalized Korteweg-de Vries equation adapted to any substrate geometry. When multiple solitons are present, they interact and form a soliton turbulencelike spectrum. PMID:26274114

  8. From Classical Nonlinear Integrable Systems to Quantum Shortcuts to Adiabaticity

    NASA Astrophysics Data System (ADS)

    Okuyama, Manaka; Takahashi, Kazutaka

    2016-08-01

    Using shortcuts to adiabaticity, we solve the time-dependent Schrödinger equation that is reduced to a classical nonlinear integrable equation. For a given time-dependent Hamiltonian, the counterdiabatic term is introduced to prevent nonadiabatic transitions. Using the fact that the equation for the dynamical invariant is equivalent to the Lax equation in nonlinear integrable systems, we obtain the counterdiabatic term exactly. The counterdiabatic term is available when the corresponding Lax pair exists and the solvable systems are classified in a unified and systematic way. Multisoliton potentials obtained from the Korteweg-de Vries equation and isotropic X Y spin chains from the Toda equations are studied in detail.

  9. Discrete reductive perturbation technique

    SciTech Connect

    Levi, Decio; Petrera, Matteo

    2006-04-15

    We expand a partial difference equation (P{delta}E) on multiple lattices and obtain the P{delta}E which governs its far field behavior. The perturbative-reductive approach is here performed on well-known nonlinear P{delta}Es, both integrable and nonintegrable. We study the cases of the lattice modified Korteweg-de Vries (mKdV) equation, the Hietarinta equation, the lattice Volterra-Kac-Van Moerbeke equation and a nonintegrable lattice KdV equation. Such reductions allow us to obtain many new P{delta}Es of the nonlinear Schroedinger type.

  10. On the Prediction of the Number of Solitons Excited by an Arbitrary Potential: An Observation from Inverse Scattering

    NASA Technical Reports Server (NTRS)

    Hansen, P. J.; Lonngren, K. E.

    1993-01-01

    A heuristic estimate for the soliton production rate by a pulse is verified for the Korteweg - de Vries equation using inverse scattering. An observation from this result, which is shown to hold for some other nonlinear equations and for the case of the 'forced' nonlinear Schroedinger equation, is that production is determined by quantities that are invariant under rescaling of the original nonlinear equations. We speculate that this result may be useful to the development of an inverse scattering theory for 'forced' nonlinear systems.

  11. The properties of the Neckel-Chini VRI system

    NASA Technical Reports Server (NTRS)

    Taylor, Benjamin J.; Joner, Michael D.; Johnson, Scott B.

    1989-01-01

    Cousins (1980) data for 54 of the standard stars of Neckel and Chini (1980) and published measurements are used to investigate the properties of the Neckel-Chini VRI system. For red stars, this system diverges from the Johnson (1962) system, despite frequent claims of identity between the two. The Neckel-Chini and Cousins systems, however, are closely comparable. Both of these conclusions were previously reached in a paper by Bessell (1983); fair to good quantitative agreement with his results are obtained. Reddening ratios, the scatter in the Neckel-Chini standard-star data, and the effect of this scatter on published measurements for program stars, are discussed. Transformations from the Neckel-Chini system to the Cousins system are given.

  12. Genetics Home Reference: Koolen-de Vries syndrome

    MedlinePlus

    ... Genet. 2011 Mar-Apr;54(2):144-51. doi: 10.1016/j.ejmg.2010.11.003. Epub ... Genet A. 2013 Jan;161A(1):21-6. doi: 10.1002/ajmg.a.35652. Epub 2012 Nov ... Genet. 2012 Apr 6;90(4):599-613. doi: 10.1016/j.ajhg.2012.02.013. Citation ...

  13. Effect of adiabatic trapping on vortices and solitons in degenerate plasma in the presence of a quantizing magnetic field

    NASA Astrophysics Data System (ADS)

    Arshad, S.; Shah, H. A.; Qureshi, M. N. S.

    2014-07-01

    The effect of adiabatic trapping as a microscopic phenomenon in an inhomogeneous degenerate plasma is investigated in the presence of a quantizing magnetic field, and a modified Hasegawa Mima equation for the drift ion-acoustic wave is obtained. The linear dispersion relation in the presence of the quantizing magnetic field is investigated. The modified Hasegawa Mima equation is investigated to obtain bounce frequencies of the trapped particles. The Korteweg-de Vries equation is derived for the two-dimensional case and finally the Sagdeev potential approach is used to obtain solitary structures. The theoretically obtained results have been analyzed numerically for different astrophysical plasma and quantizing magnetic field values.

  14. Umbral Vade Mecum

    NASA Astrophysics Data System (ADS)

    Curtright, Thomas L.; Zachos, Cosmas K.

    2013-10-01

    In recent years the umbral calculus has emerged from the shadows to provide an elegant correspondence framework that automatically gives systematic solutions of ubiquitous difference equations --- discretized versions of the differential cornerstones appearing in most areas of physics and engineering --- as maps of well-known continuous functions. This correspondence deftly sidesteps the use of more traditional methods to solve these difference equations. The umbral framework is discussed and illustrated here, with special attention given to umbral counterparts of the Airy, Kummer, and Whittaker equations, and to umbral maps of solitons for the Sine-Gordon, Korteweg--de Vries, and Toda systems.

  15. A centre manifold approach to solitary waves in a sheared, stably stratified fluid layer

    NASA Astrophysics Data System (ADS)

    Zimmerman, W. B.; Velarde, M. G.

    The centre manifold approach is used to derive an approximate equation for nonlinear waves propagating in a sheared, stably stratified fluid layer. The evolution equation matches limiting forms derived by other methods, including the inviscid, long wave approximation leading to the Korteweg- deVries equation. The model given here allows large modulations of the height of the waveguide. This permits the crude modelling of shear layer instabilities at the upper material surface of the waveguide which excite solitary internal waves in the waveguide. An energy argument is used to support the existence of these waves.

  16. Wheeler-DeWitt equation in 3+1 dimensions

    NASA Astrophysics Data System (ADS)

    Hamber, Herbert W.; Toriumi, Reiko; Williams, Ruth M.

    2013-10-01

    Physical properties of the quantum gravitational vacuum state are explored by solving a lattice version of the Wheeler-DeWitt equation. The constraint of diffeomorphism invariance is strong enough to uniquely determine part of the structure of the vacuum wave functional in the limit of infinitely fine triangulations of the three-sphere. In the large fluctuation regime, the nature of the wave function solution is such that a physically acceptable ground state emerges, with a finite nonperturbative correlation length naturally cutting off any infrared divergences. The location of the critical point in Newton’s constant Gc, separating the weak from the strong coupling phase, is obtained, and it is inferred from the general structure of the wave functional that fluctuations in the curvatures become unbounded at this point. Investigations of the vacuum wave functional further suggest that for weak enough coupling, G

  17. Solution of the Dyson-Schwinger equation on a de Sitter background in the infrared limit

    NASA Astrophysics Data System (ADS)

    Akhmedov, E. T.; Burda, Ph.

    2012-08-01

    We propose an ansatz which solves the Dyson-Schwinger equation for the real scalar fields in a Poincaré patch of de Sitter space in the infrared limit. The Dyson-Schwinger equation for this ansatz reduces to the kinetic equation, if one considers scalar fields from the principal series. Solving the latter equation we show that under the adiabatic switching on and then off of the coupling constant, the Bunch-Davies vacuum relaxes in future infinity to the state with the flat Gibbons-Hawking density of out-Jost harmonics on top of the corresponding de Sitter invariant out vacuum.

  18. Unravelling the interaction dynamics of a carbonatite-silicate magmatic pair: A numerical approach based on Korteweg Stress theory

    NASA Astrophysics Data System (ADS)

    Valentini, L.; Moore, K. R.; Chazot, G.

    2009-04-01

    Most of the worldwide carbonatites occur in spatial association with silicate rocks. Even when unquestionable evidence for the associated carbonatite and silicate rocks to represent contemporaneous liquids exists, the modes of interaction between the two liquids can be difficult to infer. In general, the retrieval of information about the mechanisms of interaction between magmas can be complicated by the intrinsic dynamical nature of such systems. The development of new physico-chemical equilibria (e.g. hybridization) can erase any information about the previous stages of interaction. However, the occurrence of magmatic heterogeneities, such as enclaves and flow bands, as well as mineral disequilibrium textures, may serve as dynamic markers for the underlying interaction processes. Small-scale heterogeneities, in the form of micron to millimetre sized globules, characterized by more or less smooth interfaces, are frequently observed in carbonatite-silicate pairs. Textural observation, as well as the lack of suitable mechanisms for the dispersion of a discrete magmatic liquid in the form of a small-scale emulsion, have lead many petrologists to advocate immiscible separation as the process capable of forming such textures. However, the geochemical criteria for liquid immiscibility are not always met, and when not coupled with geochemical and dynamical arguments, textural observation may lead to ambiguous conclusions. In this study we adopted an integrated approach in order to infer the details of magmatic interaction of a carbonatite-silicate pair from Massif Central (France). The studied samples display emulsion-like textures, formed by micro-scale dolomitic globules dispersed in a trachytic glassy matrix. Our approach is based on a novel numerical method, coupled with textural observation and geochemical analyses. The novelty of our numerical model consists in the inclusion, in the adopted advection-diffusion equations, of a term that takes into account the effect

  19. Infinitely many generalized symmetries and Painlevé analysis of a (2 + 1)-dimensional Burgers system

    NASA Astrophysics Data System (ADS)

    Wang, Jian-Yong; Liang, Zu-Feng; Tang, Xiao-Yan

    2014-02-01

    Infinitely many generalized symmetries of a coupled (2 + 1)-dimensional Burgers system are obtained by means of the formal series symmetry approach. It is found that the generalized symmetries constitute a closed infinite-dimensional Lie algebra. Three interesting special cases are presented, including a closed infinite-dimensional Lie algebra and a Kac-Moody-Virasoro-type Lie symmetry algebra. From the first one of the positive flow, a new integrable coupled system of the modified Korteweg-de Vries equation and the potential Boiti-Leon-Manna-Pempinelli equation is constructed. In addition, it is demonstrated that the coupled Burgers system can pass the Painlevé test.

  20. Higher order solutions to ion-acoustic solitons in a weakly relativistic two-fluid plasma

    SciTech Connect

    Gill, Tarsem Singh; Bala, Parveen; Kaur, Harvinder

    2008-12-15

    The nonlinear wave structure of small amplitude ion-acoustic solitary waves (IASs) is investigated in a two-fluid plasma consisting of weakly relativistic streaming ions and electrons. Using the reductive perturbation theory, the basic set of governing equations is reduced to the Korteweg-de Vries (KdV) equation for the lowest order perturbation. This analysis is further extended using the renormalization technique for the inclusion of higher order nonlinear and dispersive effects for better accuracy. The effect of higher order correction and various parameters on the soliton characteristics is investigated and also discussed.

  1. Nonlinear propagation of small-amplitude modified electron acoustic solitary waves and double layer in semirelativistic plasmas

    SciTech Connect

    Sah, O.P.; Goswami, K.S. )

    1994-10-01

    Considering an unmagnetized plasma consisting of relativistic drifting electrons and nondrifting thermal ions and by using reductive perturbation method, a usual Korteweg--de Vries (KdV) equation and a generalized form of KdV equation are derived. It is found that while the former governs the dynamics of a small-amplitude rarefactive modified electron acoustic (MEA) soliton, the latter governs the dynamics of a weak compressive modified electron acoustic double layer. The influences of relativistic effect on the propagation of such a soliton and double layer are examined. The relevance of this investigation to space plasma is pointed out.

  2. Nonlinear wave propagation in a strongly coupled collisional dusty plasma

    SciTech Connect

    Ghosh, Samiran; Gupta, Mithil Ranjan; Chakrabarti, Nikhil; Chaudhuri, Manis

    2011-06-15

    The propagation of a nonlinear low-frequency mode in a strongly coupled dusty plasma is investigated using a generalized hydrodynamical model. For the well-known longitudinal dust acoustic mode a standard perturbative approach leads to a Korteweg-de Vries (KdV) soliton. The strong viscoelastic effect, however, introduced a nonlinear forcing and a linear damping in the KdV equation. This novel equation is solved analytically to show a competition between nonlinear forcing and dissipative damping. The physical consequence of such a solution is also sketched.

  3. Nonlinear wave propagation in a strongly coupled collisional dusty plasma.

    PubMed

    Ghosh, Samiran; Gupta, Mithil Ranjan; Chakrabarti, Nikhil; Chaudhuri, Manis

    2011-06-01

    The propagation of a nonlinear low-frequency mode in a strongly coupled dusty plasma is investigated using a generalized hydrodynamical model. For the well-known longitudinal dust acoustic mode a standard perturbative approach leads to a Korteweg-de Vries (KdV) soliton. The strong viscoelastic effect, however, introduced a nonlinear forcing and a linear damping in the KdV equation. This novel equation is solved analytically to show a competition between nonlinear forcing and dissipative damping. The physical consequence of such a solution is also sketched. PMID:21797497

  4. Shock wave in magnetized dusty plasmas with dust charging and nonthermal ion effects

    SciTech Connect

    Zhang Liping; Xue Jukui

    2005-04-15

    The effects of the external magnetized field, nonadiabatic dust charge fluctuation, and nonthermally distributed ions on three-dimensional dust acoustic shock wave in dusty plasmas have been investigated. By using the reductive perturbation method, a Korteweg-de Vries (KdV) Burger equation governing the dust acoustic shock wave is derived. The results of numerical integrations of KdV Burger equation show that the external magnetized field, nonthermally distributed ions, and nonadiabatic dust charge fluctuation have strong influence on the shock structures.

  5. On Fay identity

    SciTech Connect

    Michev, Iordan P.

    2006-09-15

    In the first part of this paper we consider the transformation of the cubic identities for general Korteweg-de Vries (KdV) tau functions from [Mishev, J. Math. Phys. 40, 2419-2428 (1999)] to the specific identities for trigonometric KdV tau functions. Afterwards, we consider the Fay identity as a functional equation and provide a wide set of solutions of this equation. The main result of this paper is Theorem 3.4, where we generalize the identities from Mishev. An open problem is the transformation of the cubic identities from Mishev to the specific identities for elliptic KdV tau functions.

  6. Ion acoustic shocks in magneto rotating Lorentzian plasmas

    SciTech Connect

    Hussain, S.; Akhtar, N.; Hasnain, H.

    2014-12-15

    Ion acoustic shock structures in magnetized homogeneous dissipative Lorentzian plasma under the effects of Coriolis force are investigated. The dissipation in the plasma system is introduced via dynamic viscosity of inertial ions. The electrons are following the kappa distribution function. Korteweg-de Vries Burger (KdVB) equation is derived by using reductive perturbation technique. It is shown that spectral index, magnetic field, kinematic viscosity of ions, rotational frequency, and effective frequency have significant impact on the propagation characteristic of ion acoustic shocks in such plasma system. The numerical solution of KdVB equation is also discussed and transition from oscillatory profile to monotonic shock for different plasma parameters is investigated.

  7. Ion acoustic shocks in magneto rotating Lorentzian plasmas

    NASA Astrophysics Data System (ADS)

    Hussain, S.; Akhtar, N.; Hasnain, H.

    2014-12-01

    Ion acoustic shock structures in magnetized homogeneous dissipative Lorentzian plasma under the effects of Coriolis force are investigated. The dissipation in the plasma system is introduced via dynamic viscosity of inertial ions. The electrons are following the kappa distribution function. Korteweg-de Vries Burger (KdVB) equation is derived by using reductive perturbation technique. It is shown that spectral index, magnetic field, kinematic viscosity of ions, rotational frequency, and effective frequency have significant impact on the propagation characteristic of ion acoustic shocks in such plasma system. The numerical solution of KdVB equation is also discussed and transition from oscillatory profile to monotonic shock for different plasma parameters is investigated.

  8. Dust ion acoustic solitary waves in a collisional dusty plasma with dust grains having Gaussian distribution

    SciTech Connect

    Maitra, Sarit; Banerjee, Gadadhar

    2014-11-15

    The influence of dust size distribution on the dust ion acoustic solitary waves in a collisional dusty plasma is investigated. It is found that dust size distribution changes the amplitude and width of a solitary wave. A critical wave number is derived for the existence of purely damping mode. A deformed Korteweg-de Vries (dKdV) equation is obtained for the propagation of weakly nonlinear dust ion acoustic solitary waves and the effect of different plasma parameters on the solution of this equation is also presented.

  9. Nonlinear dynamics; Proceedings of the International Conference, New York, NY, December 17-21, 1979

    NASA Astrophysics Data System (ADS)

    Helleman, R. H. G.

    1980-12-01

    Papers were presented on turbulence, ergodic and integrable behavior, chaotic maps and flows, chemical and fully developed turbulence, and strange attractors. Specific attention was given to measures describing a turbulent flow, stochastization and collapse of vortex systems, a subharmonic route to turbulent convection, and weakly nonlinear turbulence in a rotating convection layer. The Korteweg-de Vries and Hill equations, plasma transport in three dimensions, a horseshoe in the dynamics of a forced beam, and the explosion of strange attractors exhibited by Duffing's equation were also considered.

  10. Applicability of the Equation: dE = TdS - PdV

    ERIC Educational Resources Information Center

    Nash, Leonard K.

    1977-01-01

    Presents a detailed analysis of the thermodynamic equation dE = TdS - PdV to illustrate how chemistry teachers may present chemical potential by a route free from the terrors of partial derivatives. (MR)

  11. Nonlinear shear wave in a non Newtonian visco-elastic medium

    SciTech Connect

    Banerjee, D.; Janaki, M. S.; Chakrabarti, N.

    2012-06-15

    An analysis of nonlinear transverse shear wave has been carried out on non-Newtonian viscoelastic liquid using generalized hydrodynamic model. The nonlinear viscoelastic behavior is introduced through velocity shear dependence of viscosity coefficient by well known Carreau-Bird model. The dynamical feature of this shear wave leads to the celebrated Fermi-Pasta-Ulam problem. Numerical solution has been obtained which shows that initial periodic solutions reoccur after passing through several patterns of periodic waves. A possible explanation for this periodic solution is given by constructing modified Korteweg de Vries equation. This model has application from laboratory to astrophysical plasmas as well as in biological systems.

  12. Ion acoustic shock waves in degenerate plasmas

    SciTech Connect

    Akhtar, N.; Hussain, S.

    2011-07-15

    Korteweg de Vries Burgers equation for negative ion degenerate dissipative plasma has been derived using reductive perturbation technique. The quantum hydrodynamic model is used to study the quantum ion acoustic shock waves. The effects of different parameters on quantum ion acoustic shock waves are studied. It is found that quantum parameter, electrons Fermi temperature, temperature of positive and negative ions, mass ratio of positive to negative ions, viscosity, and density ratio have significant impact on the shock wave structure in negative ion degenerate plasma.

  13. Cylindrical and spherical electron acoustic solitary waves with nonextensive hot electrons

    SciTech Connect

    Pakzad, Hamid Reza

    2011-08-15

    Nonlinear propagation of cylindrical and spherical electron-acoustic solitons in an unmagnetized plasma consisting cold electron fluid, hot electrons obeying a nonextensive distribution and stationary ions, are investigated. For this purpose, the standard reductive perturbation method is employed to derive the cylindrical/spherical Korteweg-de-Vries equation, which governs the dynamics of electron-acoustic solitons. The effects of nonplanar geometry and nonextensive hot electrons on the behavior of cylindrical and spherical electron acoustic solitons are also studied by numerical simulations.

  14. Multi-ion Double Layers in a Magnetized Plasma

    NASA Astrophysics Data System (ADS)

    Shahmansouri, M.; Alinejad, H.; Tribeche, M.

    2015-11-01

    A theoretical investigation is carried out to study the existence, formation and basic properties of ion acoustic (IA) double layers (DLs) in a magnetized bi-ion plasma consisting of warm/cold ions and Boltzmann distributed electrons. Based on the reductive perturbation technique, an extended Korteweg de-Vries (KdV) equation is derived. The propagation of two possible modes (fast and slow), and their evolution are investigated. The effects of obliqueness, magnitude of the magnetic field, ion concentration, polarity of ions, and ion temperature on the IA DL profile are analyzed, and then the ranges of parameters for which the IA DLs exist are investigated in details.

  15. Nonplanar waves with electronegative dusty plasma

    SciTech Connect

    Zobaer, M. S.; Mukta, K. N.; Nahar, L.; Mamun, A. A.; Roy, N.

    2013-04-15

    A rigorous theoretical investigation has been made of basic characteristics of the nonplanar dust-ion-acoustic shock and solitary waves in electronegative dusty plasma containing Boltzmann electrons, Boltzmann negative ions, inertial positive ions, and charge fluctuating (negatively charged) stationary dust. The Burgers' and Korteweg-de Vries (K-dV) equations, which is derived by reductive perturbation technique, is numerically solved to examine the effects of nonplanar geometry on the basic features of the DIA shock and solitary waves formed in the electronegative dusty plasma. The implications of the results (obtained from this investigation) in space and laboratory experiments are briefly discussed.

  16. Imploding and exploding shocks in negative ion degenerate plasmas

    SciTech Connect

    Hussain, S.; Akhtar, N.

    2011-08-15

    Imploding and exploding shocks are studied in nonplanar geometries for negative ion degenerate plasma. Deformed Korteweg de Vries Burgers (DKdVB) equation is derived by using reductive perturbation method. Two level finite difference scheme is used for numerical analysis of DKdVB. It is observed that compressive and rarefactive shocks are observed depending on the value of quantum parameter. The effects of temperature, kinematic viscosity, mass ratio of negative to positive ions and quantum parameter on diverging and converging shocks are presented.

  17. Head-on collision of dust-ion-acoustic soliton in quantum pair-ion plasma

    SciTech Connect

    Chatterjee, Prasanta; Ghorui, Malay kr.; Wong, C. S.

    2011-10-15

    In this paper, we study the head-on collision between two dust ion acoustic solitons in quantum pair-ion plasma. Using the extended Poincare-Lighthill-Kuo method, we obtain the Korteweg-de Vries equation, the phase shifts, and the trajectories after the head-on collision of the two dust ion acoustic solitons. It is observed that the phase shifts are significantly affected by the values of the quantum parameter H, the ratio of the multiples of the charge state and density of positive ions to that of the negative ions {beta} and the concentration of the negatively charged dust particles {delta}.

  18. Rarefaction solitons initiated by sheath instability

    SciTech Connect

    Levko, Dmitry

    2015-09-15

    The instability of the cathode sheath initiated by the cold energetic electron beam is studied by the one-dimensional fluid model. Numerical simulations show the generation of travelling rarefaction solitons at the cathode. It is obtained that the parameters of these solitons strongly depend on the parameters of electron beam. The “stretched” variables are derived using the small-amplitude analysis. These variables are used in order to obtain the Korteweg-de Vries equation describing the propagation of the rarefaction solitons through the plasma with cold energetic electron beam.

  19. Charging-delay induced dust acoustic collisionless shock wave: Roles of negative ions

    SciTech Connect

    Ghosh, Samiran; Bharuthram, R.; Khan, Manoranjan; Gupta, M. R.

    2006-11-15

    The effects of charging-delay and negative ions on nonlinear dust acoustic waves are investigated. It has been found that the charging-delay induced anomalous dissipation causes generation of dust acoustic collisionless shock waves in an electronegative dusty plasma. The small but finite amplitude wave is governed by a Korteweg-de Vries Burger equation in which the Burger term arises due to the charging-delay. Numerical investigations reveal that the charging-delay induced dissipation and shock strength decreases (increases) with the increase of negative ion concentration (temperature)

  20. Interaction of fast magnetoacoustic solitons in dense plasmas

    SciTech Connect

    Jahangir, R.; Saleem, Khalid; Masood, W.; Siddiq, M.; Batool, Nazia

    2015-09-15

    One dimensional propagation of fast magnetoacoustic solitary waves in dense plasmas with degenerate electrons is investigated in this paper in the small amplitude limit. In this regard, Korteweg deVries equation is derived and discussed using the plasma parameters that are typically found in white dwarf stars. The interaction of fast magnetoacoustic solitons is explored by using the Hirota bilinear formalism, which admits multi soliton solutions. It is observed that the values of the propagation vectors determine the interaction of solitary waves. It is further noted that the amplitude of the respective solitary waves remain unchanged after the interaction; however, they do experience a phase shift.

  1. Solitary waves in two-dimensional dusty plasma crystal: Effects of weak magnetic field

    SciTech Connect

    Ghosh, Samiran; Gupta, M. R.

    2010-03-15

    It is shown that in the presence of weak magnetic field, the dust lattice solitary wave in two-dimensional (2D) hexagonal dusty plasma crystal is governed by a gyration-modified 2D Korteweg-de Vries equation due to the action of Lorentz force on the dust particles. Numerical solutions reveal that only for weak magnetic field an apparently single hump solitary wave solution exist. But, for strong magnetic field dust lattice solitary wave becomes unstable showing repetitive solitary hump of increasing magnitude with time.

  2. Dust-acoustic shock waves in a charge varying electronegative magnetized dusty plasma with suprathermal electrons

    SciTech Connect

    Tribeche, Mouloud; Bacha, Mustapha

    2012-12-15

    The combined effects of an oblique magnetic field and electron suprathermality on weak dust-acoustic (DA) waves in a charge varying electronegative dusty plasmas with application to the Halley Comet are investigated. The correct suprathermal electron charging current is derived based on the orbit-motion limited approach. A weakly nonlinear analysis is carried out to derive a Korteweg-de Vries-Burger equation. The electron suprathermality, the obliqueness, and magnitude of the magnetic field are found to modify the dispersive properties of the DA shock structure. Our results may aid to explain and interpret the nonlinear oscillations that may occur in the Halley Comet plasma.

  3. Dust-acoustic shock waves in a charge varying electronegative magnetized dusty plasma with nonthermal ions: Application to Halley Comet plasma

    SciTech Connect

    Tribeche, Mouloud; Bacha, Mustapha

    2013-10-15

    Weak dust-acoustic waves (DAWs) are addressed in a nonthermal charge varying electronegative magnetized dusty plasmas with application to the Halley Comet. A weakly nonlinear analysis is carried out to derive a Korteweg-de Vries-Burger equation. The positive ion nonthermality, the obliqueness, and magnitude of the magnetic field are found to modify the dispersive and dissipative properties of the DA shock structure. Our results may aid to explain and interpret the nonlinear oscillations that may occur in the Halley Comet Plasma.

  4. Weakly nonlinear dust ion-acoustic shock waves in a dusty plasma with nonthermal electrons

    SciTech Connect

    Berbri, Abderrezak; Tribeche, Mouloud

    2009-05-15

    Weakly nonlinear dust ion-acoustic (DIA) shock waves are investigated in a dusty plasma with nonthermal electrons. A modified Korteweg-de Vries equation with a cubic nonlinearity is derived. Due to the net negative dust charge {mu}Z{sub d} and electron nonthermality, the present plasma model can admit compressive and rarefactive weak DIA shock waves. The effect of increasing {mu}Z{sub d} is to lower the critical nonthermal parameter {beta}{sub c} above which only rarefactive DIA shock waves are admitted. Our investigation may help to understand the nonlinear structures observed in the auroral acceleration regions.

  5. Small amplitude nonlinear electrostatic waves in a collisional complex plasma with positively charged dust

    SciTech Connect

    Fedila, D. Ali; Djebli, M.

    2010-10-15

    The effect of collision on small amplitude dust-acoustic waves is investigated for a plasma with positively charged dust grains. Taking into account the presence of different electron populations in thermal equilibrium, a modified Korteweg-de Vries equation is established. The existence conditions and nature of the waves, i.e., rarefactive or compressive, are found to be mainly dependent on the temperature and the density of the cold electrons. The present model is used to understand the salient features of the fully nonlinear dust-acoustic waves in the lower region of the Earth's ionosphere, at an altitude of {approx}85 km with the presence of an external heating source.

  6. Waveguide coupling in the few-cycle regime

    NASA Astrophysics Data System (ADS)

    Leblond, Hervé; Terniche, Said

    2016-04-01

    We consider the coupling of two optical waveguides in the few-cycle regime. The analysis is performed in the frame of a generalized Kadomtsev-Petviashvili model. A set of two coupled modified Korteweg-de Vries equations is derived, and it is shown that three types of coupling can occur, involving the linear index, the dispersion, or the nonlinearity. The linear nondispersive coupling is investigated numerically, showing the formation of vector solitons. Separate pulses may be trapped together if they have not initially the same location, size, or phase, and even if their initial frequencies differ.

  7. A new car-following model with consideration of the prevision driving behavior

    NASA Astrophysics Data System (ADS)

    Zhou, Tong; Sun, Dihua; Kang, Yirong; Li, Huamin; Tian, Chuan

    2014-10-01

    In the paper, a new car-following model is presented with the consideration of the prevision driving behavior on a single-lane road. The model’s linear stability condition is obtained by applying the linear stability theory. And through nonlinear analysis, a modified Korteweg-de Vries (mKdV) equation is derived to describe the propagating behavior of traffic density wave near the critical point. Numerical simulation shows that the new model can improve the stability of traffic flow by adjusting the driver’s prevision intensity parameter, which is consistent with the theoretical analysis.

  8. Surface solitary waves and solitons. [in solar atmosphere and solar wind magnetic structure

    NASA Technical Reports Server (NTRS)

    Hollweg, J. V.; Roberts, B.

    1984-01-01

    The solar atmosphere and solar wind are magnetically structured. The structuring can include tangential discontinuities, which can support surface waves. Such waves can be dispersive. This means that dispersion and nonlinearity can balance in such a way that solitary waves (or solitons) can result. This general point is illustrated by a two-dimensional nonlinear analysis which explicitly demonstrates the presence of long-wavelength solitary waves propagating on tangential discontinuities. If the waves are only weakly nonlinear, then they obey the Korteweg-de Vries equation and are true solitons.

  9. Time evolution of nonplanar electron acoustic shock waves in a plasma with superthermal electrons

    NASA Astrophysics Data System (ADS)

    Pakzad, Hamid Reza; Javidan, Kurosh; Tribeche, Mouloud

    2014-07-01

    The propagation of cylindrical and spherical electron acoustic (EA) shock waves in unmagnetized plasmas consisting of cold fluid electrons, hot electrons obeying a superthermal distribution and stationary ions, has been investigated. The standard reductive perturbation method (RPM) has been employed to derive the cylindrical/spherical Korteweg-de-Vries-Burger (KdVB) equation which governs the dynamics of the EA shock structures. The effects of nonplanar geometry, plasma kinematic viscosity and electron suprathermality on the temporal evolution of the cylindrical and spherical EA shock waves are numerically examined.

  10. Oblique shock dynamics in nonextensive magnetized plasma

    NASA Astrophysics Data System (ADS)

    Bains, A. S.; Tribeche, M.

    2014-05-01

    A study is presented for the oblique propagation of low-frequency ion-acoustic ( IA) shock waves in a magnetized plasma having cold viscous ion fluid and nonextensively distributed electrons. A weakly nonlinear analysis is carried out to derive a Korteweg de-Vries-Burger like equation. Dependence of the shock wave characteristics (height, width and nature) on plasma parameters is then traced and studied in details. We hope that our results will aid to explain and interpret the nonlinear oscillations occurring in magnetized space plasmas.

  11. Dissipative shocks in multicomponent magneto rotating Lorentzian plasmas

    NASA Astrophysics Data System (ADS)

    Hussain, S.; Akhtar, N.; Hasnain, H.

    2015-11-01

    Nonlinear ion acoustic shocks in homogenous multicomponent electron-positron-ion (e-p-i) dissipative magneto rotating plasmas are studied. Dissipation in the plasma system is included via kinematic viscosity of ions. The electrons and positrons are Lorentzian and following kappa distribution function. Reductive perturbation technique is applied to derive Korteweg de Vries Burgers (KdVB) equation. The effects of variation of positron density, positron spectral index, temperature ratio of kappa distributed electrons to kappa distributed positrons, ion kinematic viscosity and rotational frequency effects are discussed in the context of pulsar magnetosphere.

  12. Drift solitons and shocks in inhomogeneous quantum magnetoplasmas

    SciTech Connect

    Haque, Q.; Mahmood, S.

    2008-03-15

    Linear and nonlinear drift waves are studied in inhomogeneous electron-ion quantum magnetoplasma with neutrals in the background. The Korteweg-de Vries-Burgers equation is derived by using the quantum hydrodynamic model for nonlinear drift waves with quantum corrections. Both soliton and shock solutions are obtained in different limits. It is noticed that the width of the solitary hump is decreased with the increase in the quantum parameter. However this effect is reversed for the solitary dip case. It is also found that oscillatory shock wave is dependent on the quantum parameter. However, the monotonic shock formation is independent of the quantum parameter.

  13. ION SOLITARY PULSES IN WARM PLASMAS WITH ULTRARELATIVISTIC DEGENERATE ELECTRONS AND POSITRONS

    SciTech Connect

    Zeba, I.; Moslem, W. M.; Shukla, P. K. E-mail: zeba.israr@rub.de E-mail: wmm@tp4.rub.de

    2012-05-01

    The nonlinear propagation of ion solitary pulses in a warm collisionless electron-positron-ion plasma with ultrarelativistic degenerate electrons and positrons has been investigated. Arbitrary and small- (but finite-) amplitude ion solitary pulses are investigated by deriving the Korteweg-de Vries equation and an energy-balance-like expression involving a Sagdeev-like pseudopotential. The existence regions for ion solitary pulses have been precisely defined and numerically investigated. The ion solitary pulse profiles are also displayed. Applications to the interior of white dwarf stars and the corona of magnetars are discussed.

  14. Study of non-Maxwellian trapped electrons by using generalized (r,q) distribution function and their effects on the dynamics of ion acoustic solitary wave

    SciTech Connect

    Mushtaq, A.; Shah, H.A.

    2006-01-15

    By using the generalized (r,q) distribution function, the effect of particle trapping on the linear and nonlinear evolution of an ion-acoustic wave in an electron-ion plasma has been discussed. The spectral indices q and r contribute to the high-energy tails and flatness on top of the distribution function respectively. The generalized Korteweg-de Vries equations with associated solitary wave solutions for different ranges of parameter r are derived by employing a reductive perturbation technique. It is shown that spectral indices r and q affect the trapping of electrons and subsequently the dynamics of the ion acoustic solitary wave significantly.

  15. A novel car following model considering average speed of preceding vehicles group

    NASA Astrophysics Data System (ADS)

    Sun, Dihua; Kang, Yirong; Yang, Shuhong

    2015-10-01

    In this paper, a new car following model is presented by considering the average speed effect of preceding vehicles group in cyber-physical systems (CPS) environment. The effect of this new consideration upon the stability of traffic flow is examined through linear stability analysis. A modified Korteweg-de Vries (mKdV) equation was derived via nonlinear analysis to describe the propagating behavior of traffic density wave near the critical point. Good agreement between the simulation and the analytical results shows that average speed of preceding vehicles group leads to the stabilization of traffic systems, and thus can efficiently suppress the emergence of traffic jamming.

  16. Incompatibility of Time-Dependent Bogoliubov-de-Gennes and Ginzburg-Landau Equations

    NASA Astrophysics Data System (ADS)

    Frank, Rupert L.; Hainzl, Christian; Schlein, Benjamin; Seiringer, Robert

    2016-07-01

    We study the time-dependent Bogoliubov-de-Gennes equations for generic translation-invariant fermionic many-body systems. For initial states that are close to thermal equilibrium states at temperatures near the critical temperature, we show that the magnitude of the order parameter stays approximately constant in time and, in particular, does not follow a time-dependent Ginzburg-Landau equation, which is often employed as a phenomenological description and predicts a decay of the order parameter in time. The full non-linear structure of the equations is necessary to understand this behavior.

  17. Incompatibility of Time-Dependent Bogoliubov-de-Gennes and Ginzburg-Landau Equations

    NASA Astrophysics Data System (ADS)

    Frank, Rupert L.; Hainzl, Christian; Schlein, Benjamin; Seiringer, Robert

    2016-05-01

    We study the time-dependent Bogoliubov-de-Gennes equations for generic translation-invariant fermionic many-body systems. For initial states that are close to thermal equilibrium states at temperatures near the critical temperature, we show that the magnitude of the order parameter stays approximately constant in time and, in particular, does not follow a time-dependent Ginzburg-Landau equation, which is often employed as a phenomenological description and predicts a decay of the order parameter in time. The full non-linear structure of the equations is necessary to understand this behavior.

  18. Conformally invariant spin-3/2 field equation in de Sitter space-time

    NASA Astrophysics Data System (ADS)

    Fatahi, N.

    2015-09-01

    In the previous paper (Behroozi et al., Phys Rev D 74:124014, 2006; Dehghani et al., Phys Rev D 77:064028, 2008), conformal invariance for massless tensor fields (scalar, vector and spin-2 fields) was studied and the solutions of their wave equations and two-point functions were obtained. In the present paper, conformally invariant wave equation for massless spinor field in de Sitter space-time has been obtained. For this propose, we use Dirac's six-cone formalism. The solutions of massless spin-1/2 and -3/2 equations, in the ambient space notation, have been calculated.

  19. Cosmological constant from a deformation of the Wheeler-DeWitt equation

    NASA Astrophysics Data System (ADS)

    Garattini, Remo; Faizal, Mir

    2016-04-01

    In this paper, we consider the Wheeler-DeWitt equation modified by a deformation of the second quantized canonical commutation relations. Such modified commutation relations are induced by a Generalized Uncertainty Principle. Since the Wheeler-DeWitt equation can be related to a Sturm-Liouville problem where the associated eigenvalue can be interpreted as the cosmological constant, it is possible to explicitly relate such an eigenvalue to the deformation parameter of the corresponding Wheeler-DeWitt equation. The analysis is performed in a Mini-Superspace approach where the scale factor appears as the only degree of freedom. The deformation of the Wheeler-DeWitt equation gives rise to a Cosmological Constant even in absence of matter fields. As a Cosmological Constant cannot exist in absence of the matter fields in the undeformed Mini-Superspace approach, so the existence of a non-vanishing Cosmological Constant is a direct consequence of the deformation by the Generalized Uncertainty Principle. In fact, we are able to demonstrate that a non-vanishing Cosmological Constant exists even in the deformed flat space. We also discuss the consequences of this deformation on the big bang singularity.

  20. Nonlinear Laplace equation, de Sitter vacua, and information geometry

    SciTech Connect

    Loran, Farhang

    2005-06-15

    Three exact solutions say {phi}{sub 0} of massless scalar theories on Euclidean space, i.e. D=6 {phi}{sup 3}, D=4 {phi}{sup 4} and D=3 {phi}{sup 6} models are obtained which share similar properties. The information geometry of their moduli spaces coincide with the Euclidean AdS{sub 7}, AdS{sub 5} and AdS{sub 4} respectively on which {phi}{sub 0} can be described as a stable tachyon. In D=4 we recognize that the SU(2) instanton density is proportional to {phi}{sub 0}{sup 4}. The original action S[{phi}] written in terms of new scalars {phi}-tilde={phi}-{phi}{sub 0} is shown to be equivalent to an interacting scalar theory on D-dimensional de Sitter background.

  1. Dust acoustic solitary and shock excitations in a Thomas-Fermi magnetoplasma

    SciTech Connect

    Rahim, Z.; Qamar, A.; Ali, S.

    2014-07-15

    The linear and nonlinear properties of dust-acoustic waves are investigated in a collisionless Thomas-Fermi magnetoplasma, whose constituents are electrons, ions, and negatively charged dust particles. At dust time scale, the electron and ion number densities follow the Thomas-Fermi distribution, whereas the dust component is described by the classical fluid equations. A linear dispersion relation is analyzed to show that the wave frequencies associated with the upper and lower modes are enhanced with the variation of dust concentration. The effect of the latter is seen more strongly on the upper mode as compared to the lower mode. For nonlinear analysis, we obtain magnetized Korteweg-de Vries (KdV) and Zakharov-Kuznetsov (ZK) equations involving the dust-acoustic solitary waves in the framework of reductive perturbation technique. Furthermore, the shock wave excitations are also studied by allowing dissipation effects in the model, leading to the Korteweg-de Vries-Burgers (KdVB) and ZKB equations. The analysis reveals that the dust-acoustic solitary and shock excitations in a Thomas-Fermi plasma are strongly influenced by the plasma parameters, e.g., dust concentration, dust temperature, obliqueness, magnetic field strength, and dust fluid viscosity. The present results should be important for understanding the solitary and shock excitations in the environments of white dwarfs or supernova, where dust particles can exist.

  2. Dust acoustic solitary and shock excitations in a Thomas-Fermi magnetoplasma

    NASA Astrophysics Data System (ADS)

    Rahim, Z.; Ali, S.; Qamar, A.

    2014-07-01

    The linear and nonlinear properties of dust-acoustic waves are investigated in a collisionless Thomas-Fermi magnetoplasma, whose constituents are electrons, ions, and negatively charged dust particles. At dust time scale, the electron and ion number densities follow the Thomas-Fermi distribution, whereas the dust component is described by the classical fluid equations. A linear dispersion relation is analyzed to show that the wave frequencies associated with the upper and lower modes are enhanced with the variation of dust concentration. The effect of the latter is seen more strongly on the upper mode as compared to the lower mode. For nonlinear analysis, we obtain magnetized Korteweg-de Vries (KdV) and Zakharov-Kuznetsov (ZK) equations involving the dust-acoustic solitary waves in the framework of reductive perturbation technique. Furthermore, the shock wave excitations are also studied by allowing dissipation effects in the model, leading to the Korteweg-de Vries-Burgers (KdVB) and ZKB equations. The analysis reveals that the dust-acoustic solitary and shock excitations in a Thomas-Fermi plasma are strongly influenced by the plasma parameters, e.g., dust concentration, dust temperature, obliqueness, magnetic field strength, and dust fluid viscosity. The present results should be important for understanding the solitary and shock excitations in the environments of white dwarfs or supernova, where dust particles can exist.

  3. Thermal diffusion of Boussinesq solitons.

    PubMed

    Arévalo, Edward; Mertens, Franz G

    2007-10-01

    We consider the problem of the soliton dynamics in the presence of an external noisy force for the Boussinesq type equations. A set of ordinary differential equations (ODEs) of the relevant coordinates of the system is derived. We show that for the improved Boussinesq (IBq) equation the set of ODEs has limiting cases leading to a set of ODEs which can be directly derived either from the ill-posed Boussinesq equation or from the Korteweg-de Vries (KdV) equation. The case of a soliton propagating in the presence of damping and thermal noise is considered for the IBq equation. A good agreement between theory and simulations is observed showing the strong robustness of these excitations. The results obtained here generalize previous results obtained in the frame of the KdV equation for lattice solitons in the monatomic chain of atoms. PMID:17995127

  4. Solution of Dirac equation in Reissner-Nordström de Sitter space

    NASA Astrophysics Data System (ADS)

    Lyu, Yan; Cui, Song

    2009-02-01

    The radial parts of the Dirac equation between the outer black hole horizon and the cosmological horizon are solved in Reissner-Nordström de Sitter (RNdS) space numerically. An accurate approximation, the polynomial approximation, is used to approximate the modified tortoise coordinate \\hat r_* , which leads to the inverse function r = r(\\hat r_* ) and the potential V(\\hat r_* ). The potential V(\\hat r_* ) is replaced by a collection of step functions in sequence. Then the solution of the wave equation as well as the reflection and transmission coefficients is computed by a quantum mechanical method.

  5. On the solution of the Dirac equation in de Sitter space

    NASA Astrophysics Data System (ADS)

    Klishevich, V. V.; Tyumentsev, V. A.

    2005-10-01

    It is shown that the maximal number of first-order symmetry operators for the Dirac equation (including spin symmetries), both in arbitrary signature flat space and in de Sitter space, is equal. The isomorphic representation of 11-dimensional nonlinear symmetry algebra (W-algebra) of first-order operators for the Dirac operator in flat space and de Sitter space is considered. The algebra is an extension of the Lie algebra of the group of pseudo-orthogonal rotations and this extension is unique. We have found all linear Lie subalgebras in the nonlinear algebra that satisfy the conditions of the noncommutative integration theorem. Using one subalgebra we have integrated the Dirac equation in the generalized spherical system of coordinates and have constructed the complete class of exact solutions. The solution is found by a method that differs from the variable separation method and is new in the literature. The massive particle spectrum, models of particle into antiparticle transmutation, the disappearance of particles and the quantization conditions of the motion are discussed. One can use the results of the paper to pose the boundary problem for the Dirac equation in de Sitter space if the interval is used in the boundary condition. As an example, we consider a model of asymptotically flat space that is glued from the de Sitter space and flat space. We interpret the model as a gravitational well or barrier.

  6. Soliton defects in one-gap periodic system and exotic supersymmetry

    NASA Astrophysics Data System (ADS)

    Arancibia, Adrián; Correa, Francisco; Jakubský, Vít; Mateos Guilarte, Juan; Plyushchay, Mikhail S.

    2014-12-01

    By applying Darboux-Crum transformations to the quantum one-gap Lamé system, we introduce an arbitrary countable number of bound states into forbidden bands. The perturbed potentials are reflectionless and contain two types of soliton defects in the periodic background. The bound states with a finite number of nodes are supported in the lower forbidden band by the periodicity defects of the potential well type, while the pulse-type bound states in the gap have an infinite number of nodes and are trapped by defects of the compression modulations nature. We investigate the exotic nonlinear N =4 supersymmetric structure in such paired Schrödinger systems, which extends an ordinary N =2 supersymmetry and involves two bosonic generators composed from Lax-Novikov integrals of the subsystems. One of the bosonic integrals has a nature of a central charge and allows us to liaise the obtained systems with the stationary equations of the Korteweg-de Vries and modified Korteweg-de Vries hierarchies. This exotic supersymmetry opens the way for the construction of self-consistent condensates based on the Bogoliubov-de Gennes equations and associated with them new solutions to the Gross-Neveu model. They correspond to the kink or kink-antikink defects of the crystalline background in dependence on whether the exotic supersymmetry is unbroken or spontaneously broken.

  7. A method of studying the Bogoliubov-de Gennes equations for the superconducting vortex lattice state.

    PubMed

    Han, Qiang

    2010-01-27

    In this paper, we present a method to construct the eigenspace of the tight-binding electrons moving on a 2D square lattice with nearest-neighbor hopping in the presence of a perpendicular uniform magnetic field which imposes (quasi-)periodic boundary conditions for the wavefunctions in the magnetic unit cell. Exact unitary transformations are put forward to correlate the discrete eigenvectors of the 2D electrons with those of the Harper equation. The cyclic tridiagonal matrix associated with the Harper equation is then tridiagonalized by another unitary transformation. The obtained truncated eigenbasis is utilized to expand the Bogoliubov-de Gennes equations for the superconducting vortex lattice state, which shows the merit of our method in studying large-sized systems. To test our method, we have applied our results to study the vortex lattice state of an s-wave superconductor. PMID:21386295

  8. Wheeler-DeWitt equation and Lie symmetries in Bianchi scalar-field cosmology

    NASA Astrophysics Data System (ADS)

    Paliathanasis, A.; Karpathopoulos, L.; Wojnar, A.; Capozziello, S.

    2016-04-01

    Lie symmetries are discussed for the Wheeler-De Witt equation in Bianchi Class A cosmologies. In particular, we consider general relativity, minimally coupled scalar-field gravity and hybrid gravity as paradigmatic examples of the approach. Several invariant solutions are determined and classified according to the form of the scalar-field potential. The approach gives rise to a suitable method to select classical solutions and it is based on the first principle of the existence of symmetries.

  9. Marine seismic observation of internal solitary wave packets in the northeast South China Sea

    NASA Astrophysics Data System (ADS)

    Tang, Qunshu; Hobbs, Richard; Wang, Dongxiao; Sun, Longtao; Zheng, Chan; Li, Jiabiao; Dong, Chongzhi

    2015-12-01

    Recently the novel seismic oceanography method has been reported to be an effective way to study the energetic internal solitary waves (ISWs) in the northern South China Sea. An optimized seismic-oceanographic cruise was carried out to observe such near-surface ISWs on Dongsha Plateau in July 2014. Several soliton trains rather than single solitons were captured using the seismic technique. After seismic data processing, one prototypical rank-ordered ISW packet on northeast side of Dongsha Island was clearly identified for further analysis. This included waveforms, propagation velocities, and vertical velocities for individual solitons. In this study, an improved scheme was applied to derive the transient phase velocities from the seismic data which is verified from independent satellite and hydrographic data. Analytical predictions from Korteweg-de Vries equation fit better than the extended Korteweg-de Vries equation ignoring background currents. Our results show that the seismic method can be successfully used to image targets in shallow water below 40 m and that seismic oceanography is a promising technique for studying near-surface phenomena with high spatial resolution.

  10. Magnetoacoustic solitons and shocks in dense astrophysical plasmas with relativistic degenerate electrons

    NASA Astrophysics Data System (ADS)

    Irfan, M.; Ali, S.; Mirza, Arshad M.

    2016-02-01

    Two-fluid quantum magnetohydrodynamic (QMHD) equations are employed to investigate linear and nonlinear properties of the magnetosonic waves in a semi-relativistic dense plasma accounting for degenerate relativistic electrons. In the linear analysis, a plane wave solution is used to derive the dispersion relation of magnetosonic waves, which is significantly modified due to relativistic degenerate electrons. However, for a nonlinear investigation of solitary and shock waves, we employ the reductive perturbation technique for the derivation of Korteweg-de Vries (KdV) and Korteweg-de Vries Burger (KdVB) equations, admitting nonlinear wave solutions. Numerically, it is shown that the wave frequency decreases to attain a lowest possible value at a certain critical number density Nc(0), and then increases beyond Nc(0) as the plasma number density increases. Moreover, the relativistic electrons and associated pressure degeneracy lead to a reduction in the spatial extents of the magnetosonic waves and a strengthening of the shock amplitude. The results might be important for understanding the linear and nonlinear magnetosonic excitations in dense astrophysical plasmas, such as in white dwarfs, magnetars and neutron stars, etc., where relativistic degenerate electrons are present.

  11. Statistical moments of soliton field in shallow water

    NASA Astrophysics Data System (ADS)

    Shurgalina, Ekaterina; Pelinovsky, Efim

    2013-04-01

    The ensemble of solitons plays an important role in the long-term dynamics of a wave field which can be interpreted as soliton turbulence. Dynamics of a soliton field in shallow water in the framework of Korteweg - de Vries equation is studied. The statistical ensemble is generated from the isolated solitons with random phases and amplitudes. Main interest is paid to the first four statistical moments (mean, variance, skewness and kurtosis) playing an important role in the turbulence theory. They are computed analytically for initial random soliton field presenting the linear superposition of the solitary pulses. It is demonstrated that the random soliton field is not Gaussian. Then the time evolution of the statistical moments is studied numerically. It is confirmed that first two moments being the invariants of the Korteweg - de Vries equation remain to be constant. The skewness and kurtosis vary in time in each realization but tends to the constants in the average. The averaged magnitude of these moments is decreased to compare with initial values with increase of the soliton density. This effect is related with features of the two-soliton interaction described in (E.N.Pelinovsky et al., Physics Letters A (2012) http://dx.doi.org/10.1016/j.physleta.2012.11.037). As a result, the nonlinear soliton interaction leads to tendency of normalization of the random process. This study was supported by the Federal Targeted Program "Research and educational personnel of innovation Russia" for 2009-2013 and Dynasty Foundation.

  12. Inhomogeneities in the early universe

    NASA Technical Reports Server (NTRS)

    Canuto, V.

    1976-01-01

    The paper investigates certain nonlinear processes that are viable candidates for the mechanisms which produced large-scale inhomogeneities in the early Universe. Several nonlinear Lagrangians are presented for matter, the Korteweg-de Vries equation is analyzed, and the existence of solitons among its solutions is noted. A model based on the possibility of generating a cascade of solitons from an initial perturbation is proposed, and it is shown how large-scale inhomogeneities can be generated when an initial soliton fragments into many others through the nonlinear action of the terms in the Korteweg-de Vries equation. A second model is examined which is based on the interaction of matter with a strong radiation field (an almost monochromatic photon gas) and which involves changes in the refractive index of the vacuum. It is found that matter and radiation will not mix if the radiation field has a nonuniform intensity and that the matter will separate into dense portions or 'cosmological protogalaxies'. The evolution of these portions of matter is studied, and it is found that conditions would be appropriate for the interface between them and the surrounding radiation field to become unstable, giving rise to a turbulent layer.

  13. Key concepts from Gibbs that empowered Van der Waals, Korteweg and Kamerlingh Onnes

    NASA Astrophysics Data System (ADS)

    Levelt Sengers, Johanna

    2003-03-01

    Gibbs founded his theory of the equilibrium of heterogeneous systems (1873-1878) on the following pillars: thermodynamic stability; phase equilibrium from tangent planes rolling across thermodynamic energy surfaces; the chemical potential; degrees of freedom; the phase rule; and criticality. These concepts inspired major interdisciplinary research on mixture phase behavior in the Netherlands.(J. Levelt Sengers, How Fluids Unmix, Edita, Amsterdam (2002)) Mathematician Korteweg and physicist Van der Waals, at the University of Amsterdam, used Gibbs's geometric approach to produce the first formulation of the Helmholtz energy of binary fluid mixtures in 1891. Physicist Kamerlingh Onnes and his students at the University of Leiden studied binary mixtures experimentally, confirming Van der Waals's model, and built many 3-D models of thermodynamic surfaces. Misconceptions about criticality abounded in Europe from 1880 to 1908, provoking attacks by Kamerlingh Onnes. Between 1907 and 1913, Amsterdam chemist Bakhuis Roozeboom and his school produced an influential book series on binary and ternary, fluid and solid phase equilibria, including reacting systems.

  14. Huygens' principle for the Klein-Gordon equation in the de Sitter spacetime

    SciTech Connect

    Yagdjian, Karen

    2013-09-15

    In this article we prove that the Klein-Gordon equation in the de Sitter spacetime obeys the Huygens' principle only if the physical mass m of the scalar field and the dimension n⩾ 2 of the spatial variable are tied by the equation m{sup 2}= (n{sup 2}−1)/4. Moreover, we define the incomplete Huygens' principle, which is the Huygens' principle restricted to the vanishing second initial datum, and then reveals that the massless scalar field in the de Sitter spacetime obeys the incomplete Huygens' principle and does not obey the Huygens' principle, for the dimensions n= 1, 3, only. Thus, in the de Sitter spacetime the existence of two different scalar fields (in fact, with m= 0 and m{sup 2}= (n{sup 2}−1)/4), which obey incomplete Huygens' principle, is equivalent to the condition n= 3, the spatial dimension of the physical world. In fact, Paul Ehrenfest in 1917 addressed the question: “Why has our space just three dimensions?”. For n= 3 these two values of the mass are the endpoints of the so-called in quantum field theory the Higuchi bound. The value m{sup 2}= (n{sup 2}−1)/4 of the physical mass allows us also to obtain complete asymptotic expansion of the solution for the large time.

  15. Numerical solution of the Dirac equation in Schwarzschild de Sitter spacetime

    NASA Astrophysics Data System (ADS)

    Lyu, Y.; Gui, Y. X.

    2007-02-01

    The radial parts of the Dirac equation between the inner and the outer horizon in Schwarzschild-de Sitter geometry are solved. Two limiting cases are concerned. The first case is when the two horizons are far apart and the second case is when the horizons are close to each other. In each case, a 'tangent' approximation is used to replace the modified 'tortoise' coordinate r*, which leads to a simple analytically invertible relation between r* and the radius r. The potential V(r*) is replaced by a collection of step functions in sequence. Then the solutions of the wave equation as well as the reflection and transmission coefficients are computed by a quantum mechanical method.

  16. The Solution of Dirac Equation in Quasi-Extreme REISSNER-NORDSTRÖM de Sitter Space

    NASA Astrophysics Data System (ADS)

    Lyu, Yan; Cui, Song; Liu, Ling

    The radial parts of Dirac equation between the outer black hole horizon and the cosmological horizon in quasi-extreme Reissner-Nordström de Sitter (RNdS) geometry is solved numerically. We use an accurate polynomial approximation to mimic the modified tortoise coordinate hat r*(r), for obtaining the inverse function r=r(hat r*) and V=V(hat r*). We then use a quantum mechanical method to solve the wave equation and give the reflection and transmission coefficients. We concentrate on two limiting cases. The first case is when the two horizons are close to each other, and the second case is when the horizons are far apart.

  17. The Tolman-Oppenheimer Equations and the Spacetime Properties of the Schwarzschild-De Sitter Constant Density Interior Solution

    NASA Astrophysics Data System (ADS)

    Zou, Li; Li, Fang-Yu; Li, Tao

    2014-11-01

    In this paper, we first deduce the Tolman-Oppenheimer-Volkoff (TOV) equations and Schwarzschild-de Sitter (SdS) constant-density interior solutions of perfect fluid spheres in hydrostatic equilibrium by the Einstein equations with a nonzero cosmological constant. The TOV equations and the spacetime properties of exact solutions inside uniform perfect fluid spheres with different spatial curvature and cosmological constants will be respectively analyzed in detail. Moreover, a brief comparison between the internal static solutions of the SdS type and the dynamical Einstein-Strauss-de Sitter (ESdS) vacuole spacetime is obtained.

  18. The equations of relative motion in the orbital reference frame

    NASA Astrophysics Data System (ADS)

    Casotto, Stefano

    2016-03-01

    The analysis of relative motion of two spacecraft in Earth-bound orbits is usually carried out on the basis of simplifying assumptions. In particular, the reference spacecraft is assumed to follow a circular orbit, in which case the equations of relative motion are governed by the well-known Hill-Clohessy-Wiltshire equations. Circular motion is not, however, a solution when the Earth's flattening is accounted for, except for equatorial orbits, where in any case the acceleration term is not Newtonian. Several attempts have been made to account for the J_2 effects, either by ingeniously taking advantage of their differential effects, or by cleverly introducing ad-hoc terms in the equations of motion on the basis of geometrical analysis of the J_2 perturbing effects. Analysis of relative motion about an unperturbed elliptical orbit is the next step in complexity. Relative motion about a J_2-perturbed elliptic reference trajectory is clearly a challenging problem, which has received little attention. All these problems are based on either the Hill-Clohessy-Wiltshire equations for circular reference motion, or the de Vries/Tschauner-Hempel equations for elliptical reference motion, which are both approximate versions of the exact equations of relative motion. The main difference between the exact and approximate forms of these equations consists in the expression for the angular velocity and the angular acceleration of the rotating reference frame with respect to an inertial reference frame. The rotating reference frame is invariably taken as the local orbital frame, i.e., the RTN frame generated by the radial, the transverse, and the normal directions along the primary spacecraft orbit. Some authors have tried to account for the non-constant nature of the angular velocity vector, but have limited their correction to a mean motion value consistent with the J_2 perturbation terms. However, the angular velocity vector is also affected in direction, which causes precession

  19. Exact solutions of the Wheeler–DeWitt equation and the Yamabe construction

    SciTech Connect

    Ita III, Eyo Eyo; Soo, Chopin

    2015-08-15

    Exact solutions of the Wheeler–DeWitt equation of the full theory of four dimensional gravity of Lorentzian signature are obtained. They are characterized by Schrödinger wavefunctionals having support on 3-metrics of constant spatial scalar curvature, and thus contain two full physical field degrees of freedom in accordance with the Yamabe construction. These solutions are moreover Gaussians of minimum uncertainty and they are naturally associated with a rigged Hilbert space. In addition, in the limit the regulator is removed, exact 3-dimensional diffeomorphism and local gauge invariance of the solutions are recovered.

  20. Soliton turbulence in shallow water ocean surface waves.

    PubMed

    Costa, Andrea; Osborne, Alfred R; Resio, Donald T; Alessio, Silvia; Chrivì, Elisabetta; Saggese, Enrica; Bellomo, Katinka; Long, Chuck E

    2014-09-01

    We analyze shallow water wind waves in Currituck Sound, North Carolina and experimentally confirm, for the first time, the presence of soliton turbulence in ocean waves. Soliton turbulence is an exotic form of nonlinear wave motion where low frequency energy may also be viewed as a dense soliton gas, described theoretically by the soliton limit of the Korteweg-deVries equation, a completely integrable soliton system: Hence the phrase "soliton turbulence" is synonymous with "integrable soliton turbulence." For periodic-quasiperiodic boundary conditions the ergodic solutions of Korteweg-deVries are exactly solvable by finite gap theory (FGT), the basis of our data analysis. We find that large amplitude measured wave trains near the energetic peak of a storm have low frequency power spectra that behave as ∼ω-1. We use the linear Fourier transform to estimate this power law from the power spectrum and to filter densely packed soliton wave trains from the data. We apply FGT to determine the soliton spectrum and find that the low frequency ∼ω-1 region is soliton dominated. The solitons have random FGT phases, a soliton random phase approximation, which supports our interpretation of the data as soliton turbulence. From the probability density of the solitons we are able to demonstrate that the solitons are dense in time and highly non-Gaussian. PMID:25238388

  1. Studies on soliton energy at critical and noncritical densities of negative ions in an inhomogeneous magnetized warm plasma

    SciTech Connect

    Singh, Dhananjay K.; Malik, Hitendra K.

    2007-11-15

    Considering an inhomogeneous plasma having finite-temperature negative and positive ions, and the isothermal electrons in the presence of an external magnetic field, the solitons at noncritical and critical densities of the negative ions are studied through Korteweg-deVries (KdV) and modified Korteweg-deVries (mKdV) equations, respectively. The compressive (rarefactive) KdV solitons are found to propagate when the negative ion concentration is less (greater) than the critical density of the negative ions. At the critical density, both the compressive and the rarefactive solitons of equal amplitudes are found to occur. The energies of the compressive KdV soliton and the mKdV solitons are found to increase and that of the rarefactive KdV soliton is found to decrease with the negative ion density. Soliton energy for both the KdV and the mKdV solitons gets lowered under the effect of stronger magnetic field. The effect of ion temperature is to increase the energy of the compressive KdV soliton, whereas the energy of the rarefactive KdV soliton as well as of the mKdV solitons gets decreased. The variation of the energy with the obliqueness of the magnetic field is different for the KdV and the mKdV solitons.

  2. Solitary wave dynamics in shallow water over periodic topography.

    PubMed

    Nakoulima, Ousseynou; Zahibo, Narcisse; Pelinovsky, Efim; Talipova, Tatiana; Kurkin, Andrey

    2005-09-01

    The problem of long-wave scattering by piecewise-constant periodic topography is studied both for a linear solitary-like wave pulse, and for a weakly nonlinear solitary wave [Korteweg-de Vries (KdV) soliton]. If the characteristic length of the topographic irregularities is larger than the pulse length, the solution of the scattering problem is obtained analytically for a leading wave in the framework of linear shallow-water theory. The wave decrement in the case of the small height of the topographic irregularities is proportional to delta2, where delta is the relative height of the topographic obstacles. An analytical approximate solution is also obtained for the weakly nonlinear problem when the length of the irregularities is larger than the characteristic nonlinear length scale. In this case, the Korteweg-de Vries equation is solved for each piece of constant depth by using the inverse scattering technique; the solutions are matched at each step by using linear shallow-water theory. The weakly nonlinear solitary wave decays more significantly than the linear solitary pulse. Solitary wave dynamics above a random seabed is also discussed, and the results obtained for random topography (including experimental data) are in reasonable agreement with the calculations for piecewise topography. PMID:16253002

  3. Analysis of a novel two-lane lattice model on a gradient road with the consideration of relative current

    NASA Astrophysics Data System (ADS)

    Cao, Jin-Liang; Shi, Zhong-Ke

    2016-04-01

    In this paper, a novel hydrodynamic lattice model is proposed by considering of relative current for two-lane gradient road system. The stability condition is obtained by using linear stability theory and shown that the stability of traffic flow varies with three parameters, that is, the slope, the sensitivity of response to the relative current and the rate of lane changing. The stable region increases with the increasing of one of them when another two parameters are constant. By using nonlinear analysis, the Burgers, Korteweg-de Vries, and modified Korteweg-de Vries equations are derived to describe the phase transition of traffic flow. Their solutions present the density wave as the triangular shock wave, soliton wave, and kink-antikink wave in the stable, metastable, and unstable region, respectively, which can explain the phase transitions from free traffic to stop-and-go traffic, and finally to congested traffic. To verify the theoretical results, a series of numerical simulations are carried out. The numerical results are consistent with the analytical results. To check the novel model, calibration are taken based on the empirical traffic flow data. The theoretical results and numerical results show that the traffic flow on the gradient road becomes more stable and the traffic congestion can be efficiently suppressed by considering the relative current and lane changing, and the empirical analysis shows that the novel lattice model is reasonable.

  4. Soliton Turbulence in Shallow Water Ocean Surface Waves

    NASA Astrophysics Data System (ADS)

    Costa, Andrea; Osborne, Alfred R.; Resio, Donald T.; Alessio, Silvia; Chrivı, Elisabetta; Saggese, Enrica; Bellomo, Katinka; Long, Chuck E.

    2014-09-01

    We analyze shallow water wind waves in Currituck Sound, North Carolina and experimentally confirm, for the first time, the presence of soliton turbulence in ocean waves. Soliton turbulence is an exotic form of nonlinear wave motion where low frequency energy may also be viewed as a dense soliton gas, described theoretically by the soliton limit of the Korteweg-deVries equation, a completely integrable soliton system: Hence the phrase "soliton turbulence" is synonymous with "integrable soliton turbulence." For periodic-quasiperiodic boundary conditions the ergodic solutions of Korteweg-deVries are exactly solvable by finite gap theory (FGT), the basis of our data analysis. We find that large amplitude measured wave trains near the energetic peak of a storm have low frequency power spectra that behave as ˜ω-1. We use the linear Fourier transform to estimate this power law from the power spectrum and to filter densely packed soliton wave trains from the data. We apply FGT to determine the soliton spectrum and find that the low frequency ˜ω-1 region is soliton dominated. The solitons have random FGT phases, a soliton random phase approximation, which supports our interpretation of the data as soliton turbulence. From the probability density of the solitons we are able to demonstrate that the solitons are dense in time and highly non-Gaussian.

  5. Dust acoustic dressed soliton with dust charge fluctuations

    SciTech Connect

    Asgari, H.; Muniandy, S. V.; Wong, C. S.

    2010-06-15

    Modeling of dust acoustic solitons observed in dusty plasma experiment [Bandyopadhyay et al., Phys. Rev. Lett. 101, 065006 (2008)] using the Korteweg-de Vries (KdV) equation showed significant discrepancies in the regime of large amplitudes (or high soliton speed). In this paper, higher order perturbation corrections to the standard KdV soliton are proposed and the resulting dressed soliton is shown to describe the experimental data better, in particular, at high soliton speed. The effects of dust charge fluctuations on the dust acoustic dressed soliton in a dusty plasma system are also investigated. The KdV equation and a linear inhomogeneous equation, governing the evolution of first and second order potentials, respectively, are derived for the system by using reductive perturbation technique. Renormalization procedure is used to obtain nonsecular solutions of these coupled equations. The characteristics of dust acoustic dressed solitons with and without dust charge fluctuations are discussed.

  6. Higher-order corrections to dust ion-acoustic soliton in a quantum dusty plasma

    SciTech Connect

    Chatterjee, Prasanta; Das, Brindaban; Mondal, Ganesh; Muniandy, S. V.; Wong, C. S.

    2010-10-15

    Dust ion-acoustic soliton is studied in an electron-dust-ion plasma by employing a two-fluid quantum hydrodynamic model. Ions and electrons are assumed to follow quantum mechanical behaviors in dust background. The Korteweg-de Vries (KdV) equation and higher order contribution to KdV equations are derived using reductive perturbation technique. The higher order contribution is obtained as a higher order inhomogeneous differential equation. The nonsecular solution of the higher order contribution is obtained by using the renormalization method and the particular solution of the inhomogeneous equation is determined using a truncated series solution method. The effects of dust concentration, quantum parameter for ions and electrons, and soliton velocity on the amplitude and width of the dressed soliton are discussed.

  7. Head on collision of multi-solitons in an electron-positron-ion plasma having superthermal electrons

    SciTech Connect

    Roy, Kaushik; Chatterjee, Prasanta Roychoudhury, Rajkumar

    2014-10-15

    The head-on collision and overtaking collision of four solitons in a plasma comprising superthermal electrons, cold ions, and Boltzmann distributed positrons are investigated using the extended Poincare-Lighthill-Kuo (PLK) together with Hirota's method. PLK method yields two separate Korteweg-de Vries (KdV) equations where solitons obtained from any KdV equation move along a direction opposite to that of solitons obtained from the other KdV equation, While Hirota's method gives multi-soliton solution for each KdV equation all of which move along the same direction where the fastest moving soliton eventually overtakes the other ones. We have considered here two soliton solutions obtained from Hirota's method. Phase shifts acquired by each soliton due to both head-on collision and overtaking collision are calculated analytically.

  8. Ion acoustic shock and solitary waves in highly relativistic plasmas with nonextensive electrons and positrons

    NASA Astrophysics Data System (ADS)

    Hafez, M. G.; Talukder, M. R.; Hossain Ali, M.

    2016-01-01

    The Korteweg-de Vries Burgers (KdVB) -like equation is derived to study the characteristics of nonlinear propagation of ion acoustic solitions in a highly relativistic plasma containing relativistic ions and nonextensive distribution of electrons and positrons using the well known reductive perturbation technique. The KdVB-like equation is solved employing the Bernoulli's equation method taking unperturbed positron to electron concentration ratio, electron to positron temperature ratio, strength of nonextensivity, ion kinematic viscosity, and highly relativistic streaming factor. It is found that these parameters significantly modify the structures of the solitonic excitation. The ion acoustic shock profiles are observed due to the influence of ion kinematic viscosity. In the absence of dissipative term to the KdVB equation, compressive and rarefactive solitons are observed in case of superthermality, but only compressive solitons are found for the case of subthermality.

  9. VizieR Online Data Catalog: IC 2602 VRI photometry (Foster+ 1997)

    NASA Astrophysics Data System (ADS)

    Foster, D. C.; Byrne, P. B.; Hawley, S. L.; Rolleston, W. R. J.

    1997-03-01

    We present the results of VRI photometry of the young open cluster IC 2602. Two 15x15arcmin2 fields were observed in February and May 1991 using the 1-m Swope telescope at Las Campanas. Using theoretical isochrones obtained from D'Antona & Mazzitelli (1994ApJS...90..467D), and allowing for observational and other uncertainties, we identify 78 primary candidate members with 12=50%, as might be expected given its low galactic latitude. We also compare our photometry with that given for the X-ray detected stars of Randich et al. (1995A&A...300..134R) present complimentary narrow band Hα photometry for a subset of the stars. (1 data file).

  10. Some notes on the Gunn-Stryker spectrophotometry and synthetic VRI colors

    NASA Astrophysics Data System (ADS)

    Taylor, Benjamin J.; Joner, Michael D.

    1990-09-01

    Cousins VRI photometry is presented for 26 stars with continuous scans by Gunn and Stryker. This photometry is combined with literature data and a few unpublished results to critique synthetic colors from the Gunn-Stryker scans. For V - R, it is found that all pertinent results are consistent at the several-mmag level. For R - I, however, systematic differences are found which are most simply interpreted as a declination effect in the Gunn-Stryker scans. In addition, it is found that the Gunn-Stryker synthetic colors are unexpectedly noisy, with sigma per datum of about 0.02 mag. It is suggested that future users of the Gunn-Stryker data keep both these effects in mind.

  11. Quantum Numbers of Eigenstates of Generalized de Broglie-Bargmann- Wigner Equations for Fermions with Partonic Substructure

    NASA Astrophysics Data System (ADS)

    Stumpf, H.

    2003-01-01

    Generalized de Broglie-Bargmann-Wigner (BBW) equations are relativistically invariant quantum mechanical many body equations with nontrivial interaction, selfregularization and probability interpretation. Owing to these properties these equations are a suitable means for describing relativistic bound states of fermions. In accordance with de Broglie's fusion theory and modern assumptions about the partonic substructure of elementary fermions, i.e., leptons and quarks, the three-body generalized BBW-equations are investigated. The transformation properties and quantum numbers of the three-parton equations under the relevant group actions are elaborated in detail. Section 3 deals with the action of the isospin group SU(2), a U(1) global gauge group for the fermion number, the hypercharge and charge generators. The resulting quantum numbers of the composite partonic systems can be adapted to those of the phenomenological particles to be described. The space-time transformations and in particular rotations generated by angular momentum operators are considered in Section 4. Based on the compatibility of the BBW-equations and the group theoretical constraints, in Sect. 5 integral equations are formulated in a representation with diagonal energy and total angular momentum variables. The paper provides new insight into the solution space and quantum labels of resulting integral equations for three parton states and prepares the ground for representing leptons and quarks as composite systems.

  12. Critical density of a soliton gas

    NASA Astrophysics Data System (ADS)

    El, G. A.

    2016-02-01

    We quantify the notion of a dense soliton gas by establishing an upper bound for the integrated density of states of the quantum-mechanical Schrödinger operator associated with the Korteweg-de Vries soliton gas dynamics. As a by-product of our derivation, we find the speed of sound in the soliton gas with Gaussian spectral distribution function.

  13. Dr. Michael DeBakey "is a magician of the heart…"

    MedlinePlus

    ... a South African surgeon, performs the first whole heart transplant from one person to another. — 1982 Willem DeVries, an American surgeon, implants a permanent artificial heart, designed by Robert Jarvik, an American physician, into ...

  14. From weak discontinuities to nondissipative shock waves

    SciTech Connect

    Garifullin, R. N. Suleimanov, B. I.

    2010-01-15

    An analysis is presented of the effect of weak dispersion on transitions from weak to strong discontinuities in inviscid fluid dynamics. In the neighborhoods of transition points, this effect is described by simultaneous solutions to the Korteweg-de Vries equation u{sub t}'+ uu{sub x}' + u{sub xxx}' = 0 and fifth-order nonautonomous ordinary differential equations. As x{sup 2} + t{sup 2} {yields}{infinity}, the asymptotic behavior of these simultaneous solutions in the zone of undamped oscillations is given by quasi-simple wave solutions to Whitham equations of the form r{sub i}(t, x) = tl{sub i} x/t{sup 2}.

  15. The nonadiabatic dust charge variation on dust acoustic solitary and shock waves in strongly coupled dusty plasmas

    NASA Astrophysics Data System (ADS)

    Wang, Yunliang; Guo, Xiaoyan; Lu, Yanzhen; Wang, Xiaodan

    2016-01-01

    The combined effects of nonadiabatic dust charge fluctuation and strongly coupled dust particles on the nonlinear propagation of dust acoustic (DA) waves in dusty plasma consisting of nonthermal electrons and trapped ions with vortex-like distribution are presented here. We use generalized viscoelastic hydrodynamic model for dust particles. In the weak nonlinearity limit, a modified Korteweg-de Vries (KdV) equation with a damping term and a KdV-Burger equation have been derived in the kinetic regime and hydrodynamic regime, respectively. The approximate analytical solitary solution of modified KdV equation is derived in the weak nonadiabatic dust charge variation limit, which shows that the amplitude of DA solitary waves decreases with time. The presence of viscosity due to strong coupling stands for the formation of DA shock waves in the hydrodynamic regime. The results show that the DA shock waves will be oscillating one for weak viscosity and will become monotonic ones for large viscosity.

  16. Beyond the KdV: Post-explosion development.

    PubMed

    Ostrovsky, L; Pelinovsky, E; Shrira, V; Stepanyants, Y

    2015-09-01

    Several threads of the last 25 years' developments in nonlinear wave theory that stem from the classical Korteweg-de Vries (KdV) equation are surveyed. The focus is on various generalizations of the KdV equation which include higher-order nonlinearity, large-scale dispersion, and a non-local integral dispersion. We also discuss how relatively simple models can capture strongly nonlinear dynamics and how various modifications of the KdV equation lead to qualitatively new, non-trivial solutions and regimes of evolution observable in the laboratory and in nature. As the main physical example, we choose internal gravity waves in the ocean for which all these models are applicable and have genuine importance. We also briefly outline the authors' view of the future development of the chosen lines of nonlinear wave theory. PMID:26428573

  17. Dressed ion-acoustic solitons in magnetized dusty plasmas

    SciTech Connect

    El-Labany, S. K.; El-Shamy, E. F.; El-Warraki, S. A.

    2009-01-15

    In the present research paper, the characteristics of ion acoustic solitary waves are investigated in hot magnetized dusty plasmas consisting of negatively charged dust grains, positively charged ion fluid, and isothermal electrons. Applying a reductive perturbation theory, a nonlinear Korteweg-de Vries (KdV) equation for the first-order perturbed potential and a linear inhomogeneous KdV-type equation for the second-order perturbed potentials are derived. Stationary solutions of these coupled equations are obtained using a renormalization method. The effects of the external oblique magnetic field, hot ion fluid, and higher-order nonlinearity on the nature of the ion acoustic solitary waves are discussed. The results complement and provide new insights into previously published results on this problem [R. S. Tiwari and M. K. Mishra, Phys. Plasmas 13, 062112 (2006)].

  18. Traffic jams, granular flow, and soliton selection

    SciTech Connect

    Kurtze, D.A.; Hong, D.C.

    1995-07-01

    The flow of traffic on a long section of road without entrances or exits can be modeled by continuum equations similar to those describing fluid flow. In a certain range of traffic density, steady flow becomes unstable against the growth of a cluster, or ``phantom`` traffic jam, which moves at a slower speed than the otherwise homogeneous flow. We show that near the onset of this instability, traffic flow is described by a perturbed Korteweg--de Vries (KdV) equation. The traffic jam can be identified with a soliton solution of the KdV equation. The perturbation terms select a unique member of the continuous family of KdV solitons. These results may also apply to the dynamics of granular relaxation.

  19. Modulational instability of co-propagating internal wavetrains under rotation.

    PubMed

    Whitfield, A J; Johnson, E R

    2015-02-01

    Weakly-nonlinear unidirectional long internal waves in a non-rotating frame are well described by the Korteweg-de Vries equation (KdV). Within the KdV framework, all isolated monochromatic wavetrains are stable to modulational instability. However, analysis of a coupled nonlinear Schrödinger equation system (CNLS) has shown that all systems of two co-propagating monochromatic wavetrains in the KdV are modulationally unstable. To take into account the effect of the background rotation of the Earth on long internal waves, this analysis is extended here to derive the CNLS for the rotation-modified KdV, or Ostrovsky, equation. Rotation stabilises wavetrain pairs when the wavelengths of both waves comprising the wavetrains are longer than the linear wave with maximum group velocity. The particular case when the wavetrains have different wavenumbers but the same linear group speed is emphasised. PMID:25725645

  20. Solitary and freak waves in a dusty plasma with negative ions

    SciTech Connect

    Abdelsalam, U. M.; Moslem, W. M.; Khater, A. H.; Shukla, P. K.

    2011-09-15

    It is shown that solitary and freak waves can propagate in a dusty plasma composed of positive and negative ions, as well as nonextensive electrons. The evolution of the solitary waves is described by the Korteweg-de Vries (KdV) equation. However, when the frequency of the carrier wave is much smaller than the ion plasma frequency then the KdV equation is also used to study the nonlinear evolution of modulationally unstable modified ion-acoustic wavepackets through the derivation of the nonlinear Schroedinger (NLS) equation. In order to show that the characteristics of the solitary and freak waves are influenced by the plasma parameters, the relevant numerical analysis of the appropriate nonlinear solutions is presented. The relevance of the present investigation to nonlinear waves in astrophysical plasma environments is discussed.

  1. Semiclassical solitons in strongly correlated systems of ultracold bosonic atoms in optical lattices

    SciTech Connect

    Demler, Eugene; Maltsev, Andrei

    2011-07-15

    Highlights: > Dynamics of their formation in strongly correlated systems of ultracold bosonic atoms in optical lattices. > Regime of very strong interactions between atoms, the so-called hard core bosons regime. > Character of soliton excitations is dramatically different from the usual Gross-Pitaevskii regime. - Abstract: We investigate theoretically soliton excitations and dynamics of their formation in strongly correlated systems of ultracold bosonic atoms in two and three dimensional optical lattices. We derive equations of nonlinear hydrodynamics in the regime of strong interactions and incommensurate fillings, when atoms can be treated as hard core bosons. When parameters change in one direction only we obtain Korteweg-de Vries type equation away from half-filling and modified KdV equation at half-filling. We apply this general analysis to a problem of the decay of the density step. We consider stability of one dimensional solutions to transverse fluctuations. Our results are also relevant for understanding nonequilibrium dynamics of lattice spin models.

  2. Nonlinear compressional waves in a two-dimensional Yukawa lattice.

    PubMed

    Avinash, K; Zhu, P; Nosenko, V; Goree, J

    2003-10-01

    A modified Korteweg-de Vries (KdV) equation is obtained for studying the propagation of nonlinear compressional waves and pulses in a chain of particles including the effect of damping. Suitably altering the linear phase velocity makes this equation useful also for the problem of phonon propagation in a two-dimensional (2D) lattice. Assuming a Yukawa potential, we use this method to model compressional wave propagation in a 2D plasma crystal, as in a recent experiment. By integrating the modified KdV equation the pulse is allowed to evolve, and good agreement with the experiment is found. It is shown that the speed of a compressional pulse increases with its amplitude, while the speed of a rarefactive pulse decreases. It is further discussed how the drag due to the background gas has a crucial role in weakening nonlinear effects and preventing the emergence of a soliton. PMID:14683049

  3. Collisionless damping of dust-acoustic waves in a charge varying dusty plasma with nonextensive ions

    SciTech Connect

    Amour, Rabia; Tribeche, Mouloud

    2014-12-15

    The charge variation induced nonlinear dust-acoustic wave damping in a charge varying dusty plasma with nonextensive ions is considered. It is shown that the collisionless damping due to dust charge fluctuation causes the nonlinear dust acoustic wave propagation to be described by a damped Korteweg-de Vries (dK-dV) equation the coefficients of which depend sensitively on the nonextensive parameter q. The damping term, solely due to the dust charge variation, is affected by the ion nonextensivity. For the sake of completeness, the possible effects of nonextensivity and collisionless damping on weakly nonlinear wave packets described by the dK-dV equation are succinctly outlined by deriving a nonlinear Schrödinger-like equation with a complex nonlinear coefficient.

  4. Collisionless damping of dust-acoustic waves in a charge varying dusty plasma with nonextensive ions

    NASA Astrophysics Data System (ADS)

    Amour, Rabia; Tribeche, Mouloud

    2014-12-01

    The charge variation induced nonlinear dust-acoustic wave damping in a charge varying dusty plasma with nonextensive ions is considered. It is shown that the collisionless damping due to dust charge fluctuation causes the nonlinear dust acoustic wave propagation to be described by a damped Korteweg-de Vries (dK-dV) equation the coefficients of which depend sensitively on the nonextensive parameter q. The damping term, solely due to the dust charge variation, is affected by the ion nonextensivity. For the sake of completeness, the possible effects of nonextensivity and collisionless damping on weakly nonlinear wave packets described by the dK-dV equation are succinctly outlined by deriving a nonlinear Schrödinger-like equation with a complex nonlinear coefficient.

  5. Universal power law for the spectrum of breaking Riemann waves

    NASA Astrophysics Data System (ADS)

    Pelinovsky, Dmitry; Pelinovsky, Efim; Kartashova, Elena; Talipova, Tatiana

    2014-05-01

    The universal power law for the spectrum of one-dimensional breaking Riemann waves is justified for the simple wave equation with arbitrary nonlinearity. This equation describe the long surface and internal wave in the coastal zone. The spectrum of spatial amplitudes at the breaking time has an power asymptotic decay with exponent - 4/3. This spectrum is formed by the singularity of the form like x1/3 in the wave shape at the breaking time. In addition, we demonstrate numerically that the universal power law is observed for long time in the range of small wave numbers if small dissipation or dispersion is accounted in the viscous Burgers or Korteweg-de Vries equations.

  6. Numerical simulations of Kadomtsev-Petviashvili soliton interactions

    NASA Astrophysics Data System (ADS)

    Infeld, E.; Senatorski, A.; Skorupski, A. A.

    1995-04-01

    The Kadomtsev-Petviashvili equation generalizes that of Korteweg and de Vries to two space dimensions and arises in various weakly dispersive media. Two very different species of soliton solutions are known for one variant, KPI. The first species to be discovered are line solitons, the second are two dimensional lumps. This paper describes numerical simulations, consistent with all constraints of the equation, in which very distorted line solitons break up into smaller line solitons and arrays of lumps. The arrays can interact with one another. In some cases, aspects of the results of the simulations can be understood in the light of specially constructed exact solutions. Simulations in which initial conditions fail to satisfy the constraints of the equation are also described.

  7. Beyond the KdV: Post-explosion development

    NASA Astrophysics Data System (ADS)

    Ostrovsky, L.; Pelinovsky, E.; Shrira, V.; Stepanyants, Y.

    2015-09-01

    Several threads of the last 25 years' developments in nonlinear wave theory that stem from the classical Korteweg-de Vries (KdV) equation are surveyed. The focus is on various generalizations of the KdV equation which include higher-order nonlinearity, large-scale dispersion, and a non-local integral dispersion. We also discuss how relatively simple models can capture strongly nonlinear dynamics and how various modifications of the KdV equation lead to qualitatively new, non-trivial solutions and regimes of evolution observable in the laboratory and in nature. As the main physical example, we choose internal gravity waves in the ocean for which all these models are applicable and have genuine importance. We also briefly outline the authors' view of the future development of the chosen lines of nonlinear wave theory.

  8. Stability of periodic waves generated by long-wavelength instabilities in isotropic and anisotropic systems

    NASA Astrophysics Data System (ADS)

    Bar, Doron E.; Nepomnyashchy, Alexander A.

    1999-08-01

    We consider spontaneous generation of long waves in the presence of a conservation law in both cases of isotropic systems (e.g., Bénard-Marangoni waves) and anisotropic systems (e.g., waves in a film on an inclined plane). We found that near the instability threshold the problem is governed by the dissipation-modified Kadomtsev-Petviashvili equation in the former case and by the anisotropic dissipation-modified Korteweg-de Vries equation in the latter case. In frames of the derived 2+1-dimensional amplitude equations, we investigate the stability of one-dimensional waves. In isotropic systems the one-dimensional waves turned out to be always unstable with respect to a long-wave transverse modulation of the front. In anisotropic systems, only the one-dimensional periodic waves moving in the most preferred direction are found to be stable. Any deviation from this direction leads to instability of such an oblique wave.

  9. A note on the cylindrical solitary waves in an electron-acoustic plasma with vortex electron distribution

    SciTech Connect

    Demiray, Hilmi; Bayındır, Cihan

    2015-09-15

    In the present work, we consider the propagation of nonlinear electron-acoustic non-planar waves in a plasma composed of a cold electron fluid, hot electrons obeying a trapped/vortex-like distribution, and stationary ions. The basic nonlinear equations of the above described plasma are re-examined in the cylindrical coordinates through the use reductive perturbation method in the long-wave approximation. The modified cylindrical Korteweg-de Vries equation with fractional power nonlinearity is obtained as the evolution equation. Due to the nature of nonlinearity, which is fractional, this evolution equation cannot be reduced to the conventional Korteweg–de Vries equation. An analytical solution to the evolution equation, by use of the method developed by Demiray [Appl. Math. Comput. 132, 643 (2002); Comput. Math. Appl. 60, 1747 (2010)] and a numerical solution by employing a spectral scheme are presented and the results are depicted in a figure. The numerical results reveal that both solutions are in good agreement.

  10. Some Comments on the Use of de Moivre's Theorem to Solve Quadratic Equations with Real or Complex Coefficients

    ERIC Educational Resources Information Center

    Bardell, Nicholas S.

    2014-01-01

    This paper describes how a simple application of de Moivre's theorem may be used to not only find the roots of a quadratic equation with real or generally complex coefficients but also to pinpoint their location in the Argand plane. This approach is much simpler than the comprehensive analysis presented by Bardell (2012, 2014), but it does not…

  11. Global classical solutions to the one-dimensional compressible fluid models of Korteweg type with large initial data

    NASA Astrophysics Data System (ADS)

    Chen, Zhengzheng; Chai, Xiaojuan; Dong, Boqing; Zhao, Huijiang

    2015-10-01

    This paper is concerned with the global existence of classical solutions with large initial data away from vacuum to the Cauchy problem of the one-dimensional isothermal compressible fluid models of Korteweg type with density-dependent viscosity coefficient and capillarity coefficient. The case when the viscosity coefficient μ (ρ) =ρα and the capillarity coefficient κ (ρ) =ρβ for some parameters α, β ∈ R is considered. Under some conditions on α, β, we first show the global existence of large solutions around constant states if the far-fields of the initial data are the same, while if the far-fields of the initial data are different, we prove the global stability of rarefaction waves with large strength. Here global stability means the initial perturbation can be arbitrarily large. Our analysis is based on the elementary energy method and the technique developed by Y. Kanel' [29].

  12. Dirac equation for massive neutrinos in a Schwarzschild-de Sitter spacetime from a 5D vacuum

    NASA Astrophysics Data System (ADS)

    Sánchez, Pablo Alejandro; Anabitarte, Mariano; Bellini, Mauricio

    2011-11-01

    Starting from a Dirac equation for massless neutrino in a 5D Ricci-flat background metric, we obtain the effective 4D equation for massive neutrino in a Schwarzschild-de Sitter (SdS) background metric from an extended SdS 5D Ricci-flat metric. We use the fact that the spin connection is defined to an accuracy of a vector, so that the covariant derivative of the spinor field is strongly dependent of the background geometry. We show that the mass of the neutrino can be induced from the extra space-like dimension.

  13. Spin field equations and Heun's equations

    NASA Astrophysics Data System (ADS)

    Jiang, Min; Wang, Xuejing; Li, Zhongheng

    2015-06-01

    The Kerr-Newman-(anti) de Sitter metric is the most general stationary black hole solution to the Einstein-Maxwell equation with a cosmological constant. We study the separability of the equations of the massless scalar (spin s=0), neutrino ( s=1/2), electromagnetic ( s=1), Rarita-Schwinger ( s=3/2), and gravitational ( s=2) fields propagating on this background. We obtain the angular and radial master equations, and show that the master equations are transformed to Heun's equation. Meanwhile, we give the condition of existence of event horizons for Kerr-Newman-(anti) de Sitter spacetime by using Sturm theorem.

  14. The characteristics of ion acoustic shock waves in non-Maxwellian plasmas with ( G'/ G)-expansion method

    NASA Astrophysics Data System (ADS)

    Mehdipoor, M.

    2012-03-01

    Korteweg-de-Vries-Burger (K-dVB) equation is derived for ion acoustic shock waves in electron-positron-ion plasmas. Electrons and positrons are considered superthermal and are effectively modeled by a kappa distribution in which ions are as cold fluid. The analytical traveling wave solutions of the K-dVB equation investigated, through the ( G'/ G)-expansion method. These traveling wave solutions are expressed by hyperbolic function, trigonometric functions are rational functions. When the parameters are taken special values, the shock waves are derived from the traveling waves. It is observed that the amplitude ion acoustic shock waves increase as spectral index κ and kinematic viscosity η i,0 increases in which with increasing positron density β and electron temperature σ the shock amplitude decreases. Also, numerically the effect different parameters on the nonlinearity A and dispersive B terms and wave velocity V investigated.

  15. Propagation of ion acoustic shock waves in negative ion plasmas with nonextensive electrons

    SciTech Connect

    Hussain, S.; Akhtar, N.; Mahmood, S.

    2013-09-15

    Nonlinear ion acoustic shocks (monotonic as well as oscillatory) waves in negative ion plasmas are investigated. The inertialess electron species are assumed to be nonthermal and follow Tsallis distribution. The dissipation in the plasma is considered via kinematic viscosities of both positive and negative ion species. The Korteweg-de Vries Burgers (KdVB) equation is derived using small amplitude reductive perturbation technique and its analytical solution is presented. The effects of variation of density and temperature of negative ions and nonthermal parameter q of electrons on the strength of the shock structures are plotted for illustration. The numerical solutions of KdVB equation using Runge Kutta method are obtained, and transition from oscillatory to monotonic shock structures is also discussed in detail for negative ions nonthermal plasmas.

  16. Planar and cylindrical magnetosonic solitary and shock waves in dissipative, hot electron-positron-ion plasma

    SciTech Connect

    Jehan, Nusrat; Mirza, Arshad M.; Salahuddin, M.

    2011-05-15

    Planar and cylindrical magnetosonic solitary and shock structures are studied in a hot and dissipative plasma consisting of electrons, positrons, and ions. By employing the reductive perturbative method, a modified Korteweg-de Vries Burgers (mKdVB) equation is derived in the limit of low frequency and long wavelength by taking into account viscous dissipation of the three species. The effects of variation of various plasma parameters on the profiles of planar and cylindrical solitary and shock structures are discussed. In the limit, when certain terms of the mKdVB equation are small enough to be treated as perturbation, analytical solutions are obtained and compared with the corresponding numerical ones.

  17. Nonlinear ion-acoustic waves in a degenerate plasma with nuclei of heavy elements

    SciTech Connect

    Hossen, M. A. Mamun, A. A.

    2015-10-15

    The ion-acoustic (IA) solitary waves propagating in a fully relativistic degenerate dense plasma (containing relativistic degenerate electron and ion fluids, and immobile nuclei of heavy elements) have been theoretically investigated. The relativistic hydrodynamic model is used to derive the Korteweg-de Vries (K-dV) equation by the reductive perturbation method. The stationary solitary wave solution of this K-dV equation is obtained to characterize the basic features of the IA solitary structures that are found to exist in such a degenerate plasma. It is found that the effects of electron dynamics, relativistic degeneracy of the plasma fluids, stationary nuclei of heavy elements, etc., significantly modify the basic properties of the IA solitary structures. The implications of this results in astrophysical compact objects like white dwarfs are briefly discussed.

  18. Propagation of shock waves through petroleum suspensions

    NASA Astrophysics Data System (ADS)

    Mukuk, K. V.; Makhkamov, S. M.; Azizov, K. K.

    1986-01-01

    Anomalous shock wave propagation through petroleum with a high paraffin content was studied in an attempt to confirm the theoretically predicted breakdown of a forward shock wave into oscillating waves and wave packets as well as individual solitons. Tests were performed in a shock tube at 10, 20, and 50 to 60 C, with pure kerosene as reference and with kerosene + 5, 10, 15, and 20% paraffin. The addition of paraffin was found to radically alter the rheodynamic characteristics of the medium and, along with it, the pattern of shock wave propagation. The integro-differential equation describing a one dimensional hydraulic shock process in viscoelastic fluids is reduced to the Burgers-Korteweg-deVries equation, which is solved numerically for given values of the system parameters. The results indicate that the theory of shock wave propagation through such an anomalous suspension must be modified.

  19. Nonlinear waves in coherently coupled Bose-Einstein condensates

    NASA Astrophysics Data System (ADS)

    Congy, T.; Kamchatnov, A. M.; Pavloff, N.

    2016-04-01

    We consider a quasi-one-dimensional two-component Bose-Einstein condensate subject to a coherent coupling between its components, such as realized in spin-orbit coupled condensates. We study how nonlinearity modifies the dynamics of the elementary excitations. The spectrum has two branches, which are affected in different ways. The upper branch experiences a modulational instability, which is stabilized by a long-wave-short-wave resonance with the lower branch. The lower branch is stable. In the limit of weak nonlinearity and small dispersion it is described by a Korteweg-de Vries equation or by the Gardner equation, depending on the value of the parameters of the system.

  20. No-hair theorems for analogue black holes

    NASA Astrophysics Data System (ADS)

    Michel, Florent; Parentani, Renaud; Zegers, Robin

    2016-03-01

    We show that transonic one-dimensional flows which are analogous to black holes obey no-hair theorems both at the level of linear perturbations and in nonlinear regimes. Considering solutions of the Gross-Pitaevskii (or Korteweg-de Vries) equation, we show that stationary flows which are asymptotically uniform on both sides of the horizon are stable and act as attractors. Using Whitham's modulation theory, we analytically characterize the emitted waves when starting from uniform perturbations. Numerical simulations confirm the validity of this approximation and extend the results to more general perturbations and to the (nonintegrable) cubic-quintic Gross-Pitaevskii equation. When considering time-reversed flows that correspond to white holes, the asymptotically uniform flows are unstable to sufficiently large perturbations and emit either a macroscopic undulation in the supersonic side or a nonlinear superposition of soliton trains.

  1. Dissipative dust-acoustic shock waves in a varying charge electronegative magnetized dusty plasma with trapped electrons

    NASA Astrophysics Data System (ADS)

    Bacha, Mustapha; Tribeche, Mouloud

    2016-08-01

    The combined effects of an oblique magnetic field and electron trapping on dissipative dust-acoustic waves are examined in varying charge electronegative dusty plasmas with application to the Halley Comet plasma (˜104 km from the nucleus). A weakly nonlinear analysis is carried out to derive a modified Korteweg-de Vries-Burger-like equation. Making use of the equilibrium current balance equation, the physically admissible values of the electron trapping parameter are first constrained. We then show that the Burger dissipative term is solely due to the dust charge variation process. It is found that an increase of the magnetic field obliqueness or a decrease of its magnitude renders the shock structure more dispersive.

  2. Head-on collisions of electrostatic solitons in multi-ion plasmas

    SciTech Connect

    Verheest, Frank; Hellberg, Manfred A.; Hereman, Willy A.

    2012-09-15

    Head-on collisions between two electrostatic solitons are dealt with by the Poincare-Lighthill-Kuo method of strained coordinates, for a plasma composed of a number of cold (positive and negative) ion species and Boltzmann electrons. The nonlinear evolution equations for both solitons and their phase shift due to the collision, resulting in time delays, are established. A Korteweg-de Vries description is the generic conclusion, except when the plasma composition is special enough to replace the quadratic by a cubic nonlinearity in the evolution equations, with concomitant repercussions on the phase shifts. Applications include different two-ion plasmas, showing positive or negative polarity solitons in the generic case. At critical composition, a combination of a positive and a negative polarity soliton is possible.

  3. Dust acoustic solitary wave with variable dust charge: Role of negative ions

    SciTech Connect

    Ghosh, Samiran

    2005-09-15

    The role of negative ions on small but finite amplitude dust acoustic solitary wave including the effects of high and low charging rates of dust grains compared to the dust oscillation frequency in electronegative dusty plasma is investigated. In the case of high charging rate, the solitary wave is governed by Korteweg-de Vries (KdV) equation, but in the case of low charging rate, it is governed by KdV equation with a linear damping term. Numerical investigations reveal that in both cases dust acoustic soliton sharpens (flatens) and soliton width decreases (increases) with the increase of negative-ion number density (temperature). Also, the negative ions reduce the damping rate.

  4. Solitary waves in particle beams

    SciTech Connect

    Bisognano, J.J.

    1996-07-01

    Since space charge waves on a particle beam exhibit both dispersive and nonlinear character, solitary waves or solitons are possible. Dispersive, nonlinear wave propagation in high current beams is found to be similar to ion-acoustic waves in plasmas with an analogy between Debye screening and beam pipe shielding. Exact longitudinal solitary wave propagation is found for potentials associated with certain transverse distributions which fill the beam pipe. For weak dispersion, the waves satisfy the Korteweg-deVries (KdV) equation, but for strong dispersion they exhibit breaking. More physically realizable distributions which do not fill the beam pipe are investigated and shown to also satisfy a KdV equation for weak dispersion if averaging over rapid transverse motion is physically justified. Scaling laws are presented to explore likely parameter regimes where these phenomena may be observed experimentally.

  5. New experimental capabilities and theoretical insights of high pressure compression waves

    SciTech Connect

    Orlikowski, D; Nguyen, J; Patterson, J R; Minich, R; Martin, L P; Holmes, N

    2007-07-20

    Currently there are three platforms that offer quasi-isentropic compression or ramp-wave compression (RWC): light-gas gun, magnetic flux (Z-pinch), and laser. We focus here on the light-gas gun technique and on some current theoretical insights from experimental data. A gradient impedance through the length of the impactor provides the pressure pulse upon impactor to the subject material. Applications and results are given concerning high-pressure strength and liquid to solid, phase transition of water plus its associated phase fraction history. We also introduce the Korteweg-deVries-Burgers equation as a means to understand the evolution these RWC waves that propagate through the thickness of the subject material. This equation has the necessary competition between non-linear, dispersion, and dissipation processes, which is shown through observed structures that are manifested in the experimental particle velocity histories. Such methodology points towards a possible quantifiable dissipation, through which RWC experiments may be analyzed.

  6. Nonlinear features of ion acoustic shock waves in dissipative magnetized dusty plasma

    SciTech Connect

    Sahu, Biswajit; Sinha, Anjana; Roychoudhury, Rajkumar

    2014-10-15

    The nonlinear propagation of small as well as arbitrary amplitude shocks is investigated in a magnetized dusty plasma consisting of inertia-less Boltzmann distributed electrons, inertial viscous cold ions, and stationary dust grains without dust-charge fluctuations. The effects of dissipation due to viscosity of ions and external magnetic field, on the properties of ion acoustic shock structure, are investigated. It is found that for small amplitude waves, the Korteweg-de Vries-Burgers (KdVB) equation, derived using Reductive Perturbation Method, gives a qualitative behaviour of the transition from oscillatory wave to shock structure. The exact numerical solution for arbitrary amplitude wave differs somehow in the details from the results obtained from KdVB equation. However, the qualitative nature of the two solutions is similar in the sense that a gradual transition from KdV oscillation to shock structure is observed with the increase of the dissipative parameter.

  7. Critical density solitary waves structures in a hot magnetized dusty plasma with vortexlike ion distribution in phase space

    SciTech Connect

    El-Labany, S.K.; El-Shamy, E.F.

    2005-04-15

    The nonlinear properties of solitary waves structures in a hot magnetized dusty plasma consisting of isothermal hot electrons, nonisothermal ions, and high negatively charged massive dust grains are reported. A modified Korteweg-de Vries (modified KdV) equation, which admits a solitary waves solution, for small but finite amplitude, is derived using a reductive perturbation theory. A nonisothermal ion distribution provides the possibility of existence of rarefactive solitary waves. On the other hand, the dynamics of solitary waves at a critical ion density is governed by KdV equation. The modification in the amplitude and width of the solitary waves structures due to the inclusion of obliqueness and external magnetic field are also investigated.

  8. Ion-acoustic compressive and rarefactive solitons in an electron-beam plasma system

    SciTech Connect

    Yadav, L.L.; Tiwari, R.S.; Sharma, S.R. )

    1994-03-01

    Using the general formulation of reductive perturbation method, the Korteweg--de Vries (KdV) equation is derived for an electron-beam plasma with hot isothermal beam and plasma electrons and warm ions. The soliton solution of the KdV equation is discussed in detail. It is found that above a critical velocity of electron-beam two additional ion-acoustic soliton branches appear. It is found that corresponding to two linear modes, the system supports the existence of compressive as well as rarefactive solitons depending upon the plasma parameters, while corresponding to other two wave modes, the system supports only rarefactive solitons. The effect of different parameters on the characteristics of solitons have been investigated in detail.

  9. Ion acoustic solitons in a solar wind magnetoplasma with Kappa distributed electrons

    NASA Astrophysics Data System (ADS)

    Devanandhan, Selvaraj; Singh, Satyavir; Singh Lakhina, Gurbax; Sreeraj, T.

    2016-07-01

    In many space plasma environments, the velocity distribution of particles often deviates from Maxwellian and is well-modelled by a kappa distribution function. We have analyzed the ion acoustic soliton in a magnetized consisting of plasma Protons, Helium ions, an electron beam and superthermal hot electrons following kappa distribution function. Under the assumption of weak nonlinearity, the ion-acoustic solitons are described by the Korteweg-de-Vries-Zakharov-Kuznetsov (KdV-ZK) equation. The solution of KdV-ZK equation is used to model the characteristics of the ion acoustic solitary waves in a solar wind magnetoplasma observed at 1 AU. We have found both slow and fast ion acoustic solitons in our study. It is found that the superthermality of hot electrons greatly influence the existence regime of the solitary waves. The numerical results of this study to explain solar wind observations will be discussed in detail.

  10. Soliton and kink jams in traffic flow with open boundaries.

    PubMed

    Muramatsu, M; Nagatani, T

    1999-07-01

    Soliton density wave is investigated numerically and analytically in the optimal velocity model (a car-following model) of a one-dimensional traffic flow with open boundaries. Soliton density wave is distinguished from the kink density wave. It is shown that the soliton density wave appears only at the threshold of occurrence of traffic jams. The Korteweg-de Vries (KdV) equation is derived from the optimal velocity model by the use of the nonlinear analysis. It is found that the traffic soliton appears only near the neutral stability line. The soliton solution is analytically obtained from the perturbed KdV equation. It is shown that the soliton solution obtained from the nonlinear analysis is consistent with that of the numerical simulation. PMID:11969749

  11. Nonlinear waves in nonplanar and nonuniform dusty plasmas

    SciTech Connect

    Xue Jukui; Zhang Liping

    2006-02-15

    The nonlinear properties of the dust acoustic solitary wave and shock wave in inhomogeneous nonplanar dusty plasmas are considered theoretically and numerically. The effects of nonthermally distributed ions, nonadiabatic dust charge fluctuation, and the inhomogeneity caused by nonuniform equilibrium particle density, nonuniform equilibrium charging, and nonplanar geometry on waves are presented. When {tau}{sub ch}/{tau}{sub d} is small but finite, where {tau}{sub ch} is the charging time scale and {tau}{sub d} is the hydrodynamical time scale, a variable coefficients nonplanar Korteweg-de Vries (KdV) Burgers equation governing the nonlinear waves is derived by the perturbation method. The analytical expressions for the evolution of soliton and shock wave (both oscillatory and monotone shock) are obtained and the theoretical results are confirmed by the numerical solution of the nonlinear wave equation.

  12. Fate of classical solitons in one-dimensional quantum systems.

    SciTech Connect

    Pustilnik, M.; Matveev, K. A.

    2015-11-23

    We study one-dimensional quantum systems near the classical limit described by the Korteweg-de Vries (KdV) equation. The excitations near this limit are the well-known solitons and phonons. The classical description breaks down at long wavelengths, where quantum effects become dominant. Focusing on the spectra of the elementary excitations, we describe analytically the entire classical-to-quantum crossover. We show that the ultimate quantum fate of the classical KdV excitations is to become fermionic quasiparticles and quasiholes. We discuss in detail two exactly solvable models exhibiting such crossover, the Lieb-Liniger model of bosons with weak contact repulsion and the quantum Toda model, and argue that the results obtained for these models are universally applicable to all quantum one-dimensional systems with a well-defined classical limit described by the KdV equation.

  13. On shallow water waves in a medium with time-dependent dispersion and nonlinearity coefficients.

    PubMed

    Abdel-Gawad, Hamdy I; Osman, Mohamed

    2015-07-01

    In this paper, we studied the progression of shallow water waves relevant to the variable coefficient Korteweg-de Vries (vcKdV) equation. We investigated two kinds of cases: when the dispersion and nonlinearity coefficients are proportional, and when they are not linearly dependent. In the first case, it was shown that the progressive waves have some geometric structures as in the case of KdV equation with constant coefficients but the waves travel with time dependent speed. In the second case, the wave structure is maintained when the nonlinearity balances the dispersion. Otherwise, water waves collapse. The objectives of the study are to find a wide class of exact solutions by using the extended unified method and to present a new algorithm for treating the coupled nonlinear PDE's. PMID:26199750

  14. Dispersive shock wave interactions and asymptotics.

    PubMed

    Ablowitz, Mark J; Baldwin, Douglas E

    2013-02-01

    Dispersive shock waves (DSWs) are physically important phenomena that occur in systems dominated by weak dispersion and weak nonlinearity. The Korteweg-de Vries (KdV) equation is the universal model for systems with weak dispersion and weak, quadratic nonlinearity. Here we show that the long-time-asymptotic solution of the KdV equation for general, steplike data is a single-phase DSW; this DSW is the "largest" possible DSW based on the boundary data. We find this asymptotic solution using the inverse scattering transform and matched-asymptotic expansions. So while multistep data evolve to have multiphase dynamics at intermediate times, these interacting DSWs eventually merge to form a single-phase DSW at large time. PMID:23496590

  15. Nonlinear ion-acoustic waves in a degenerate plasma with nuclei of heavy elements

    NASA Astrophysics Data System (ADS)

    Hossen, M. A.; Mamun, A. A.

    2015-10-01

    The ion-acoustic (IA) solitary waves propagating in a fully relativistic degenerate dense plasma (containing relativistic degenerate electron and ion fluids, and immobile nuclei of heavy elements) have been theoretically investigated. The relativistic hydrodynamic model is used to derive the Korteweg-de Vries (K-dV) equation by the reductive perturbation method. The stationary solitary wave solution of this K-dV equation is obtained to characterize the basic features of the IA solitary structures that are found to exist in such a degenerate plasma. It is found that the effects of electron dynamics, relativistic degeneracy of the plasma fluids, stationary nuclei of heavy elements, etc., significantly modify the basic properties of the IA solitary structures. The implications of this results in astrophysical compact objects like white dwarfs are briefly discussed.

  16. Ion-acoustic shocks in quantum electron-positron-ion plasmas

    SciTech Connect

    Roy, K.; Misra, A. P.; Chatterjee, P.

    2008-03-15

    Nonlinear propagation of quantum ion-acoustic waves (QIAWs) in a dense quantum plasma whose constituents are electrons, positrons, and positive ions is investigated using a quantum hydrodynamic model. The standard reductive perturbation technique is used to derive the Korteweg-de Vries-Burger (KdVB) equation for QIAWs. It is shown by numerical simulation that the KdVB equation has either oscillatory or monotonic shock wave solutions depending on the system parameters H proportional to quantum diffraction, {mu}{sub i} the effect of ion kinematic viscosity, and {mu} the equilibrium electron to ion density ratio. The results may have relevance in dense astrophysical plasmas (such as neutron stars) as well as in intense laser solid density plasma experiments where the particle density is about 10{sup 25}-10{sup 28} m{sup -3}.

  17. Implosion and explosion of electrostatic cylindrical and spherical shocks in asymmetric pair-ion plasmas

    SciTech Connect

    Masood, W.; Rizvi, H.

    2011-04-15

    Nonlinear electrostatic shock waves are studied in unmagnetized, dissipative pair-ion plasmas. The dissipation in the system is taken into account by considering the effect of kinematic viscosity of both positive and negative ions in plasmas. The system of fluid equations for asymmetric pair-ion plasma is reduced to Korteweg-deVries-Burgers equation in the limit of small amplitude perturbation. It is observed that the system under consideration admits rarefactive shocks. Keeping in view the practical applications, the nonlinear propagation of both the exploding and imploding shocks is investigated and the differences are expounded in detail. The present study may have relevance in the study of the formation of electrostatic shocks in laser-induced implosion devices, star formation, supernovae explosion, etc.

  18. Oblique shock waves in a two electron temperature superthermally magnetized plasma

    NASA Astrophysics Data System (ADS)

    Bains, A. S.; Panwar, A.; Ryu, C. M.

    2015-11-01

    A study is presented for the oblique propagation of low-frequency ion acoustic ( IA) shock waves in a magnetized plasma consisting of cold ions and two temperature superthermally distributed electrons. A nonlinear Korteweg de-Vries-Burger ( KdV-Burger) equation is obtained by using the reductive perturbation method (RPM) which governs the dynamics of the IA shock wave. Using the solution of KdV-Burger equation, the characteristics of the IA shock wave have been studied for various plasma parameters. The combined effects of the cold to hot electron temperature ratio (σ), the density ratio of hot electrons to ions (f), the superthermality of cold and hot electrons (κc, κh), the strength of the magnetic field (ω_{ci}), and the obliqueness (θ), significantly influence the profile of the shock wave. The findings in the present study could be important for the electrostatic wave structures in the Saturn's magnetosphere, where two temperature electrons exist with a kappa distribution.

  19. Conditions for reflection and transmission of an ion acoustic soliton in a dusty plasma with variable charge dust

    SciTech Connect

    Malik, Hitendra K.; Tomar, Renu; Dahiya, Raj P.

    2014-07-15

    Modified Korteweg-de Vries (mKdV) equations are derived for the incident, reflected, and transmitted waves in order to examine the soliton reflection and its transmission through an inhomogeneous plasma comprising ions, dust grains with fluctuating charge and two types of electrons, namely nonisothermal electrons and isothermal electrons. All the mKdV equations are coupled at the point of reflection and solved for the reflected soliton. Unlike others, a relation is established between the velocity shifts of the incident, reflected and transmitted solitons, and based on a critical value of the shift of incident soliton the strengths of the soliton reflection and transmission are talked about. Conditions are obtained for the soliton reflection and its transmission, and a comparative study is made for the two cases of fixed and fluctuating charges on the dust grains.

  20. Ion acoustic solitary waves in plasmas with nonextensive electrons, Boltzmann positrons and relativistic thermal ions

    NASA Astrophysics Data System (ADS)

    Hafez, M. G.; Talukder, M. R.

    2015-09-01

    This work investigates the theoretical and numerical studies on nonlinear propagation of ion acoustic solitary waves (IASWs) in an unmagnetized plasma consisting of nonextensive electrons, Boltzmann positrons and relativistic thermal ions. The Korteweg-de Vries (KdV) equation is derived by using the well known reductive perturbation method. This equation admits the soliton like solitary wave solution. The effects of phase velocity, amplitude of soliton, width of soliton and electrostatic nonlinear propagation of weakly relativistic ion-acoustic solitary waves have been discussed with graphical representation found in the variation of the plasma parameters. The obtained results can be helpful in understanding the features of small but finite amplitude localized relativistic ion-acoustic waves for an unmagnetized three component plasma system in astrophysical compact objects.

  1. New exact solutions for nonlinear solitary waves in Thomas-Fermi plasmas with ( G'/ G)-expansion method

    NASA Astrophysics Data System (ADS)

    Mehdipoor, M.; Neirameh, A.

    2012-01-01

    The nonlinear propagation of ion acoustic waves in an ideal plasmas containing degenerate electrons is investigated. The Korteweg-de-Vries (K-dV) equation is derived for ion acoustic waves by using reductive perturbation method. The analytical traveling wave solutions of the K-dV equation investigated, through the ( G'/ G)-expansion method. These traveling wave solutions are expressed by hyperbolic function, trigonometric functions are rational functions. When the parameters are taken special values, the solitary waves are derived from the traveling waves. Also, numerically the effect different parameters on these solitary waves investigated and it is seen that exist only the compressive solitary waves in Thomas-Fermi plasmas.

  2. Dust-acoustic solitary waves in a magnetized opposite polarity dust-plasma medium

    NASA Astrophysics Data System (ADS)

    Mamun, A. A.; Ferdousi, M.; Sultana, S.

    2015-08-01

    The basic features of obliquely propagating dust-acoustic (DA) solitary waves (SWs) in a three-component magnetized dusty plasma (containing inertial negatively as well as positively charged dust grains, and nonextensive ions) have been theoretically investigated. The reductive perturbation technique is employed in order to derive the Korteweg-de Vries (K-dV) equation. The stationary solitary wave solution of the K-dV equation, which describes the characteristics of SWs associated with ultra-low-frequency, long wavelength DA waves, is obtained and numerically analyzed. It is observed that the basic characteristics (polarity, amplitude, width, speed, etc) of the DA SWs are significantly modified by the effects of ion nonextensivity, external magnetic field, and angle between the directions of external magnetic field and wave propagation. The findings of this investigation may be used in understanding the wave propagation in space and laboratory plasmas in which dust of opposite polarity coexists.

  3. Nonplanar shocks in a warm electronegative plasma with electron nonextensivity effects

    NASA Astrophysics Data System (ADS)

    Ali Shan, S.; Ali, S.; Aman-ur-Rehman

    2014-09-01

    By employing the reductive perturbation technique, nonlinear cylindrical and spherical Korteweg-de Vries Burgers (KdVB) equation is derived for ion acoustic shock waves in an unmagnetized electronegative plasma. The latter is composed of warm positive and warm negative ions as well as q-distributed nonextensive electrons. Numerically, the modified KdVB equation is solved to examine the impact of nonthermal electrons on the profiles of nonplanar fast ion acoustic shocks. With the help of experimental parameters, it is found that the variations of different quantities, like q (nonextensive parameter), α (the negative-to-positive ion mass ratio), μ (the electron-to-positive ion density ratio) and θ i (the positive ion-to-electron temperature ratio), η i0, n0 (the positive/negative ion viscosities) significantly modify the propagation characteristics of nonplanar shocks in electronegative plasmas. The relevance to a laboratory experiment is highlighted, where positive and negative ions are present.

  4. Nonlinear oscillatory and monotonic shocks in dense plasmas with ultra-relativistic degenerate electrons

    NASA Astrophysics Data System (ADS)

    Hussain, S.; Rehman, Aman-ur; Hasnain, H.; Mustafa, N.

    2015-09-01

    In this paper we study the ion acoustic oscillatory and monotonic shocks in dissipative homogeneous magnetized plasmas. The dissipation in the plasma system is considered via kinematic viscosity of ions and quantum effects are included through degeneracy pressure of ultra-relativistic electrons. Korteweg de Vries Burgers (KdVB) equation is derived by using reductive perturbation method. Numerical and analytical solutions of KdVB equation are presented. The transition from oscillatory profile to monotonic shock are studied numerically at different values of kinematic viscosity. We also analyzed the effects of variations of different plasma parameters on the strength of the shock structure in dense plasmas. The relevance of the work to astrophysical plasma conditions such as in compact stars is also pointed out.

  5. Nonlinear features of ion acoustic shock waves in dissipative magnetized dusty plasma

    NASA Astrophysics Data System (ADS)

    Sahu, Biswajit; Sinha, Anjana; Roychoudhury, Rajkumar

    2014-10-01

    The nonlinear propagation of small as well as arbitrary amplitude shocks is investigated in a magnetized dusty plasma consisting of inertia-less Boltzmann distributed electrons, inertial viscous cold ions, and stationary dust grains without dust-charge fluctuations. The effects of dissipation due to viscosity of ions and external magnetic field, on the properties of ion acoustic shock structure, are investigated. It is found that for small amplitude waves, the Korteweg-de Vries-Burgers (KdVB) equation, derived using Reductive Perturbation Method, gives a qualitative behaviour of the transition from oscillatory wave to shock structure. The exact numerical solution for arbitrary amplitude wave differs somehow in the details from the results obtained from KdVB equation. However, the qualitative nature of the two solutions is similar in the sense that a gradual transition from KdV oscillation to shock structure is observed with the increase of the dissipative parameter.

  6. Nonlinear ion-acoustic structures in dusty plasma with superthermal electrons and positrons

    SciTech Connect

    El-Tantawy, S. A.; El-Bedwehy, N. A.; Moslem, W. M.

    2011-05-15

    Nonlinear ion-acoustic structures are investigated in an unmagnetized, four-component plasma consisting of warm ions, superthermal electrons and positrons, as well as stationary charged dust impurities. The basic set of fluid equations is reduced to modified Korteweg-de Vries equation. The latter admits both solitary waves and double layers solutions. Numerical calculations indicate that these nonlinear structures cannot exist for all physical parameters. Therefore, the existence regions for both solitary and double layers excitations have been defined precisely. Furthermore, the effects of temperature ratios of ions-to-electrons and electrons-to-positrons, positrons and dust concentrations, as well as superthermal parameters on the profiles of the nonlinear structures are investigated. Also, the acceleration and deceleration of plasma species have been highlight. It is emphasized that the present investigation may be helpful in better understanding of nonlinear structures which propagate in astrophysical environments, such as in interstellar medium.

  7. Dust acoustic shock wave in electronegative dusty plasma: Roles of weak magnetic field

    SciTech Connect

    Ghosh, Samiran; Ehsan, Z.; Murtaza, G.

    2008-02-15

    The effects of nonsteady dust charge variations and weak magnetic field on small but finite amplitude nonlinear dust acoustic wave in electronegative dusty plasma are investigated. The dynamics of the nonlinear wave are governed by a Korteweg-de Vries Burger equation that possesses dispersive shock wave. The weak magnetic field is responsible for the dispersive term, whereas nonsteady dust charge variation is responsible for dissipative term, i.e., the Burger term. The coefficient of dissipative term depends only on the obliqueness of the magnetic field. It is found that for parallel propagation the dynamics of the nonlinear wave are governed by the Burger equation that possesses monotonic shock wave. The relevances of the findings to cometary dusty plasma, e.g., Comet Halley are briefly discussed.

  8. Comparing the full time-dependent Bogoliubov-de-Gennes equations to their linear approximation: a numerical investigation

    NASA Astrophysics Data System (ADS)

    Hainzl, Christian; Seyrich, Jonathan

    2016-05-01

    In this paper we report on the results of a numerical study of the nonlinear time-dependent Bardeen-Cooper-Schrieffer (BCS) equations, often also denoted as Bogoliubov-de-Gennes (BdG) equations, for a one-dimensional system of fermions with contact interaction. We show that, even above the critical temperature, the full equations and their linear approximation give rise to completely different evolutions. In contrast to its linearization, the full nonlinear equation does not show any diffusive behavior in the order parameter. This means that the order parameter does not follow a Ginzburg-Landau-type of equation, in accordance with a recent theoretical result in [R.L. Frank, C. Hainzl, B. Schlein, R. Seiringer, to appear in Lett. Math. Phys., arXiv:1504.05885 (2016)]. We include a full description on the numerical implementation of the partial differential BCS/BdG equations.

  9. [Destruction of radioactive particles by strains of Cladosporium cladosporoides (FRES.) de Vries].

    PubMed

    Zhdanova, N N; Redchits, T I; Lashko, T N; Zheltonozhskiĭ, V A; Sadovnikov, L V

    2002-01-01

    Reactions on the ionizing radiation of 14 Cladosporium cladosporioides strains were studied. Only 5 of them displayed radiotropizm. The ability of C. cladosporioides strains 4 and 5 with positive radiotropizm and museum C. cladosporioides strain 396 and its alb-mutant SM without positive radiotropizm to destruct radioactive particles of Chernobyl and explosion origin was studied. Two ways of radioactive particles destruction by C. cladosporioides were established, one of them is a direct way by fungal overgrowth of hot particles and the second one an indirect way only by fungal metabolites. Mycelium of the studied C. cladosporioides strains sorbed radionuclides from radioactive particles during cultivation on the liquid and agarized media. No certain inclinations of the individual strains to accumulation of radionuclides 137Cs or 152Eu were ascertained. PMID:12664550

  10. Promising Practices Supporting Low-Income, First-Generation Students at DeVry University

    ERIC Educational Resources Information Center

    Miller, Abby; Taylor Smith, Chandra; Nichols, Andrew

    2011-01-01

    This paper offers a comprehensive description of the academic and social support systems for low-income, first-generation students attending a major four-year, for-profit, multi-campus university. College retention and success research has determined that effective support services succeed in retaining and graduating low-income, first-generation…

  11. Piaget-Based Curriculum for Early Childhood Education: The Kamii-DeVries Approach.

    ERIC Educational Resources Information Center

    Kamii, Constance; DeVries, Rheta

    An outline for Piaget-based early childhood education curricula is presented. Long term objectives of the curriculum are the facilitation of moral and social growth, and intellectual development leading to formal operational functioning. Education is seen as a process that encourages creative and critical thinking. Short-term objectives are listed…

  12. The extended Estabrook-Wahlquist method

    NASA Astrophysics Data System (ADS)

    Choudhury, S. Roy; Russo, Matthew

    2016-07-01

    Variable Coefficient Korteweg de Vries (vcKdV), modified Korteweg de Vries (vcMKdV), and nonlinear Schrödinger (NLS) equations have a long history dating from their derivation in various applications. A technique based on extended Lax Pairs has been devised recently to derive time-and-space-dependent-coefficient generalizations of various such Lax-integrable NLPDE hierarchies, which are thus more general than almost all cases considered earlier via methods such as the Painlevé Test, Bell Polynomials, and similarity methods. However, this technique, although operationally effective, has the significant disadvantage that, for any integrable system with spatiotemporally varying coefficients, one must 'guess' a generalization of the structure of the known Lax Pair for the corresponding system with constant coefficients. Motivated by the somewhat arbitrary nature of the above procedure, we embark in this paper on an attempt to systematize the derivation of Lax-integrable systems with variable coefficients. We consider the Estabrook-Wahlquist (EW) prolongation technique, a relatively self-consistent procedure requiring little prior information. However, this immediately requires that the technique be significantly generalized in several ways, including solving matrix partial differential equations instead of algebraic ones as the structure of the Lax Pair is systematically computed, and also in solving the constraint equations to deduce the explicit forms for various 'coefficient' matrices. The new and extended EW technique which results is illustrated by algorithmically deriving generalized Lax-integrable versions of the NLS, generalized fifth-order KdV, MKdV, and derivative nonlinear Schrödinger (DNLS) equations. We also show how this method correctly excludes the existence of a nontrivial Lax pair for a nonintegrable NLPDE such as the variable-coefficient cubic-quintic NLS.

  13. Class of solutions of the Wheeler-DeWitt equation in the Friedmann-Robertson-Walker universe

    NASA Astrophysics Data System (ADS)

    Vieira, H. S.; Bezerra, V. B.

    2016-07-01

    We show that the solutions of the Wheeler-DeWitt equation in a homogeneous and isotropic universe are given by triconfluent Heun functions for the spatially closed, flat, and open geometries of the Friedmann-Robertson-Walker universe filled with different forms of energy. In a matter-dominated universe, we find the polynomial solution and the energy density spectrum. In the cases of radiation-dominated and vacuum universes, there are no polynomial solutions as shown.

  14. Dust acoustic double layers in a magnetized dusty self-gravitating plasma with superthermal particles

    NASA Astrophysics Data System (ADS)

    Sabetkar, Akbar; Dorranian, Davoud

    2016-08-01

    Our prime objective of this paper is to examine the parametric regimes for the existence and polarity of dust acoustic double layers (DADLs) and its solitary structures arising from a magnetized self-gravitating opposite polarity dust-plasma (OPDP) model. The constituents of the OPDP model are two species of positively and negatively charged dust grains, Maxwellian electrons and kappa distributed ions. Contributions of gravitational force only on dust grains are taken into account. For weakly nonlinear analysis, the multiple time scale technique has been used to construct the extended Korteweg-de Vries (E-KdV) and modified Korteweg-de Vries (M-KdV) equations. They pinpoint the evolution of DADLs and solitary structures associated with dust acoustic (DA) mode, respectively. The relevant configurational parameters in our study include the superthermality of ions (κ), obliqueness of propagation (θ), ion concentration (δi), static magnetic field B0 (via ω c p , ω c n ), and self-gravitational field (via γ), as well as the density (μ0), charge (α), and mass (β) ratio of positive to negative dust species. The proposed OPDP model permits positive and negative double layer polarities, while higher order nonlinear equation dictates us only positive polarity solitary structures. The main modification due to an increase in self-gravitational field (via γ) is an enhancement in the spatial width of double layers, yet leaving their amplitude, phase speed, and polarity practically unaffected. With enhanced superthermality and other intrinsic parameters in OPDP model, there is an opposite trend in both amplitude and width of double layers, while the amplitude and the width of solitary waves (via M-KdV equation) undergo the identical behaviors. In particular, the amplitude of solitary waves manifests monotonic behavior for permissible range of obliqueness θ, whereas this scenario is acceptable to only width of double layers. The results are discussed in the context of

  15. VEGFR tyrosine kinase inhibitor II (VRI) induced vascular insufficiency in zebrafish as a model for studying vascular toxicity and vascular preservation

    SciTech Connect

    Li, Shang; Dang, Yuan Ye; Oi Lam Che, Ginny; Kwan, Yiu Wa; Chan, Shun Wan; Leung, George Pak Heng; Lee, Simon Ming Yuen; Hoi, Maggie Pui Man

    2014-11-01

    In ischemic disorders such as chronic wounds and myocardial ischemia, there is inadequate tissue perfusion due to vascular insufficiency. Besides, it has been observed that prolonged use of anti-angiogenic agents in cancer therapy produces cardiovascular toxicity caused by impaired vessel integrity and regeneration. In the present study, we used VEGFR tyrosine kinase inhibitor II (VRI) to chemically induce vascular insufficiency in zebrafish in vivo and human umbilical vein endothelial cells (HUVEC) in vitro to further study the mechanisms of vascular morphogenesis in these pathological conditions. We also explored the possibility of treating vascular insufficiency by enhancing vascular regeneration and repair with pharmacological intervention. We observed that pretreatment of VRI induced blood vessel loss in developing zebrafish by inhibiting angiogenesis and increasing endothelial cell apoptosis, accompanied by down-regulation of kdr, kdrl and flt-1 genes expression. The VRI-induced blood vessel loss in zebrafish could be restored by post-treatment of calycosin, a cardiovascular protective isoflavone. Similarly, VRI induced cytotoxicity and apoptosis in HUVEC which could be rescued by calycosin post-treatment. Further investigation of the underlying mechanisms showed that the PI3K/AKT/Bad cell survival pathway was a main contributor of the vascular regenerative effect of calycosin. These findings indicated that the cardiovascular toxicity in anti-angiogenic therapy was mainly caused by insufficient endothelial cell survival, suggesting its essential role in vascular integrity, repair and regeneration. In addition, we showed that VRI-induced blood vessel loss in zebrafish represented a simple and effective in vivo model for studying vascular insufficiency and evaluating cancer drug vascular toxicities. - Highlights: • In vivo VRI model • Rescue effects of calycosin • Calycosin EC survival pathways.

  16. Effects of plasma particle trapping on dust-acoustic solitary waves in an opposite polarity dust-plasma medium

    SciTech Connect

    Ahmad, Zulfiqar; Mushtaq, A.; Mamun, A. A.

    2013-03-15

    Dust acoustic solitary waves in a dusty plasma containing dust of opposite polarity (adiabatic positive and negative dust), non-isothermal electrons and ions (following vortex like distribution) are theoretically investigated by employing pseudo-potential approach, which is valid for arbitrary amplitude structures. The propagation of small but finite amplitude solitary structures is also examined by using the reductive perturbation method. The basic properties of large (small) amplitude solitary structures are investigated by analyzing the energy integral (modified Korteweg-de Vries equation). It is shown that the effects of dust polarity, trapping of plasma particles (electrons and ions), and temperatures of dust fluids significantly modify the basic features of the dust-acoustic solitary structures that are found to exist in such an opposite polarity dust-plasma medium. The relevance of the work in opposite polarity dust-plasma, which may occur in cometary tails, upper mesosphere, Jupiter's magnetosphere, is briefly discussed.

  17. Ion-acoustic shock waves in a plasma with weakly relativistic warm ions, thermal positrons and a background electron nonextensivity

    NASA Astrophysics Data System (ADS)

    Tribeche, Mouloud; Pakzad, Hamid Reza

    2012-06-01

    A weakly nonlinear analysis is carried out to derive a Korteweg-de Vries-Burgers-like equation for small, but finite amplitude, ion-acoustic waves in a dissipative plasma consisting of weakly relativistic ions, thermal positrons and nonextensive electrons. The travelling wave solution has been acquired by employing the tangent hyperbolic method. Our results show that in a such plasma, ion-acoustic shock waves, the strength and steepness of which are significantly modified by relativistic, nonextensive and dissipative effects, may exist. Interestingly, we found that because of ion kinematic viscosity, an initial solitonic profile develops into a shock wave. This later evolves towards a monotonic profile (dissipation-dominant case) as the electrons deviate from their Maxwellian equilibrium. Our investigation may help to understand the dissipative structures that may occur in high-energy astrophysical plasmas.

  18. Ion-acoustic cnoidal waves in a quantum plasma

    SciTech Connect

    Mahmood, S.; Haas, F.

    2014-10-15

    Nonlinear ion-acoustic cnoidal wave structures are studied in an unmagnetized quantum plasma. Using the reductive perturbation method, a Korteweg-de Vries equation is derived for appropriate boundary conditions and nonlinear periodic wave solutions are obtained. The corresponding analytical solution and numerical plots of the ion-acoustic cnoidal waves and solitons in the phase plane are presented using the Sagdeev pseudo-potential approach. The variations in the nonlinear potential of the ion-acoustic cnoidal waves are studied at different values of quantum parameter H{sub e} which is the ratio of electron plasmon energy to electron Fermi energy defined for degenerate electrons. It is found that both compressive and rarefactive ion-acoustic cnoidal wave structures are formed depending on the value of the quantum parameter. The dependence of the wavelength and frequency on nonlinear wave amplitude is also presented.

  19. Nonlinear coupling of acoustic and shear mode in a strongly coupled dusty plasma with a density dependent viscosity

    NASA Astrophysics Data System (ADS)

    Garai, S.; Janaki, M. S.; Chakrabarti, N.

    2016-09-01

    The nonlinear propagation of low frequency waves, in a collisionless, strongly coupled dusty plasma (SCDP) with a density dependent viscosity, has been studied with a proper Galilean invariant generalized hydrodynamic (GH) model. The well known reductive perturbation technique (RPT) has been employed in obtaining the solutions of the longitudinal and transverse perturbations. It has been found that the nonlinear propagation of the acoustic perturbations govern with the modified Korteweg-de Vries (KdV) equation and are decoupled from the sheared fluctuations. In the regions, where transversal gradients of the flow exists, coupling between the longitudinal and transverse perturbations occurs due to convective nonlinearity which is true for the homogeneous case also. The results, obtained here, can have relative significance to astrophysical context as well as in laboratory plasmas.

  20. Dissipative solitons in pair-ion plasmas

    SciTech Connect

    Ghosh, Samiran; Adak, Ashish Khan, Manoranjan

    2014-01-15

    The effects of ion-neutral collisions on the dynamics of the nonlinear ion acoustic wave in pair-ion plasma are investigated. The standard perturbative approach leads to a Korteweg-de Vries equation with a linear damping term for the dynamics of the finite amplitude wave. The ion-neutral collision induced dissipation is responsible for the linear damping. The analytical solution and numerical simulation reveal that the nonlinear wave propagates in the form of a weakly dissipative compressive solitons. Furthermore, the width of the soliton is proportional to the amplitude of the wave for fixed soliton velocity. Results are discussed in the context of the fullerene pair-ion plasma experiment.

  1. Observation of dust acoustic shock wave in a strongly coupled dusty plasma

    NASA Astrophysics Data System (ADS)

    Sharma, Sumita K.; Boruah, A.; Nakamura, Y.; Bailung, H.

    2016-05-01

    Dust acoustic shock wave is observed in a strongly coupled laboratory dusty plasma. A supersonic flow of charged microparticles is allowed to perturb a stationary dust fluid to excite dust acoustic shock wave. The evolution process beginning with steepening of initial wave front and then formation of a stable shock structure is similar to the numerical results of the Korteweg-de Vries-Burgers equation. The measured Mach number of the observed shock wave agrees with the theoretical results. Reduction of shock amplitude at large distances is also observed due to the dust neutral collision and viscosity effects. The dispersion relation and the spatial damping of a linear dust acoustic wave are also measured and compared with the relevant theory.

  2. On the problem of periodicity and hidden solitons for the KdV model.

    PubMed

    Engelbrecht, Jüri; Salupere, Andrus

    2005-03-01

    In continuum limit, the Fermi-Pasta-Ulam lattice is modeled by a Korteweg-de Vries (KdV) equation. It is shown that the long-time behavior of a KdV soliton train emerging from a harmonic excitation has a regular periodicity of right- and left-going trajectories. In a soliton train not all the solitons are visible, the solitons with smaller amplitude are hidden and their influence is seen through the changes of phase shifts of larger solitons. In the case of an external harmonic force several resonance schemes are revealed where both visible and hidden solitons have important roles. The weak, moderate, strong, and dominating fields are distinguished and the corresponding solution types presented. PMID:15836291

  3. Nonlinear ion modes in a strongly coupled plasma in the presence of nonthermal ion fluids and polarization force

    NASA Astrophysics Data System (ADS)

    Ema, S. A.; Hossen, M. R.; Mamun, A. A.

    2016-04-01

    The nonlinear propagation of ion-acoustic (IA) waves in a strongly coupled plasma system containing Maxwellian electrons and nonthermal ions has been theoretically and numerically investigated. The well-known reductive perturbation technique is used to derive both the Burgers and Korteweg-de Vries (KdV) equations. Their shock and solitary wave solutions have also been numerically analyzed in understanding localized electrostatic disturbances. It has been observed that the basic features (viz. polarity, amplitude, width, etc.) of IA waves are significantly modified by the effect of polarization force and other plasma parameters (e.g., the electron-to-ion number density ratio and ion-to-electron temperature ratio). This is a unique finding among all theoretical investigations made before, whose probable implications are discussed in this investigation. The implications of the results obtained from this investigation may be useful in understanding the wave propagation in both space and laboratory plasmas.

  4. Quantum electron-acoustic double layers in a magnetoplasma

    SciTech Connect

    Misra, A. P.; Samanta, S.

    2008-12-15

    Using a quantum magnetohydrodynamic (QMHD) model, the existence of small but finite amplitude quantum electron-acoustic double layers (QEADLs) is reported in a magnetized collisionless dense quantum plasma whose constituents are two distinct groups of cold and hot electrons, and the stationary ions forming only the neutralizing background. It is shown that the existence of steady state solutions of these double layers obtained from an extended Korteweg-de Vries (KdV) equation depends parametrically on the ratio of the cold to hot electron unperturbed number density ({delta}), the quantum diffraction parameter (H), the obliqueness parameter (l{sub z}), and the external magnetic field via the normalized electron-cyclotron frequency ({omega}). It is found that the system supports both compressive and rarefactive double layers depending on the parameters {delta} and l{sub z}. The effects of all these parameters on the profiles of the double layers are also examined numerically.

  5. The effect of non-thermal electrons on obliquely propagating electron acoustic waves in a magnetized plasma

    NASA Astrophysics Data System (ADS)

    Singh, Satyavir; Bharuthram, Ramashwar

    2016-07-01

    Small amplitude electron acoustic solitary waves are studied in a magnetized plasma consisting of hot electrons following Cairn's type non-thermal distribution function and fluid cool electrons, cool ions and an electron beam. Using reductive perturbation technique, the Korteweg-de-Vries-Zakharov-Kuznetsov (KdV-ZK) equation is derived to describe the nonlinear evolution of electron acoustic waves. It is observed that the presence of non-thermal electrons plays an important role in determining the existence region of solitary wave structures. Theoretical results of this work is used to model the electrostatic solitary structures observed by Viking satellite. Detailed investigation of physical parameters such as non-thermality of hot electrons, beam electron velocity and temperature, obliquity on the existence regime of solitons will be discussed.

  6. Dissipative kinetic Alfvén solitary waves resulting from viscosity

    SciTech Connect

    Choi, C.-R.; Kang, S.-B.; Min, K.-W.; Woo, M.-H.; Hwang, J.; Park, Y.-D.

    2013-11-15

    Nonlinear small-amplitude kinetic Alfvén solitary waves (KASWs) are investigated with their “anomalous” kinetic viscosity effect on electrons. It is found that the structure of a hump-type KASW solution develops into a shock-type (or double layer) KASW solution for large amplitude KASWs when viscosity exists. For small amplitude KASWs, the Korteweg-de Vries (KdV) equation with an approximate pseudopotential was solved, and it is found that the hump-type KASWs develop into oscillating shock-type (kink-type) KASWs. It is also found that the oscillating scale of this structure is related to the propagation velocity and plasma beta, while the damping scale is inversely proportional to the viscosity.

  7. Nonlinear electrostatic drift waves in dense electron-positron-ion plasmas

    SciTech Connect

    Haque, Q.; Mahmood, S.; Mushtaq, A.

    2008-08-15

    The Korteweg-de Vries-Burgers (KdVB)-type equation is obtained using the quantum hydrodynamic model in an inhomogeneous electron-positron-ion quantum magnetoplasma with neutral particles in the background. The KdV-type solitary waves, Burgers-type monotonic, and oscillatory shock like solutions are discussed in different limits. The quantum parameter is also dependent on the positron concentration in dense multicomponent plasmas. It is found that both solitary hump and dip are formed and their amplitude and width are dependent on percentage presence of positrons in electron-ion plasmas. The height of the monotonic shock is decreased with the increase of positron concentration and it is independent of the quantum parameter in electron-positron-ion magnetized quantum plasmas. However, the amplitude of the oscillatory shock is dependent on positron concentration and quantum parameter in electron-positron-ion plasmas.

  8. Effect of nonadiabaticity of dust charge variation on dust acoustic waves: generation of dust acoustic shock waves.

    PubMed

    Gupta, M R; Sarkar, S; Ghosh, S; Debnath, M; Khan, M

    2001-04-01

    The effect of nonadiabaticity of dust charge variation arising due to small nonzero values of tau(ch)/tau(d) has been studied where tau(ch) and tau(d) are the dust charging and dust hydrodynamical time scales on the nonlinear propagation of dust acoustic waves. Analytical investigation shows that the propagation of a small amplitude wave is governed by a Korteweg-de Vries (KdV) Burger equation. Notwithstanding the soliton decay, the "soliton mass" is conserved, but the dissipative term leads to the development of a noise tail. Nonadiabaticity generated dissipative effect causes the generation of a dust acoustic shock wave having oscillatory behavior on the downstream side. Numerical investigations reveal that the propagation of a large amplitude dust acoustic shock wave with dust density enhancement may occur only for Mach numbers lying between a minimum and a maximum value whose dependence on the dusty plasma parameters is presented. PMID:11308955

  9. Nonlinear Dust Acoustic Waves in Dissipative Space Dusty Plasmas with Superthermal Electrons and Nonextensive Ions

    NASA Astrophysics Data System (ADS)

    El-Hanbaly, A. M.; El-Shewy, E. K.; Sallah, M.; Darweesh, H. F.

    2016-05-01

    The nonlinear characteristics of the dust acoustic (DA) waves are studied in a homogeneous, collisionless, unmagnetized, and dissipative dusty plasma composed of negatively charged dusty grains, superthermal electrons, and nonextensive ions. Sagdeev pseudopotential technique has been employed to study the large amplitude DA waves. It (Sagdeev pseudopotential) has an evidence for the existence of compressive and rarefractive solitons. The global features of the phase portrait are investigated to understand the possible types of solutions of the Sagdeev form. On the other hand, the reductive perturbation technique has been used to study small amplitude DA waves and yields the Korteweg-de Vries-Burgers (KdV-Burgers) equation that exhibits both soliton and shock waves. The behavior of the obtained results of both large and small amplitude is investigated graphically in terms of the plasma parameters like dust kinematic viscosity, superthermal and nonextensive parameters.

  10. Acoustic solitons in inhomogeneous pair-ion plasmas

    SciTech Connect

    Shah, Asif; Mahmood, S.; Haque, Q.

    2010-12-15

    The acoustic solitons are investigated in inhomogeneous unmagnetized pair ion plasmas. The Korteweg-de Vries (KdV) like equation with an additional term due to density gradients is deduced by employing reductive perturbation technique. It is noticed that pair-ion plasma system is conducive for the propagation of compressive as well as rarefactive solitons. The increase in the temperature ratio causes the amplitude of the rarefactive soliton to decrease. However, the amplitude of the compressive solitons is found to be increased as the temperature ratio of ions is enhanced. The amplitude of both compressive and rarefactive solitons is found to be increased as the density gradient parameter is increased. The equlibrium density profile is assumed to be exponential. The numerical results are shown for illustration.

  11. Nonlinear ion-acoustic double-layers in electronegative plasmas with electrons featuring Tsallis distribution

    NASA Astrophysics Data System (ADS)

    Ghebache, Siham; Tribeche, Mouloud

    2016-04-01

    Weakly nonlinear ion-acoustic (IA) double-layers (DLs), which accompany electronegative plasmas composed of positive ions, negative ions, and nonextensive electrons are investigated. A generalized Korteweg-de Vries equation with a cubic nonlinearity is derived using a reductive perturbation method. Different types of electronegative plasmas inspired from the experimental studies of Ichiki et al. (2001) are discussed. It is shown that the IA wave phase velocity, in different mixtures of negative and positive ions, decreases as the nonextensive parameter q increases, before levelling-off at a constant value for larger q. Moreover, a relative increase of Q involves an enhancement of the IA phase velocity. Existence domains of either solitary waves or double-layers are then presented and their parametric dependence is determined. Owing to the electron nonextensivity, our present plasma model can admit compressive as well as rarefactive IA-DLs.

  12. Oblique propagation of ion acoustic soliton-cnoidal waves in a magnetized electron-positron-ion plasma with superthermal electrons

    SciTech Connect

    Wang, Jian-Yong; Cheng, Xue-Ping; Tang, Xiao-Yan; Yang, Jian-Rong; Ren, Bo

    2014-03-15

    The oblique propagation of ion-acoustic soliton-cnoidal waves in a magnetized electron-positron-ion plasma with superthermal electrons is studied. Linear dispersion relations of the fast and slow ion-acoustic modes are discussed under the weak and strong magnetic field situations. By means of the reductive perturbation approach, Korteweg-de Vries equations governing ion-acoustic waves of fast and slow modes are derived, respectively. Explicit interacting soliton-cnoidal wave solutions are obtained by the generalized truncated Painlevé expansion. It is found that every peak of a cnoidal wave elastically interacts with a usual soliton except for some phase shifts. The influence of the electron superthermality, positron concentration, and magnetic field obliqueness on the soliton-cnoidal wave are investigated in detail.

  13. Nonlinear propagation of dust-ion-acoustic solitary waves in an unmagnetized dusty plasma with trapped particle distribution

    NASA Astrophysics Data System (ADS)

    Rahman, O.

    2015-12-01

    The nonlinear propagation of dust-ion-acoustic (DIA) solitary waves (SWs) in an unmagnetized four-component dusty plasma containing electrons and negative ions obeying vortex-like (trapped) velocity distribution, cold mobile positive ions and arbitrarily charged stationary dust has been theoretically investigated. The properties of small but finite amplitude DIASWs are studied by employing the reductive perturbation technique. It has been found that owing to the departure from the Maxwellian electron and Maxwellian negative ion distribution to a vortex-like one, the dynamics of such DIASWs is governed by a modified Korteweg-de Vries (mKdV) equation which admits SW solution under certain conditions. The basic properties (speed, amplitude, width, etc.) of such DIASWs are found to be significantly modified by the presence of trapped electron and trapped negative ions. The implications of our results to space and laboratory dusty electronegative plasmas (DENPs) are briefly discussed.

  14. Dust-ion-acoustic solitary waves in dusty plasma with arbitrarily charged dust and vortex-like electron distribution

    SciTech Connect

    Rahman, O.; Mamun, A. A.

    2011-08-15

    The nonlinear propagation of dust-ion-acoustic (DIA) waves in a dusty plasma containing trapped electrons following vortex-like distribution, cold mobile ions, and arbitrarily charged static dust is theoretically investigated. The properties of small but finite amplitude DIA solitary waves (SWs) are studied by employing the reductive perturbation technique. It is found that owing to the departure from the Maxwellian electron distribution to a vortex-like one, the dynamics of such DIA SWs is governed by a modified Korteweg-de Vries equation. The basic features (amplitude, width, speed, etc.) of such DIA SWs, which are found to be significantly modified by the vortex-like electron distribution and dust polarity, are also examined. The implications of our results to space and laboratory dusty plasmas are briefly discussed.

  15. Magnetosonic shock wave in collisional pair-ion plasma

    NASA Astrophysics Data System (ADS)

    Adak, Ashish; Sikdar, Arnab; Ghosh, Samiran; Khan, Manoranjan

    2016-06-01

    Nonlinear propagation of magnetosonic shock wave has been studied in collisional magnetized pair-ion plasma. The masses of both ions are same but the temperatures are slightly different. Two fluid model has been taken to describe the model. Two different modes of the magnetosonic wave have been obtained. The dynamics of the nonlinear magnetosonic wave is governed by the Korteweg-de Vries Burgers' equation. It has been shown that the ion-ion collision is the source of dissipation that causes the Burgers' term which is responsible for the shock structures in equal mass pair-ion plasma. The numerical investigations reveal that the magnetosonic wave exhibits both oscillatory and monotonic shock structures depending on the strength of the dissipation. The nonlinear wave exhibited the oscillatory shock wave for strong magnetic field (weak dissipation) and monotonic shock wave for weak magnetic field (strong dissipation). The results have been discussed in the context of the fullerene pair-ion plasma experiments.

  16. Magnetoacoustic shock waves in dissipative degenerate plasmas

    SciTech Connect

    Hussain, S.; Mahmood, S.

    2011-11-15

    Quantum magnetoacoustic shock waves are studied in homogenous, magnetized, dissipative dense electron-ion plasma by using two fluid quantum magneto-hydrodynamic (QMHD) model. The weak dissipation effects in the system are taken into account through kinematic viscosity of the ions. The reductive perturbation method is employed to derive Korteweg-de Vries Burgers (KdVB) equation for magnetoacoustic wave propagating in the perpendicular direction to the external magnetic field in dense plasmas. The strength of magnetoacoustic shock is investigated with the variations in plasma density, magnetic field intensity, and ion kinematic viscosity of dense plasma system. The necessary condition for the existence of monotonic and oscillatory shock waves is also discussed. The numerical results are presented for illustration by using the data of astrophysical dense plasma situations such as neutron stars exist in the literature.

  17. Formation of electrostatic solitons, monotonic, and oscillatory shocks in pair-ion plasmas

    SciTech Connect

    Mahmood, S.; Ur-Rehman, H.

    2010-07-15

    The nonlinear electrostatic structures in homogeneous, unmagnetized pair-ion plasma are studied. The dissipation in the system is taken through kinematic viscosities of both pair-ion species. The one dimensional (Korteweg-de Vries-Burgers) KdVB equation is derived using reductive perturbation method. The analytical solution of KdVB is obtained using tanh method. It is found that solitons and monotonic shocks structures are formed in such type of plasmas depending on the value of dissipation in the system. Both compressive and rarefactive structures of solitons and monotonic shocks are obtained depending on the temperatures of negative and positive ions. The oscillatory shock structure in pair-ion plasmas is obtained and its necessary conditions for formation are discussed. The numerical illustrations of potential structures for different values of dissipation in the system are also shown, which may have some relevance in the future experiments of laboratory produced pair-ion plasmas.

  18. Nonplanar converging and diverging shock waves in the presence of thermal ions in electron-positron plasma

    SciTech Connect

    Shah, Asif; Saeed, R.; Noaman-ul-Haq, Muhammad

    2010-07-15

    The cylindrical and spherical Korteweg-de Vries-Burger equations have been derived to study the ion acoustic converging and diverging shock waves. The considered plasma is comprised of inertialess electrons, positrons, and inertial thermal ions. It is noticed that the ion temperature, positron concentration, and kinematic viscosity have significant influence on the shock structure and propagation in nonplanar geometries. The strength of shock in spherical geometry is found to dominate over shock strength in cylindrical geometry. The shock wave strength and steepness escalate with time as it moves towards the center and shock enervates as it recedes away from center. The graphical view of the numerical results is presented for illustration. The results may have relevance in the inertial confinement fusion plasmas.

  19. Spherical and cylindrical imploding and exploding shock waves in plasma system dominated by pair production

    SciTech Connect

    ul Haq, Muhammad Noaman; Saeed, R.; Shah, Asif

    2010-08-15

    The propagation of ion acoustic shock waves in cylindrical and spherical geometries has been investigated. The plasma system consists of cold ions, Boltzmannian electrons and positrons. Spherical, cylindrical Korteweg-de Vries-Burger equations have been derived by reductive perturbation technique and their shock behavior is studied by employing finite difference method. Our main emphasis is on the behavior of shock as it moves toward and away from center of spherical and cylindrical geometries. It is noticed, that the shock wave strength and steepness accrues with time as it moves toward the center and shock enervates as it moves away from center. The strength of shock in spherical geometry is found to dominate over shock strength in cylindrical geometry. Positron concentration, kinematic viscosity are also found to have significant effect on the shock structure and propagation. The results may have relevance in the inertial confinement fusion plasmas.

  20. Modeling of the internal solibore evolution

    NASA Astrophysics Data System (ADS)

    Talipova, Tatiana; Kurkina, Oxana; Naumov, Aleksandr; Kurkin, Andrey

    2016-04-01

    Numerical modeling of dispersive shock waves called solibore in a stratified fluid is conducted. The theoretical model is based on the extended version of the Korteweg-de Vries equation which takes into account the effects of cubic nonlinearity, dissipation in near-bottom turbulent layer and Earth rotation. This model is now very popular in the physical oceanography. Initial conditions for simulations correspond to the real internal waves of shock-like shape in the Pechora Sea (south-eastern part of Barents Sea), the Arctic observed in 1998. The density stratification of this area is not well known and we study the sensitivity of our numerical results to density profile approximation. It is shown that although the wave kinematic parameters are sensitive for these factors nevertheless a sharp drop (like kink in the soliton theory) in the depth of the thermocline is conserved at a distance of one-three kilometers, and then it is transformed into dispersive shock waves (solibore).

  1. Interactions of nonlinear electron-acoustic solitary waves with vortex electron distribution

    SciTech Connect

    Demiray, Hilmi

    2015-02-15

    In the present work, based on a one dimensional model, we consider the head-on-collision of nonlinear electron-acoustic waves in a plasma composed of a cold electron fluid, hot electrons obeying a trapped/vortex-like distribution, and stationary ions. The analysis is based on the use of extended Poincare, Lighthill-Kuo method [C. H. Su and R. M. Mirie, J. Fluid Mech. 98, 509 (1980); R. M. Mirie and C. H. Su, J. Fluid Mech. 115, 475 (1982)]. It is shown that, for the first order approximation, the waves propagating in opposite directions are characterized by modified Korteweg-de Vries equations. In contrary to the results of previous investigations on this subject, we showed that the phase shifts are functions of both amplitudes of the colliding waves. The numerical results indicate that the waves with larger amplitude experience smaller phase shifts. Such a result seems to be plausible from physical considerations.

  2. Experimental observation of precursor solitons in a flowing complex plasma

    NASA Astrophysics Data System (ADS)

    Jaiswal, Surabhi; Bandyopadhyay, P.; Sen, A.

    2016-04-01

    The excitation of precursor solitons ahead of a rapidly moving object in a fluid, a spectacular phenomenon in hydrodynamics that has often been observed ahead of moving ships, has surprisingly not been investigated in plasmas where the fluid model holds good for low frequency excitations such as ion acoustic waves. In this Rapid Communication we report an experimental observation of precursor solitons in a flowing dusty plasma. The nonlinear solitary dust acoustic waves (DAWs) are excited by a supersonic mass flow of the dust particles over an electrostatic potential hill. In a frame where the fluid is stationary and the hill is moving the solitons propagate in the upstream direction as precursors while wake structures consisting of linear DAWs are seen to propagate in the downstream region. A theoretical explanation of these excitations based on the forced Korteweg-deVries model equation is provided and their practical implications in situations involving a charged object moving in a plasma are discussed.

  3. Exactly solvable potentials with finitely many discrete eigenvalues of arbitrary choice

    NASA Astrophysics Data System (ADS)

    Sasaki, Ryu

    2014-06-01

    We address the problem of possible deformations of exactly solvable potentials having finitely many discrete eigenvalues of arbitrary choice. As Kay and Moses showed in 1956, reflectionless potentials in one dimensional quantum mechanics are exactly solvable. With an additional time dependence these potentials are identified as the soliton solutions of the Korteweg de Vries (KdV) hierarchy. An N-soliton potential has the time t and 2N positive parameters, k1 < ⋯ < kN and {cj}, j = 1, …, N, corresponding to N discrete eigenvalues lbrace -k_j^2rbrace. The eigenfunctions are elementary functions expressed by the ratio of determinants. The Darboux-Crum-Krein-Adler transformations or the Abraham-Moses transformations based on eigenfunction deletions produce lower soliton number potentials with modified parameters lbrace c^' }_jrbrace. We explore various identities satisfied by the eigenfunctions of the soliton potentials, which reflect the uniqueness theorem of Gel'fand-Levitan-Marchenko equations for separable (degenerate) kernels.

  4. Experimental observation of precursor solitons in a flowing complex plasma.

    PubMed

    Jaiswal, Surabhi; Bandyopadhyay, P; Sen, A

    2016-04-01

    The excitation of precursor solitons ahead of a rapidly moving object in a fluid, a spectacular phenomenon in hydrodynamics that has often been observed ahead of moving ships, has surprisingly not been investigated in plasmas where the fluid model holds good for low frequency excitations such as ion acoustic waves. In this Rapid Communication we report an experimental observation of precursor solitons in a flowing dusty plasma. The nonlinear solitary dust acoustic waves (DAWs) are excited by a supersonic mass flow of the dust particles over an electrostatic potential hill. In a frame where the fluid is stationary and the hill is moving the solitons propagate in the upstream direction as precursors while wake structures consisting of linear DAWs are seen to propagate in the downstream region. A theoretical explanation of these excitations based on the forced Korteweg-deVries model equation is provided and their practical implications in situations involving a charged object moving in a plasma are discussed. PMID:27176247

  5. On the development of packets of surface gravity waves moving over an uneven bottom

    NASA Technical Reports Server (NTRS)

    Djordjevic, V. D.; Redekopp, L. G.

    1978-01-01

    The object of study is the evolution of packets of gravity waves moving over variable depth, in particular, the transformation of packets moving into a shelf of increased or decreased depth. The variable-coefficient nonlinear Schroedinger equation with inhomogeneous term is derived for gravity waves moving over an uneven bottom. A solution for an envelope-hole soliton moving over variable depth is obtained when the amplitude-length ratio of the soliton is small. For the shelf problem, it is shown that the first soliton on the shelf will be the one with smallest depression, and the last will have greatest depression. This is in contrast to Korteweg-de Vries soliton fission.

  6. Nonlinear positron-acoustic waves in fully relativistic degenerate plasmas

    NASA Astrophysics Data System (ADS)

    Hossen, M. A.; Mamun, A. A.

    2016-03-01

    The nonlinear positron-acoustic (PA) waves propagating in a fully relativistic electron-positron-ion (EPI) plasma (containing degenerate electrons and positrons, and immobile heavy ions) have been theoretically investigated. A fully relativistic hydrodynamic model, which is consistent with the relativistic principle has been used, and the reductive perturbation method is employed to derive the dynamical Korteweg-de Vries equation. The dynamics of electrons as well as positrons, and the presence of immobile heavy ions are taken into account. It is found that the effects of relativistic degeneracy of electrons and positrons, static heavy ions, plasma particles velocity, enthalpy, etc have significantly modified the basic properties of the PA solitary waves propagating in the fully relativistic EPI plasmas. The application of the results of our present work in astrophysical compact objects such as white dwarfs and neutron stars, etc are briefly discussed.

  7. Six-dimensional supersymmetric gauge theories, quantum cohomology of instanton moduli spaces and gl( N) Quantum Intermediate Long Wave Hydrodynamics

    NASA Astrophysics Data System (ADS)

    Bonelli, Giulio; Sciarappa, Antonio; Tanzini, Alessandro; Vasko, Petr

    2014-07-01

    We show that the exact partition function of U( N) six-dimensional gauge theory with eight supercharges on ℂ2 × S 2 provides the quantization of the integrable system of hydrodynamic type known as gl( N) periodic Intermediate Long Wave (ILW). We characterize this system as the hydrodynamic limit of elliptic Calogero-Moser integrable system. We compute the Bethe equations from the effective gauged linear sigma model on S 2 with target space the ADHM instanton moduli space, whose mirror computes the Yang-Yang function of gl( N) ILW. The quantum Hamiltonians are given by the local chiral ring observables of the six-dimensional gauge theory. As particular cases, these provide the gl( N) Benjamin-Ono and Korteweg-de Vries quantum Hamiltonians. In the four dimensional limit, we identify the local chiral ring observables with the conserved charges of Heisenberg plus W N algebrae, thus providing a gauge theoretical proof of AGT correspondence.

  8. Dust-acoustic solitary waves in a four-component adiabatic magnetized dusty plasma

    SciTech Connect

    Akhter, T. Mannan, A.; Mamun, A. A.

    2013-07-15

    Theoretical investigation has been made on obliquely propagating dust-acoustic (DA) solitary waves (SWs) in a magnetized dusty plasma which consists of non-inertial adiabatic electron and ion fluids, and inertial negatively as well as positively charged adiabatic dust fluids. The reductive perturbation method has been employed to derive the Korteweg-de Vries equation which admits a solitary wave solution for small but finite amplitude limit. It has been shown that the basic features (speed, height, thickness, etc.) of such DA solitary structures are significantly modified by adiabaticity of plasma fluids, opposite polarity dust components, and the obliqueness of external magnetic field. The SWs have been changed from compressive to rarefactive depending on the value of {mu} (a parameter determining the number of positive dust present in this plasma model). The present investigation can be of relevance to the electrostatic solitary structures observed in various dusty plasma environments (viz. cometary tails, upper mesosphere, Jupiter's magnetosphere, etc.)

  9. Study of nonlinear electron-acoustic solitary and shock waves in a dissipative, nonplanar space plasma with superthermal hot electrons

    SciTech Connect

    Han, Jiu-Ning He, Yong-Lin; Luo, Jun-Hua; Nan, Ya-Gong; Han, Zhen-Hai; Dong, Guang-Xing; Duan, Wen-Shan; Li, Jun-Xiu

    2014-01-15

    With the consideration of the superthermal electron distribution, we present a theoretical investigation about the nonlinear propagation of electron-acoustic solitary and shock waves in a dissipative, nonplanar non-Maxwellian plasma comprised of cold electrons, superthermal hot electrons, and stationary ions. The reductive perturbation technique is used to obtain a modified Korteweg-de Vries Burgers equation for nonlinear waves in this plasma. We discuss the effects of various plasma parameters on the time evolution of nonplanar solitary waves, the profile of shock waves, and the nonlinear structure induced by the collision between planar solitary waves. It is found that these parameters have significant effects on the properties of nonlinear waves and collision-induced nonlinear structure.

  10. Deformations of Poisson brackets and extensions of Lie algebras of contact vector fields

    NASA Astrophysics Data System (ADS)

    Ovsienko, V.; Roger, C.

    1992-12-01

    CONTENTSIntroduction § 1. Main theoremsChapter I. Algebra § 2. Moyal deformations of the Poisson bracket and *-product on \\mathbb R^{2n} § 3. Algebraic construction § 4. Central extensions § 5. ExamplesChapter II. Deformations of the Poisson bracket and *-product on an arbitrary symplectic manifold § 6. Formal deformations: definitions § 7. Graded Lie algebras as a means of describing deformations § 8. Cohomology computations and their consequences § 9. Existence of a *-productChapter III. Extensions of the Lie algebra of contact vector fields on an arbitrary contact manifold §10. Lagrange bracket §11. Extensions and modules of tensor fieldsAppendix 1. Extensions of the Lie algebra of differential operatorsAppendix 2. Examples of equations of Korteweg-de Vries typeReferences

  11. Nonlinear electron-acoustic waves in quantum plasma

    SciTech Connect

    Sah, O. P.; Manta, J.

    2009-03-15

    The nonlinear wave structure of electron-acoustic waves (EAWs) is investigated in a three component unmagnetized dense quantum plasma consisting of two distinct groups of electrons (one inertial cold electron, and other inertialess hot electrons) and immobile ions. By employing one dimensional quantum hydrodynamic model and standard reductive perturbation technique, a Korteweg-de-Vries equation governing the dynamics of EAWs is derived. Both compressive and rarefactive solitons along with periodical potential structures are found to exist for various ranges of dimensionless quantum parameter H. The quantum mechanical effects are also examined numerically on the profiles of the amplitude and the width of electron-acoustic solitary waves. It is observed that both the amplitude and the width of electron-acoustic solitary waves are significantly affected by the parameter H. The relevance of the present investigation to the astrophysical ultradense plasmas is also discussed.

  12. Dust acoustic shock waves in dusty plasma of opposite polarity with non-extensive electron and ion distributions

    NASA Astrophysics Data System (ADS)

    Zaghbeer, S. K.; Salah, H. H.; Sheta, N. H.; El-Shewy, E. K.; Elgarayhi, A.; Elgarayhi

    2014-03-01

    A theoretical investigation has been made of obliquely propagating nonlinear electrostatic shock structures. The reductive perturbation method has been used to derive the Korteweg-de Vries-Burger (KdV-Burger) equation for dust acoustic shock waves in a homogeneous system of a magnetized collisionless plasma comprising a four-component dusty plasma with massive, micron-sized, positively, negatively dust grains and non-extensive electrons and ions. The effect of dust viscosity coefficients of charged dusty plasma of opposite polarity and the non-extensive parameters of electrons and ions have been studied. The behavior of the oscillatory and monotonic shock waves in dusty plasma has been investigated. It has been found that the presence of non-extensive parameters significantly modified the basic properties of shock structures in space environments.

  13. Dust-acoustic shock waves in a magnetized non-thermal dusty plasma

    NASA Astrophysics Data System (ADS)

    Shahmansouri, M.; Mamun, A. A.; Mamun

    2014-08-01

    A theoretical investigation is carried out to study the basic properties of dust-acoustic (DA) shock waves propagating in a magnetized non-thermal dusty plasma (containing cold viscous dust fluid, non-thermal ions, and non-thermal electrons). The reductive perturbation method is used to derive the Korteweg-de Vries-Burgers equation. It is found that the basic properties of DA shock waves are significantly modified by the combined effects of dust fluid viscosity, external magnetic field, and obliqueness (angle between external magnetic field and DA wave propagation direction). It is shown that the dust fluid viscosity acts as a source of dissipation, and is responsible for the formation of DA shock structures in the dusty plasma system under consideration. The implications of our results in some space and laboratory plasma situations are briefly discussed.

  14. Nonlinear electrostatic coherent structures: solitary and shock waves in a dissipative, nonplanar multi-component quantum plasma

    NASA Astrophysics Data System (ADS)

    Han, Jiu-Ning; Luo, Jun-Hua; Li, Jun-Xiu

    2014-01-01

    The nonlinear propagation of ion-acoustic solitary and shock waves in a dissipative, nonplanar quantum plasma comprised of electrons, positrons, and ions are studied. A modified Korteweg-de Vries Burgers equation is derived in the limit of low frequency and long wavelength by taking into account the kinematic viscosity among the plasma constituents. It is shown that this plasma system supports the propagation of both compressive and rarefactive nonlinear waves. The effects of variation of various plasma parameters on the time evolution of nonplanar solitary waves, the profile of shock waves, and the nonlinear structure induced by the collision of solitary waves are discussed. It is found that these parameters have significant effects on the properties of nonlinear waves in cylindrical and spherical geometries, and these effects for compressive and rarefactive nonlinear waves are obviously different.

  15. Magnetoacoustic solitons in dense astrophysical electron-positron-ion plasmas

    NASA Astrophysics Data System (ADS)

    Hussain, S.; Mahmood, S.; Mushtaq, A.

    2013-08-01

    Nonlinear magnetoacoustic waves in dense electron-positron-ion plasmas are investigated by using three fluid quantum magnetohydrodynamic model. The quantum mechanical effects of electrons and positrons are taken into account due to their Fermionic nature (to obey Fermi statistics) and quantum diffraction effects (Bohm diffusion term) in the model. The reductive perturbation method is employed to derive the Korteweg-de Vries (KdV) equation for low amplitude magnetoacoustic soliton in dense electron-positron-ion plasmas. It is found that positron concentration has significant impact on the phase velocity of magnetoacoustic wave and on the formation of single pulse nonlinear structure. The numerical results are also illustrated by taking into account the plasma parameters of the outside layers of white dwarfs and neutron stars/pulsars.

  16. Propagation and oblique collision of ion-acoustic solitary waves in a magnetized dusty electronegative plasma

    SciTech Connect

    El-Labany, S. K.; Behery, E. E.; El-Shamy, E. F.

    2013-12-15

    The propagation and oblique collision of ion-acoustic (IA) solitary waves in a magnetized dusty electronegative plasma consisting of cold mobile positive ions, Boltzmann negative ions, Boltzmann electrons, and stationary positive/negative dust particles are studied. The extended Poincaré-Lighthill-Kuo perturbation method is employed to derive the Korteweg-de Vries equations and the corresponding expressions for the phase shifts after collision between two IA solitary waves. It turns out that the angle of collision, the temperature and density of negative ions, and the dust density of opposite polarity have reasonable effects on the phase shift. Clearly, the numerical results demonstrated that the IA solitary waves are delayed after the oblique collision. The current finding of this work is applicable in many plasma environments having negative ion species, such as D- and F-regions of the Earth's ionosphere and some laboratory plasma experiments.

  17. Low dust charging rate induced weakly dissipative dust acoustic solitary waves: Role of nonthermal ions

    SciTech Connect

    Chaudhuri, Tushar Kanti; Khan, Manoranjan; Gupta, M. R.; Ghosh, Samiran

    2007-10-15

    The effects of low dust charging rate compared to the dust oscillation frequency and nonthermal ions on small but finite amplitude nonlinear dust acoustic wave have been investigated. It is seen that because of the low dust charging rate, the nonlinear wave exhibits weakly dissipative solitary wave that is governed by a modified form of the Korteweg-de Vries equation. The solitary wave possesses both rarefactive and compressive soliton solution depending on the values of ion nonthermality parameter a. An analytical solution reveals that because of the simultaneous effects of low dust charging rate and nonthermal ions, the wave amplitude may grow exponentially with time if the ion nonthermality parameter (a) exceeds a critical value provided the ion-electron temperature ratio ({sigma}{sub i}) is less than 0.11.

  18. Observation of internal wave polarity conversion generated by a rising tide

    NASA Astrophysics Data System (ADS)

    Li, Lan; Wang, Caixia; Grimshaw, Roger

    2015-05-01

    The observations reported here are based on time series of in situ observation data in Laoshan Bay off the Qingdao coast. A chain of thermistors (T-chain) at a fixed location recorded a sequence of elevation internal waves followed by depression internal waves passing by over an elapsed time of about 1 h. This observed polarity conversion at a fixed location is caused by the vertical stratification variation mainly induced by the rising tide, which is believed to be the first reported observation of this kind. The process of an elevation internal wave train converting to a depression wave train is simulated using the variable-coefficient extended Korteweg-de Vries (veKdV) equation, which also provides a further comparison between theory and the reported observations.

  19. Study of obliquely propagating dust acoustic solitary waves in magnetized tropical mesospheric plasmas with effect of dust charge variations and rotation of the plasma

    SciTech Connect

    Mushtaq, A.; Shah, H.A.; Rubab, N.; Murtaza, G.

    2006-06-15

    The characteristics of obliquely propagating Dust Acoustic Waves (DAWs) in rotating and magnetized dusty plasma in the dayside tropical mesosphere are examined by incorporating adiabatic dust charge fluctuations. A Korteweg-de Vries equation is derived, which may support a nonlinear dust acoustic wave on a very slow time scale. The meteoritic dust in mesospheric plasmas on the dayside is charged positively due to photo- and thermionic emissions. The dynamics of the DAW with electronic, ionic, thermionic, and photoelectric currents along with obliqueness and effective gyrofrequency are studied. It is observed that the amplitude of the soliton depends directly on the obliqueness {theta} and dust charge variation, respectively, while the width is modified inversely with these parameters. It is also observed that the effective gyrofrequency modifies the width inversely.

  20. Effect of non-Maxwellian particle trapping and dust grain charging on dust acoustic solitary waves

    SciTech Connect

    Rubab, N.; Murtaza, G.; Mushtaq, A.

    2006-11-15

    The role of adiabatic trapped ions on a small but finite amplitude dust acoustic wave, including the effect of adiabatic dust charge variation, is investigated in an unmagnetized three-component dusty plasma consisting of electrons, ions and massive micron sized negatively charged dust particulates. We have assumed that electrons and ions obey (r,q) velocity distribution while the dust species is treated fluid dynamically. It is found that the dynamics of dust acoustic waves is governed by a modified r dependent Korteweg-de Vries equation. Further, the spectral indices (r,q) affect the charge fluctuation as well as the trapping of electrons and ions and consequently modify the dust acoustic solitary wave.

  1. Small and arbitrary shock structures in spin 1/2 magnetohydrodynamic quantum plasma

    SciTech Connect

    Sahu, Biswajit; Choudhury, Sourav; Sinha, Anjana

    2015-02-15

    The shock structures in spin-1/2 quantum plasma, in the presence of magnetic diffusivity, are studied in the framework of the quantum magnetohydrodynamic model. Linear dispersion relation for the system is carried out analytically, and the results are plotted numerically for several values of the plasma parameters. Numerical analysis for arbitrary amplitude waves is carried out, whereas for waves of small amplitude, the reductive perturbation technique is applied to obtain the Korteweg-de Vries-Burgers equation. Both the analyses are observed to give the same qualitative picture. Most importantly, the different plasma parameters are found to play significant roles in determining the nature of the shock waves. The parametric ranges for which monotonic shock and oscillatory shock solutions are observed, are found analytically.

  2. Some New Aspects of Degenerate Quantum Plasma

    SciTech Connect

    Tsintsadze, Nodar L.

    2010-12-14

    Answers to some salient questions, which arise in quantum plasmas, are given. Starting from the Schroedinger equation for a single particle it is demonstrated how the Wigner-Moyal equation can be derived. It is shown that the Wigner-Moyal type of equation also exists in the classical field theory. As an example, from the Maxwell equations the Wigner-Moyal type of equation is obtained for a dense photon gas, which is classical, concluding that the Wigner-Moyal type of equation can be derived for any system, classical or quantum. A new type of quantum kinetic equations are presented. These novel kinetic equations allows to obtain a set of quantum hydrodynamic equations, which is impossible to derive by the Wigner-Moyal equation. The propagation of small perturbations and instabilities of these perturbations are then discussed, presenting new modes of quantum plasma waves. In the case of low frequency oscillations with ions, a new Bogolyubov type of spectrum is found. Furthermore, the Korteweg-de Vries (KdV) equation is derived and the contribution of the Madelung term in the formation of the KdV solitons is discussed.

  3. Equating the Scales of the Prueba de Aptitud Academica and the Scholastic Aptitude Test.

    ERIC Educational Resources Information Center

    Angoff, William H.; Modu, Christopher C.

    The purpose of this study was to establish score equivalencies between the College Board Scholastic Aptitude Test (SAT) and its Spanish-language equivalent, the College Board Prueba de Aptitud Academica (PAA). The method of the study involved two phases: the selection of test items equally appropriate for Spanish- and English-speaking students for…

  4. Critical density of a soliton gas.

    PubMed

    El, G A

    2016-02-01

    We quantify the notion of a dense soliton gas by establishing an upper bound for the integrated density of states of the quantum-mechanical Schrödinger operator associated with the Korteweg-de Vries soliton gas dynamics. As a by-product of our derivation, we find the speed of sound in the soliton gas with Gaussian spectral distribution function. PMID:26931586

  5. The Solar Neighborhood. XXXVI. The Long-term Photometric Variability of Nearby Red Dwarfs in the VRI Optical Bands

    NASA Astrophysics Data System (ADS)

    Hosey, Altonio D.; Henry, Todd J.; Jao, Wei-Chun; Dieterich, Sergio B.; Winters, Jennifer G.; Lurie, John C.; Riedel, Adric R.; Subasavage, John P.

    2015-07-01

    We present an analysis of long-term photometric variability for nearby red dwarf stars at optical wavelengths. The sample consists of 264 M dwarfs south of decl. = +30 with V-K = 3.96-9.16 and MV ≈ 10-20, corresponding to spectral types M2V-M8V, most of which are within 25 pc. The stars have been observed in the VRI filters for ˜4-14 yr at the CTIO/SMARTS 0.9 m telescope. Of the 238 red dwarfs within 25 pc, we find that only ˜8% are photometrically variable by at least 20 mmag (˜2%) in the VRI bands. Only four stars have been found to vary by more than 50 mmag, including GJ 1207 at 8.6 pc, which experienced a single extraordinary flare, and GJ 2006 A, TWA 8 A, and TWA 8 B, which are all young stars beyond 25 pc linked to moving groups. We find that high variability at optical wavelengths over the long term can in fact be used to identify young stars. Overall, however, the fluxes of most red dwarfs at optical wavelengths are steady to a few percent over the long term. The low overall rate of photometric variability for red dwarfs is consistent with results found in previous work on similar stars on shorter timescales, with the body of work indicating that most red dwarfs are only mildly variable. As expected, we find that the degree of photometric variability is greater in the V band than in the R or I bands, but we do not find any obvious trends in variability over the long term with red dwarf luminosity or temperature. We highlight 17 stars that show long-term changes in brightness, sometimes because of flaring activity or spots, and sometimes because of stellar cycles similar to our Sun's solar cycle. Remarkably, two targets show brightnesses that monotonically increase (G 169-029) or decrease (WT 460AB) by several percent over a decade. We also provide long-term variability measurements for seven M dwarfs within 25 pc that host exoplanets, none of which vary by more than 20 mmag. Both as a population, and for the specific red dwarfs with exoplanets observed

  6. Solution of the Landau-de-Gennes equations of liquid crystal physics on a SIMD computer

    SciTech Connect

    Farrell, P.A.; Ruttan, A.; Zeller, R.R.

    1993-12-31

    We will describe a scalable parallel finite difference algorithm for computing the equilibrium configurations, of the order-parameter tensor field for nematic liquid crystals, in rectangular and ellipsoidal regions, but minimization of the Landau-de-Gennes free energy functional. In this formulation, we solve for a symmetric traceless 3 {times} 3 tensor at each point. Our implementation of the free energy functional includes surface, gradient and scalar bulk terms, together with the effects of electric or magnetic fields. Boundary conditions can include both strong and weak surface anchoring. The target architectures for our implementation are primarily SIMD machines, with 2 or 3 dimensional rectangular grid networks, such as the Wavetracer DTC or the MasPar MP-1 as opposed to hypercube networks such as the Thinking Machines Corporation CM-2.

  7. Solitons and kinks in a general car-following model.

    PubMed

    Kurtze, Douglas A

    2013-09-01

    We study a general car-following model of traffic flow on an infinitely long single-lane road, which assumes that a car's acceleration depends on time-delayed values of its own speed, the headway between it and the car ahead, and the rate of change of headway, but makes minimal assumptions about the functional form of that dependence. We present a detailed characterization of the onset of linear instability; in particular we find a specific limit on the delay time below which the marginal wave number at the onset of instability is zero, and another specific limit on the delay time above which steady flow is always unstable. Crucially, the threshold of absolute stability generally does not coincide with an inflection point of the steady-state velocity function. When the marginal perturbation at onset has wave number 0, we show that Burgers and Korteweg-de Vries (KdV) equations can be derived under the usual assumptions, and that corrections to the KdV equation "select" a single member of the one-parameter set of its one-soliton solutions by driving a slow evolution of the soliton parameter. While in previous models this selected soliton has always marked the threshold of a finite-amplitude instability of linearly stable steady flow, we find that it can alternatively be a stable, small-amplitude jam that occurs when steady flow is linearly unstable. The model reduces to the usual modified Korteweg-de Vries (mKdV) equation only in the special situation that the threshold of absolute stability coincides with an inflection point of the steady-state velocity function; in general, near the threshold of absolute stability the model reduces instead to a KdV equation in the regime of small solitons, while near an inflection point it reduces to a Hayakawa-Nakanishi equation. Like the mKdV equation, the Hayakawa-Nakanishi equation admits a continuous family of kink solutions, and the selection criterion arising from the corrections to this equation can be written down

  8. Governing equations for electro-conjugate fluid flow

    NASA Astrophysics Data System (ADS)

    Hosoda, K.; Takemura, K.; Fukagata, K.; Yokota, S.; Edamura, K.

    2013-12-01

    An electro-conjugation fluid (ECF) is a kind of dielectric liquid, which generates a powerful flow when high DC voltage is applied with tiny electrodes. This study deals with the derivation of the governing equations for electro-conjugate fluid flow based on the Korteweg-Helmholtz (KH) equation which represents the force in dielectric liquid subjected to high DC voltage. The governing equations consist of the Gauss's law, charge conservation with charge recombination, the KH equation, the continuity equation and the incompressible Navier-Stokes equations. The KH equation consists of coulomb force, dielectric constant gradient force and electrostriction force. The governing equation gives the distribution of electric field, charge density and flow velocity. In this study, direct numerical simulation (DNS) is used in order to get these distribution at arbitrary time. Successive over-relaxation (SOR) method is used in analyzing Gauss's law and constrained interpolation pseudo-particle (CIP) method is used in analyzing charge conservation with charge recombination. The third order Runge-Kutta method and conservative second-order-accurate finite difference method is used in analyzing the Navier-Stokes equations with the KH equation. This study also deals with the measurement of ECF ow generated with a symmetrical pole electrodes pair which are made of 0.3 mm diameter piano wire. Working fluid is FF-1EHA2 which is an ECF family. The flow is observed from the both electrodes, i.e., the flow collides in between the electrodes. The governing equation successfully calculates mean flow velocity in between the collector pole electrode and the colliding region by the numerical simulation.

  9. Internal solitary waves with a weakly stratified critical layer

    NASA Astrophysics Data System (ADS)

    Caillol, P.; Grimshaw, R. H. J.

    2012-05-01

    Motivated by observations of solitary waves in the ocean and atmosphere, this paper considers the evolution of long weakly nonlinear internal waves in an incompressible Boussinesq fluid. The motion is restricted to the vertical plane. The basic state consists of stable horizontal shear flow and density stratification. On a long time scale, the waves evolve and reach a quasi-steady régime where weak nonlinearity and weak dispersion are in balance. In many circumstances, this régime is described by a Korteweg-de-Vries equation. However, when the linear long-wave speed equals the basic flow velocity at a certain height, the critical level, the traditional assumption of weak nonlinearity breaks down due to the appearance of a singularity in the leading-order modal equation, implying a strong modification of the flow in the so-called critical layer. Since the relevant geophysical flows have high Reynolds and Péclet numbers, we invoke nonlinear effects to resolve this singularity. Viscosity and thermal conductivity are considered small but finite. Their presence renders the nonlinear-critical-layer solution unique. Crucially, the density stratification degree is assumed small at the critical level; this has the consequence that the leading-order singularity is then identical to that in an unstratified flow. Thus the asymptotic methodology employed previously for that case can be adapted to this present study. In this critical layer, the flow is fully nonlinear but laminar and quasi-steady, with a strong rearrangement of the buoyancy and vorticity contours. This inner flow is matched at the edges of the critical layer with the outer flow. The final outcome for spatially localized solutions is an integro-differential evolution equation, whose form depends on the critical-layer shape, and especially on the wave polarity, that is, depression or elevation. For a steady travelling wave, this evolution equation when expressed in terms of the streamfunction amplitude is not a

  10. Structural changes of small amplitude kinetic Alfvén solitary waves due to second-order corrections

    SciTech Connect

    Choi, Cheong R.

    2015-10-15

    The structural changes of kinetic Alfvén solitary waves (KASWs) due to higher-order terms are investigated. While the first-order differential equation for KASWs provides the dispersion relation for kinetic Alfvén waves, the second-order differential equation describes the structural changes of the solitary waves due to higher-order nonlinearity. The reductive perturbation method is used to obtain the second-order and third-order partial differential equations; then, Kodama and Taniuti's technique [J. Phys. Soc. Jpn. 45, 298 (1978)] is applied in order to remove the secularities in the third-order differential equations and derive a linear second-order inhomogeneous differential equation. The solution to this new second-order equation indicates that, as the amplitude increases, the hump-type Korteweg-de Vries solution is concentrated more around the center position of the soliton and that dip-type structures form near the two edges of the soliton. This result has a close relationship with the interpretation of the complex KASW structures observed in space with satellites.

  11. PHYSICS OF GASES, PLASMAS, AND ELECTRIC DISCHARGES Dust Acoustic Solitary Waves in Saturn F-ring's Region

    NASA Astrophysics Data System (ADS)

    E. K., El-Shewy; M. I. Abo el, Maaty; H. G., Abdelwahed; M. A., Elmessary

    2011-01-01

    Effect of hot and cold dust charge on the propagation of dust-acoustic waves (DAWs) in unmagnetized plasma having electrons, singly charged ions, hot and cold dust grains has been investigated. The reductive perturbation method is employed to reduce the basic set of fluid equations to the Kortewege-de Vries (KdV) equation. At the critical hot dusty plasma density Nh0, the KdV equation is not appropriate for describing the system. Hence, a set of stretched coordinates is considered to derive the modified KdV equation. It is found that the presence of hot and cold dust charge grains not only significantly modifies the basic properties of solitary structure, but also changes the polarity of the solitary profiles. In the vicinity of the critical hot dusty plasma density Nh0, neither KdV nor mKdV equation is appropriate for describing the DAWs. Therefore, a further modified KdV (fmKdV) equation is derived, which admits both soliton and double layer solutions.

  12. Structural changes of small amplitude kinetic Alfvén solitary waves due to second-order corrections

    NASA Astrophysics Data System (ADS)

    Choi, Cheong R.

    2015-10-01

    The structural changes of kinetic Alfvén solitary waves (KASWs) due to higher-order terms are investigated. While the first-order differential equation for KASWs provides the dispersion relation for kinetic Alfvén waves, the second-order differential equation describes the structural changes of the solitary waves due to higher-order nonlinearity. The reductive perturbation method is used to obtain the second-order and third-order partial differential equations; then, Kodama and Taniuti's technique [J. Phys. Soc. Jpn. 45, 298 (1978)] is applied in order to remove the secularities in the third-order differential equations and derive a linear second-order inhomogeneous differential equation. The solution to this new second-order equation indicates that, as the amplitude increases, the hump-type Korteweg-de Vries solution is concentrated more around the center position of the soliton and that dip-type structures form near the two edges of the soliton. This result has a close relationship with the interpretation of the complex KASW structures observed in space with satellites.

  13. Clinical outcomes of double membrane peeling with or without simultaneous phacoemulsification/gas tamponade for vitreoretinal-interface-associated (VRI) disorders.

    PubMed

    Kumar, Kshitiz; Chandnani, Nisha; Raj, Pallavi; Agarwal, Amar

    2016-08-01

    The purpose of this study is to evaluate the clinical outcomes of double membrane (ERM & ILM) peeling and the effect of combined cataract surgery and SF6 gas injection in vitreoretinal interface (VRI) disorders. This is a retrospective interventional study. Seventy-two eyes with idiopathic vitreoretinal interface abnormalities that underwent 23 gauge pars plana vitrectomy with "double stain and double peel" technique were reviewed. SD-OCT was used to classify VRI disorders into following 4 groups: 44 in ERM type, 17 in VMTS type, 7 in macular pseudohole (MPH) type, and 4 in lamellar macular hole (LMH) type. ERM was a common association in all types. Mean preoperative BCVA improved from 0.58 ± 0.14 logMAR to 0.27 ± 0.16 logMAR units (p = 0.001). Mean CFT reduced from 409.17 ± 122.31 µm preoperatively to 277.28 ± 0.16 µm postoperatively (p < 0.0001). Among the VRI subtypes, visual improvement was significant except in LMH variety (ERM type, p = 0.0029; VMTS type, p = 0.0281; MPH type, p = 0.05; and LMH type, p = 0.7926). Mean change in CFT from baseline was least in LMH cases (p = 0.0093). There was no significant difference in BCVA and CFT in the group who had combined phacovitrectomy versus pseudophakic group (p > 0.05). Use of intraocular SF6 gas tamponade did not show any added benefits among the groups (p > 0.05). Improvement in foveal contour was seen in all groups. Simultaneous removal of ILM along with ERM during surgery for VRI disorders helps in restoring normal foveal contour with a favorable visual outcome. Combined cataract extraction or use of intraocular SF6 gas injection does not affect the surgical results. PMID:26659009

  14. Explicit mathematical construction of relativistic nonlinear de Broglie waves described by three-dimensional (wave and electromagnetic) solitons ``piloted'' (controlled) by corresponding solutions of associated linear Klein-Gordon and Schrödinger equations

    NASA Astrophysics Data System (ADS)

    Vigier, Jean-Pierre

    1991-02-01

    Starting from a nonlinear relativistic Klein-Gordon equation derived from the stochastic interpretation of quantum mechanics (proposed by Bohm-Vigier, (1) Nelson, (2) de Broglie, (3) Guerra et al. (4) ), one can construct joint wave and particle, soliton-like solutions, which follow the average de Broglie-Bohm (5) real trajectories associated with linear solutions of the usual Schrödinger and Klein-Gordon equations.

  15. Nonlinear coherent structures of Alfvén wave in a collisional plasma

    NASA Astrophysics Data System (ADS)

    Jana, Sayanee; Ghosh, Samiran; Chakrabarti, Nikhil

    2016-07-01

    The Alfvén wave dynamics is investigated in the framework of two-fluid approach in a compressible collisional magnetized plasma. In the finite amplitude limit, the dynamics of the nonlinear Alfvén wave is found to be governed by a modified Korteweg-de Vries Burgers equation (mKdVB). In this mKdVB equation, the electron inertia is found to act as a source of dispersion, and the electron-ion collision serves as a dissipation. The collisional dissipation is eventually responsible for the Burgers term in mKdVB equation. In the long wavelength limit, this weakly nonlinear Alfvén wave is shown to be governed by a damped nonlinear Schrödinger equation. Furthermore, these nonlinear equations are analyzed by means of analytical calculation and numerical simulation to elucidate the various aspects of the phase-space dynamics of the nonlinear wave. Results reveal that nonlinear Alfvén wave exhibits the dissipation mediated shock, envelope, and breather like structures. Numerical simulations also predict the formation of dissipative Alfvénic rogue wave, giant breathers, and rogue wave holes. These results are discussed in the context of the space plasma.

  16. Solar wind implication on dust ion acoustic rogue waves

    NASA Astrophysics Data System (ADS)

    Abdelghany, A. M.; Abd El-Razek, H. N.; Moslem, W. M.; El-Labany, S. K.

    2016-06-01

    The relevance of the solar wind with the magnetosphere of Jupiter that contains positively charged dust grains is investigated. The perturbation/excitation caused by streaming ions and electron beams from the solar wind could form different nonlinear structures such as rogue waves, depending on the dominant role of the plasma parameters. Using the reductive perturbation method, the basic set of fluid equations is reduced to modified Korteweg-de Vries (KdV) and further modified (KdV) equation. Assuming that the frequency of the carrier wave is much smaller than the ion plasma frequency, these equations are transformed into nonlinear Schrödinger equations with appropriate coefficients. Rational solution of the nonlinear Schrödinger equation shows that rogue wave envelopes are supported by the present plasma model. It is found that the existence region of rogue waves depends on the dust-acoustic speed and the streaming temperatures for both the ions and electrons. The dependence of the maximum rogue wave envelope amplitude on the system parameters has been investigated.

  17. Mixmaster revisited: wormhole solutions to the Bianchi IX Wheeler-DeWitt equation using the Euclidean-signature semi-classical method

    NASA Astrophysics Data System (ADS)

    Bae, Joseph H.

    2015-04-01

    A modified semi-classical method is used to construct both ground and excited state solutions to the canonically quantized vacuum Bianchi IX (Mixmaster) cosmological models. Employing a modified form of the semi-classical Ansatz we solve the relevant Wheeler-DeWitt equation asymptotically by integrating a set of linear transport equations along the flow of a suitably chosen solution to the corresponding Euclidean-signature Hamilton-Jacobi equation. For the Moncrief-Ryan (or ‘wormhole’) Hamilton-Jacobi solution, we compute the ground state quantum correction term associated with operator ordering ambiguities and show how higher order correction terms can be computed. We also determine the explicit, leading order forms of a family of excited states and show how to compute their quantum corrections as smooth, globally defined functions on the Bianchi IX minisuperspace. These excited state solutions are peaked away from the minisuperspace origin and are labeled by a pair of positive integers that can be plausibly interpreted as graviton excitation numbers for the two independent anisotropy degrees of freedom. The Euclidean-signature semi-classical method used here is applicable to more general models, representing a significant progress in the Wheeler-DeWitt approach to quantum gravity.

  18. Quantum field theoretical description of unstable behavior of trapped Bose-Einstein condensates with complex eigenvalues of Bogoliubov-de Gennes equations

    SciTech Connect

    Mine, Makoto Okumura, Masahiko Sunaga, Tomoka Yamanaka, Yoshiya

    2007-10-15

    The Bogoliubov-de Gennes equations are used for a number of theoretical works on the trapped Bose-Einstein condensates. These equations are known to give the energies of the quasi-particles when all the eigenvalues are real. We consider the case in which these equations have complex eigenvalues. We give the complete set including those modes whose eigenvalues are complex. The quantum fields which represent neutral atoms are expanded in terms of the complete set. It is shown that the state space is an indefinite metric one and that the free Hamiltonian is not diagonalizable in the conventional bosonic representation. We introduce a criterion to select quantum states describing the metastablity of the condensate, called the physical state conditions. In order to study the instability, we formulate the linear response of the density against the time-dependent external perturbation within the regime of Kubo's linear response theory. Some states, satisfying all the physical state conditions, give the blow-up and damping behavior of the density distributions corresponding to the complex eigenmodes. It is qualitatively consistent with the result of the recent analyses using the time-dependent Gross-Pitaevskii equation.

  19. Slow Modulations of Periodic Waves in Hamiltonian PDEs, with Application to Capillary Fluids

    NASA Astrophysics Data System (ADS)

    Benzoni-Gavage, S.; Noble, P.; Rodrigues, L. M.

    2014-08-01

    Since its elaboration by Whitham almost 50 years ago, modulation theory has been known to be closely related to the stability of periodic traveling waves. However, it is only recently that this relationship has been elucidated and that fully nonlinear results have been obtained. These only concern dissipative systems though: reaction-diffusion systems were first considered by Doelman et al. (Mem Am Math Soc 199(934):viii+105, 2009), and viscous systems of conservation laws have been addressed by Johnson et al. (Invent Math, 2013). Here, only nondissipative models are considered, and a most basic question is investigated, namely, the expected link between the hyperbolicity of modulated equations and the spectral stability of periodic traveling waves to sideband perturbations. This is done first in an abstract Hamiltonian framework, which encompasses a number of dispersive models, in particular the well-known (generalized) Korteweg-de Vries equation and the less known Euler-Korteweg system, in both Eulerian coordinates and Lagrangian coordinates. The latter is itself an abstract framework for several models arising in water wave theory, superfluidity, and quantum hydrodynamics. As regards its application to compressible capillary fluids, attention is paid here to untangle the interplay between traveling waves/modulation equations in Eulerian coordinates and those in Lagrangian coordinates. In the most general setting, it is proved that the hyperbolicity of modulated equations is indeed necessary for the spectral stability of periodic traveling waves. This extends earlier results by Serre (Commun Partial Differ Equ 30(1-3):259-282, 2005), Oh and Zumbrun (Arch Ration Mech Anal 166(2):99-166, 2003), and Johnson et al. (Phys D 239(23-24):2057-2065, 2010). In addition, reduced necessary conditions are obtained in the small-amplitude limit. Then numerical investigations are carried out for the modulated equations of the Euler-Korteweg system with two types of "pressure

  20. Teaching Equations.

    ERIC Educational Resources Information Center

    Nibbelink, William H.

    1990-01-01

    Proposed is a gradual transition from arithmetic to the idea of an equation with variables in the elementary grades. Vertical and horizontal formats of open sentences, the instructional sequence, vocabulary, and levels of understanding are discussed in this article. (KR)

  1. Asymptotic Stability of High-dimensional Zakharov-Kuznetsov Solitons

    NASA Astrophysics Data System (ADS)

    Côte, Raphaël; Muñoz, Claudio; Pilod, Didier; Simpson, Gideon

    2016-05-01

    We prove that solitons (or solitary waves) of the Zakharov-Kuznetsov (ZK) equation, a physically relevant high dimensional generalization of the Korteweg-de Vries (KdV) equation appearing in Plasma Physics, and having mixed KdV and nonlinear Schrödinger (NLS) dynamics, are strongly asymptotically stable in the energy space. We also prove that the sum of well-arranged solitons is stable in the same space. Orbital stability of ZK solitons is well-known since the work of de Bouard [Proc R Soc Edinburgh 126:89-112, 1996]. Our proofs follow the ideas of Martel [SIAM J Math Anal 157:759-781, 2006] and Martel and Merle [Math Ann 341:391-427, 2008], applied for generalized KdV equations in one dimension. In particular, we extend to the high dimensional case several monotonicity properties for suitable half-portions of mass and energy; we also prove a new Liouville type property that characterizes ZK solitons, and a key Virial identity for the linear and nonlinear part of the ZK dynamics, obtained independently of the mixed KdV-NLS dynamics. This last Virial identity relies on a simple sign condition which is numerically tested for the two and three dimensional cases with no additional spectral assumptions required. Possible extensions to higher dimensions and different nonlinearities could be obtained after a suitable local well-posedness theory in the energy space, and the verification of a corresponding sign condition.

  2. Symmetry operators and the separability of massive Klein Gordon and Dirac equations in the general five-dimensional Kerr (anti-)de Sitter black hole background

    NASA Astrophysics Data System (ADS)

    Wu, Shuang-Qing

    2009-03-01

    It is shown that the Dirac equation is separable by variables in a five-dimensional rotating Kerr (anti-)de Sitter black hole with two independent angular momenta. A first-order symmetry operator that commutes with the Dirac operator is constructed in terms of a rank-3 Killing Yano tensor whose square is a second-order symmetric Stäckel Killing tensor admitted by the five-dimensional Kerr (anti-)de Sitter spacetime. We highlight the construction procedure of such a symmetry operator. In addition, the first law of black hole thermodynamics has been extended to the case that the cosmological constant can be viewed as a thermodynamical variable.

  3. Solitary waves and nonlinear dynamic coherent structures in magnetic metamaterials

    NASA Astrophysics Data System (ADS)

    Tankeyev, A. P.; Smagin, V. V.; Borich, M. A.; Zhuravlev, A. S.

    2009-03-01

    Within the framework of the extended nonlinear Schrödinger equation (ENSE), two types of nonlinear states of magnetization in a ferromagnet-dielectric-metal metamagnetic structure have been obtained and investigated. These states have an internal structure; e.g., a periodic sequence of compound solitons is formed by kink-antikink pairs (shock waves), and coherent periodic breather structures are formed by “bright” quasi-solitons. Conditions have been found under which the envelope of these states is described by a modified Korteweg-de Vries (mKdV) equation. It is shown that the compound solitons are described by an mKdV equation with repulsion, and the breather structures, by an mKdV equation with attraction. It is shown also that the characteristic properties of the solutions are determined by the sign of the group-velocity dispersion rather than by the sign of the group velocity itself. The results obtained can be used for searching new nonlinear dynamic coherent structures, e.g., compound solitons and breathers in high-dispersion magnetic metamaterials.

  4. Kinetic Alfvén solitary and rogue waves in superthermal plasmas

    SciTech Connect

    Bains, A. S.; Li, Bo Xia, Li-Dong

    2014-03-15

    We investigate the small but finite amplitude solitary Kinetic Alfvén waves (KAWs) in low β plasmas with superthermal electrons modeled by a kappa-type distribution. A nonlinear Korteweg-de Vries (KdV) equation describing the evolution of KAWs is derived by using the standard reductive perturbation method. Examining the dependence of the nonlinear and dispersion coefficients of the KdV equation on the superthermal parameter κ, plasma β, and obliqueness of propagation, we show that these parameters may change substantially the shape and size of solitary KAW pulses. Only sub-Alfvénic, compressive solitons are supported. We then extend the study to examine kinetic Alfvén rogue waves by deriving a nonlinear Schrödinger equation from the KdV equation. Rational solutions that form rogue wave envelopes are obtained. We examine how the behavior of rogue waves depends on the plasma parameters in question, finding that the rogue envelopes are lowered with increasing electron superthermality whereas the opposite is true when the plasma β increases. The findings of this study may find applications to low β plasmas in astrophysical environments where particles are superthermally distributed.

  5. Dressed electrostatic solitary excitations in three component pair-plasmas: Application in isothermal pair-plasma with stationary ions

    SciTech Connect

    Esfandyari-Kalejahi, A.; Akbari-Moghanjoughi, M.; Haddadpour-Khiaban, B.

    2009-10-15

    In this work electrostatic solitary waves in a three component pair-plasma consisting of hot isothermal electrons (or negative fullerene ions), positrons (or positive fullerene ions), and stationary positive ions (say, dust particulates) are studied. Using reductive perturbation method, plasma fluid equations are reduced to a Korteweg-de Vries (KdV) equation. Considering the higher-order nonlinearity, a linear inhomogeneous equation is derived, and the stationary solutions of these coupled equations are achieved by applying the renormalization procedure of Kodama-Taniuti. It is observed that in the linear approximation and applying Fourier analysis, two electrostatic modes, namely, upper or optical and lower or acoustic modes, are present. However, the application of reductive perturbation technique confirms that only acoustic-electrostatic mode can propagate in such plasma as KdV soliton, the amplitude and width of which are studied regarding to plasma parameters {sigma} (positron-to-electron temperature ratio) and {delta} (stationary cold ions-to-electron density ratio). It is also observed that the higher-order nonlinearity leads to deformation of the soliton structure from bell-shaped to W-shaped depending on the variation in values of the plasma parameters {sigma} and {delta}. It is revealed that KdV-type solitary waves cannot propagate in three component pair-plasma when the pair-species temperature is equal.

  6. An Instability Index Theory for Quadratic Pencils and Applications

    NASA Astrophysics Data System (ADS)

    Bronski, Jared; Johnson, Mathew A.; Kapitula, Todd

    2014-04-01

    Primarily motivated by the stability analysis of nonlinear waves in second-order in time Hamiltonian systems, in this paper we develop an instability index theory for quadratic operator pencils acting on a Hilbert space. In an extension of the known theory for linear pencils, explicit connections are made between the number of eigenvalues of a given quadratic operator pencil with positive real parts to spectral information about the individual operators comprising the coefficients of the spectral parameter in the pencil. As an application, we apply the general theory developed here to yield spectral and nonlinear stability/instability results for abstract second-order in time wave equations. More specifically, we consider the problem of the existence and stability of spatially periodic waves for the "good" Boussinesq equation. In the analysis our instability index theory provides an explicit, and somewhat surprising, connection between the stability of a given periodic traveling wave solution of the "good" Boussinesq equation and the stability of the same periodic profile, but with different wavespeed, in the nonlinear dynamics of a related generalized Korteweg-de Vries equation.

  7. Remark on the phase shift in the Kuzmak-Whitham ansatz

    NASA Astrophysics Data System (ADS)

    Dobrokhotov, S. Yu.; Minenkov, D. S.

    2011-03-01

    We consider one-phase ( formal) asymptotic solutions in the Kuzmak-Whitham form for the nonlinear Klein-Gordon equation and for the Korteweg-de Vries equation. In this case, the leading asymptotic expansion term has the form X( S( x, t)/ h+Φ( x, t), I( x, t), x, t) + O( h), where h ≪ 1 is a small parameter and the phase S}( x, t) and slowly changing parameters I( x, t) are to be found from the system of "averaged" Whitham equations. We obtain the equations for the phase shift Φ( x, t) by studying the second-order correction to the leading term. The corresponding procedure for finding the phase shift is then nonuniform with respect to the transition to a linear (and weakly nonlinear) case. Our observation, which essentially follows from papers by Haberman and collaborators, is that if we incorporate the phase shift Φ into the phase and adjust the parameter Ĩ by setting tilde S = S + hΦ+ O( h 2), Ĩ = I + hI 1 + O( h 2), then the functions tilde S ( x, t, h) and Ĩ( x, t, h) become solutions of the Cauchy problem for the same Whitham system but with modified initial conditions. These functions completely determine the leading asymptotic term, which is X( tilde S ( x, t, h)/ h, Ĩ( x, t, h), x, t) + O( h).

  8. Global dynamical behaviors in a physical shallow water system

    NASA Astrophysics Data System (ADS)

    Tchakoutio Nguetcho, Aurélien Serge; Li, Jibin; Bilbault, Jean-Marie

    2016-07-01

    The theory of bifurcations of dynamical systems is used to investigate the behavior of travelling wave solutions in an entire family of shallow water wave equations. This family is obtained by a perturbative asymptotic expansion for unidirectional shallow water waves. According to the parameters of the system, this family can lead to different sets of known equations such as Camassa-Holm, Korteweg-de Vries, Degasperis and Procesi and several other dispersive equations of the third order. Looking for possible travelling wave solutions, we show that different phase orbits in some regions of parametric planes are similar to those obtained with the model of the pressure waves studied by Li and Chen. Many other exact explicit travelling waves solutions are derived as well, some of them being in perfect agreement with solutions obtained in previous works by researchers using different methods. When parameters are varied, the conditions under which the above solutions appear are also shown. The dynamics of singular nonlinear travelling system is completely determined for each of the above mentioned equations. Moreover, we define sufficient conditions leading to the existence of propagating wave solutions and demonstrate how and why travelling waves lose their smoothness and develop into solutions with compact support or breaking waves.

  9. Dust-ion acoustic cnoidal waves and associated nonlinear ion flux in a nonthermal dusty plasma

    NASA Astrophysics Data System (ADS)

    Ur-Rehman, Hafeez; Mahmood, S.

    2016-09-01

    The dust-ion acoustic nonlinear periodic (cnoidal) waves and solitons are investigated in a dusty plasma containing dynamic cold ions, superthermal kappa distributed electrons and static charged dust particles. The massive dust particles can have positive or negative charge depending on the plasma environment. Using reductive perturbation method (RPM) with appropriate periodic boundary conditions, the evolution equations for the first and second order nonlinear potentials are derived. The first order potential is determined through Korteweg-de Vries (KdV) equation which gives dust-ion acoustic cnoidal waves and solitons structures. The solution of second order nonlinear potential is obtained through an inhomogeneous differential equation derived from collecting higher order terms of dynamic equations, which is linear for second order electrostatic potential. The nonlinear ion flux associated with the cnoidal waves is also found out numerically. The numerical plots of the dust-ion acoustic cnoidal wave and soliton structures for both positively and negatively charged dust particles cases and nonthermal electrons are also presented for illustration. It is found that only compressive nonlinear electrostatic structures are formed in case of positively dust charged particles while both compressive and rarefactive nonlinear structures are obtained in case of negatively charged particles depending on the negatively charged dust density in a nonthermal dusty plasma. The numerical results are obtained using data of the ionospheric region containing dusty plasma exist in the literature.

  10. Beautiful equations

    NASA Astrophysics Data System (ADS)

    Viljamaa, Panu; Jacobs, J. Richard; Chris; JamesHyman; Halma, Matthew; EricNolan; Coxon, Paul

    2014-07-01

    In reply to a Physics World infographic (part of which is given above) about a study showing that Euler's equation was deemed most beautiful by a group of mathematicians who had been hooked up to a functional magnetic-resonance image (fMRI) machine while viewing mathematical expressions (14 May, http://ow.ly/xHUFi).

  11. Higher-order nonlinearity of electron-acoustic solitary waves with vortex-like electron distribution and electron beam

    SciTech Connect

    El-Taibany, W.F.; Moslem, Waleed M.

    2005-03-01

    The nonlinear wave structure of small-amplitude electron-acoustic solitary waves (EASWs) is investigated in a four-component plasma consisting of cold electron fluid, hot electrons obeying vortex-like distribution traversed by a warm electron beam and stationary ions. The streaming velocity of the beam, u{sub o}, plays the dominant role in determining the roots of the linear dispersion relation associated with the system. Using the reductive perturbation theory, the basic set of equations is reduced to a modified Korteweg-de Vries (mKdV) equation. With the inclusion of higher-order nonlinearity, a linear inhomogeneous mKdV type equation with fifth-order dispersion term is derived and the higher-order solution is obtained using a renormalization method. However, both mKdV and mKdV-type solutions present a positive potential, which corresponds to a hole (hump) in the cold (hot) electron number density. The mKdV-type solution has a smaller energy amplitude and a wider width than that of mKdV solution. The dependence of the energy amplitude, the width, and the velocity on the system parameters is investigated. The findings of this investigation are used to interpret the electrostatic solitary waves observed by the Geotail spacecraft in the plasma sheet boundary layer of the Earth's magnetosphere.

  12. Linear and nonlinear heavy ion-acoustic waves in a strongly coupled plasma

    SciTech Connect

    Ema, S. A. Mamun, A. A.; Hossen, M. R.

    2015-09-15

    A theoretical study on the propagation of linear and nonlinear heavy ion-acoustic (HIA) waves in an unmagnetized, collisionless, strongly coupled plasma system has been carried out. The plasma system is assumed to contain adiabatic positively charged inertial heavy ion fluids, nonextensive distributed electrons, and Maxwellian light ions. The normal mode analysis is used to study the linear behaviour. On the other hand, the well-known reductive perturbation technique is used to derive the nonlinear dynamical equations, namely, Burgers equation and Korteweg-de Vries (K-dV) equation. They are also numerically analyzed in order to investigate the basic features of shock and solitary waves. The adiabatic effects on the HIA shock and solitary waves propagating in such a strongly coupled plasma are taken into account. It has been observed that the roles of the adiabatic positively charged heavy ions, nonextensivity of electrons, and other plasma parameters arised in this investigation have significantly modified the basic features (viz., polarity, amplitude, width, etc.) of the HIA solitary/shock waves. The findings of our results obtained from this theoretical investigation may be useful in understanding the linear as well as nonlinear phenomena associated with the HIA waves both in space and laboratory plasmas.

  13. A new bidirectional generalization of (2+1)-dimensional matrix k-constrained Kadomtsev-Petviashvili hierarchy

    SciTech Connect

    Chvartatskyi, O. I. Sydorenko, Yu. M.

    2013-11-15

    We introduce a new bidirectional generalization of (2+1)-dimensional k-constrained Kadomtsev-Petviashvili (KP) hierarchy ((2+1)-BDk-cKPH). This new hierarchy generalizes (2+1)-dimensional k-cKP hierarchy, (t{sub A}, τ{sub B}) and (γ{sub A}, σ{sub B}) matrix hierarchies. (2+1)-BDk-cKPH contains a new matrix (1+1)-k-constrained KP hierarchy. Some members of (2+1)-BDk-cKPH are also listed. In particular, it contains matrix generalizations of Davey-Stewartson (DS) systems, (2+1)-dimensional modified Korteweg-de Vries equation and the Nizhnik equation. (2+1)-BDk-cKPH also includes new matrix (2+1)-dimensional generalizations of the Yajima-Oikawa and Melnikov systems. Binary Darboux Transformation Dressing Method is also proposed for construction of exact solutions for equations from (2+1)-BDk-cKPH. As an example the exact form of multi-soliton solutions for vector generalization of the DS system is given.

  14. On matrix Painlevé hierarchies

    NASA Astrophysics Data System (ADS)

    Gordoa, P. R.; Pickering, A.; Zhu, Z. N.

    2016-07-01

    We define a matrix first Painlevé hierarchy and a matrix second Painlevé (PII) hierarchy. For our matrix PII hierarchy we also give auto-Bäcklund transformations and consider the iteration of solutions. This is the first paper to define matrix Painlevé hierarchies and to give auto-Bäcklund transformations for a matrix Painlevé hierarchy. We also consider, amongst other results, the derivation of sequences of special integrals and autonomous limits. Until now it has been unknown how to connect the known matrix PII equation to the obvious candidates for related completely integrable matrix partial differential equations. Our matrix PII hierarchy is placed firmly within the context of a matrix modified Korteweg-de Vries (mKdV) hierarchy. In deriving our matrix PII hierarchy we make use of the Hamiltonian structure of this matrix mKdV hierarchy. We thus see once again the importance for Painlevé hierarchies of the integrability structures of related completely integrable equations.

  15. Standard and embedded solitons in nematic optical fibers.

    PubMed

    Rodríguez, R F; Reyes, J A; Espinosa-Cerón, A; Fujioka, J; Malomed, B A

    2003-09-01

    A model for a non-Kerr cylindrical nematic fiber is presented. We use the multiple scales method to show the possibility of constructing different kinds of wave packets of transverse magnetic modes propagating through the fiber. This procedure allows us to generate different hierarchies of nonlinear partial differential equations which describe the propagation of optical pulses along the fiber. We go beyond the usual weakly nonlinear limit of a Kerr medium and derive a complex modified Korteweg-de Vries equation (CM KdV) which governs the dynamics for the amplitude of the wave packet. In this derivation the dispersion, self-focussing, and diffraction in the nematic fiber are taken into account. It is shown that this CM KdV equation has two-parameter families of bright and dark complex solitons. We show analytically that under certain conditions, the bright solitons are actually double-embedded solitons. We explain why these solitons do not radiate at all, even though their wave numbers are contained in the linear spectrum of the system. We study (numerically and analytically) the stability of these solitons. Our results show that these embedded solitons are stable solutions, which is an interesting property since in most systems the embedded solitons are weakly unstable solutions. Finally, we close the paper by making comments on the advantages as well as the limitations of our approach, and on further generalizations of the model and method presented. PMID:14524911

  16. Landau damping effects on dust-acoustic solitary waves in a dusty negative-ion plasma

    SciTech Connect

    Barman, Arnab; Misra, A. P. E-mail: apmisra@gmail.com

    2014-07-15

    The nonlinear theory of dust-acoustic waves (DAWs) with Landau damping is studied in an unmagnetized dusty negative-ion plasma in the extreme conditions when the free electrons are absent. The cold massive charged dusts are described by fluid equations, whereas the two-species of ions (positive and negative) are described by the kinetic Vlasov equations. A Korteweg-de Vries (KdV) equation with Landau damping, governing the dynamics of weakly nonlinear and weakly dispersive DAWs, is derived following Ott and Sudan [Phys. Fluids 12, 2388 (1969)]. It is shown that for some typical laboratory and space plasmas, the Landau damping (and the nonlinear) effects are more pronounced than the finite Debye length (dispersive) effects for which the KdV soliton theory is not applicable to DAWs in dusty pair-ion plasmas. The properties of the linear phase velocity, solitary wave amplitudes (in presence and absence of the Landau damping) as well as the Landau damping rate are studied with the effects of the positive ion to dust density ratio (μ{sub pd}) as well as the ratios of positive to negative ion temperatures (σ) and masses (m)

  17. Longitudinal singular response of dusty plasma medium in weak and strong coupling limits

    SciTech Connect

    Kumar Tiwari, Sanat; Das, Amita; Kaw, Predhiman; Sen, Abhijit

    2012-01-15

    The longitudinal response of a dusty plasma medium in both weak and strong coupling limits has been investigated in detail using analytic as well as numerical techniques. In particular, studies on singular response of the medium have been specifically investigated here. A proper Galilean invariant form of the generalized hydrodynamic fluid model has been adopted for the description of the dusty plasma medium. For weak non-linear response, analytic reductive perturbative approach has been adopted. It is well known that in the weak coupling regime for the dusty plasma medium, such an analysis leads to the Korteweg-de Vries equation (KdV) equation and predicts the existence of localized smooth soliton solutions. We show that the strongly coupled dust fluid with the correct Galilean invariant form does not follow the KdV paradigm. Instead, it reduces to the form of Hunter-Saxton equation, which does not permit soliton solutions. The system in this case displays singular response with both conservative as well as dissipative attributes. At arbitrary high amplitudes, the existence and spontaneous formation of sharply peaked cusp structures in both weak and strong coupling regimes has been demonstrated numerically.

  18. Ion-acoustic Gardner Solitons in electron-positron-ion plasma with two-electron temperature distributions

    NASA Astrophysics Data System (ADS)

    Rehman, Momin A.; Mishra, M. K.

    2016-01-01

    The ion-acoustic solitons in collisionless plasma consisting of warm adiabatic ions, isothermal positrons, and two temperature distribution of electrons have been studied. Using reductive perturbation method, Korteweg-de Vries (K-dV), the modified K-dV (m-KdV), and Gardner equations are derived for the system. The soliton solution of the Gardner equation is discussed in detail. It is found that for a given set of parameter values, there exists a critical value of β=Tc/Th, (ratio of cold to hot electron temperature) below which only rarefactive KdV solitons exist and above it compressive KdV solitons exist. At the critical value of β, both compressive and rarefactive m-KdV solitons co-exist. We have also investigated the soliton in the parametric regime where the KdV equation is not valid to study soliton solution. In this region, it is found that below the critical concentration the system supports rarefactive Gardner solitons and above it compressive Gardner solitons are found. The effects of temperature ratio of two-electron species, cold electron concentration, positron concentration on the characteristics of solitons are also discussed.

  19. Soliton propagation in an inhomogeneous plasma at critical density of negative ions: Effects of gyratory and thermal motions of ions

    SciTech Connect

    Malik, Hitendra K.; Kawata, Shigeo

    2007-10-15

    The effects of gyratory and thermal motions of ions on soliton propagation in an inhomogeneous plasma that contains positive ions, negative ions, and electrons are studied at a critical density of negative ions. Since at this critical negative ion density the nonlinear term of the relevant Korteweg-deVries (KdV) equation vanishes, a higher order of nonlinearity is considered by retaining higher-order perturbation terms in the expansion of dependent quantities together with the appropriate set of stretched coordinates. Under this situation, time-dependent perturbation leads to the evolution of modified KdV solitons, which are governed by a modified form of the KdV equation that has an additional term due to the density gradient present in the plasma. On the basis of the solution of this equation and obliquely applied magnetic field, the effects of gyratory and thermal motions of ions are analyzed on the soliton propagation for three cases, n{sub n0}n{sub e0}, together with n{sub n0} (n{sub e0}) as the density of negative ions (electrons). The role of the negative ions in the evolution of the modes and the solitons is also discussed. Under the limiting cases, our calculations reduce to the ones obtained by other investigators in the past. This substantiates the generality of the present analysis.

  20. Dust kinetic Alfvén solitary and rogue waves in a superthermal dusty plasma

    SciTech Connect

    Saini, N. S. Singh, Manpreet; Bains, A. S.

    2015-11-15

    Dust kinetic Alfvén solitary waves (DKASWs) have been examined in a low-β dusty plasma comprising of negatively charged dust grains, superthermal electrons, and ions. A nonlinear Korteweg-de Vries (KdV) equation has been derived using the reductive perturbation method. The combined effects of superthermality of charged particles (via κ), plasma β, obliqueness of propagation (θ), and dust concentration (via f) on the shape and size of the DKASWs have been examined. Only negative potential (rarefactive) structures are observed. Further, characteristics of dust kinetic Alfvén rogue waves (DKARWs), by deriving the non-linear Schrödinger equation (NLSE) from the KdV equation, are studied. Rational solutions of NLSE show that rogue wave envelopes are supported by this plasma model. It is observed that the influence of various plasma parameters (superthermality, plasma β, obliqueness, and dust concentration) on the characteristics of the DKARWs is very significant. This fundamental study may be helpful in understanding the formation of coherent nonlinear structures in space and astrophysical plasma environments where superthermal particles are present.

  1. Solitary wave evolution in a magnetized inhomogeneous plasma under the effect of ionization

    SciTech Connect

    Jyoti; Malik, Hitendra K.

    2011-10-15

    A modified form of Korteweg-deVries (KdV) equation appropriate to nonlinear ion acoustic solitary waves in an inhomogeneous plasma is derived in the presence of an external magnetic field and constant ionization in the plasma. This equation differs from usual version of the KdV equation because of the inclusion of two terms arising due to ionization and density gradient present in the plasma. In this plasma, only the compressive solitary waves are found to propagate corresponding to the fast and slow modes. The amplitude of the solitary wave increases with an enhancement in the ionization for the fast mode as well as for the slow mode. The effect of magnetic field is to enhance the width of the solitary structure. The amplitude is found to increase (decrease) with an enhancement in charge number of the ions for the fast (slow) mode. The tailing structure becomes more (less) prominent with the rise in ion drift velocity for the case of fast (slow) mode.

  2. Evolution of ion-acoustic solitary waves in Maxwellian dusty plasmas

    SciTech Connect

    Das, G. C.; Choudhury, Balen; Bora, M. P.

    2010-12-15

    The nonlinear wave phenomena in the vicinity of Korteweg-de Vries (KdV) equation have been derived to study the salient features of solitons in a complex plasma consisting of Maxwellian electrons, ions, and cold dust with the effect of dust charge fluctuation. The reductive perturbation method has been applied to the dynamical system causeway and the derived KdV equation predicts different natures of solitons in complex plasma. The dynamics of the soliton propagation in the considered plasma constituents in ionospheric auroral regions exhibits rarefactive solitons, which is an interesting feature. The dust charge fluctuation by the increasing impact of electrons leads the nonlinear effect to be tending to zero. Because of which, the formation of a narrow solitary wave packet with the generation of high energy becomes possible and results in the phenomena of soliton radiation. In order to probe this further, we derive a modified KdV equation to study soliton propagation which, in turn, indicates the possibility of the shock formation in solitary waves.

  3. Nature of short, high-amplitude compressive stress pulses in a periodic dissipative laminate.

    PubMed

    Franco Navarro, Pedro; Benson, David J; Nesterenko, Vitali F

    2015-12-01

    We study the evolution of high-amplitude stress pulses in periodic dissipative laminates taking into account the nonlinear constitutive equations of the components and their dissipative behavior. Aluminum-tungsten laminate was selected due to the large difference in acoustic impedances of components, the significant nonlinearity of the aluminum constitutive equation at the investigated range of stresses, and its possible practical applications. Laminates with different cell size, which controls the internal time scale, impacted by plates with different thicknesses that determine the incoming pulse duration, were investigated. It has been observed that the ratio of the duration of the incoming pulse to the internal characteristic time determines the nature of the high-amplitude dissipative propagating waves-a triangular oscillatory shock-like profile, a train of localized pulses, or a single localized pulse. These localized quasistationary waves resemble solitary waves even in the presence of dissipation: The similar pulses emerged from different initial conditions, indicating that they are inherent properties of the corresponding laminates; their characteristic length scale is determined by the scale of mesostructure, nonlinear properties of materials, and the stress amplitude; and a linear relationship exists between their speed and amplitude. They mostly recover their shapes after collision with phase shift. A theoretical description approximating the shape, length scale, and speed of these high-amplitude dissipative pulses was proposed based on the Korteweg-de Vries equation with a dispersive term determined by the mesostructure and a nonlinear term derived using Hugoniot curves of components. PMID:26764784

  4. Nature of short, high-amplitude compressive stress pulses in a periodic dissipative laminate

    NASA Astrophysics Data System (ADS)

    Franco Navarro, Pedro; Benson, David J.; Nesterenko, Vitali F.

    2015-12-01

    We study the evolution of high-amplitude stress pulses in periodic dissipative laminates taking into account the nonlinear constitutive equations of the components and their dissipative behavior. Aluminum-tungsten laminate was selected due to the large difference in acoustic impedances of components, the significant nonlinearity of the aluminum constitutive equation at the investigated range of stresses, and its possible practical applications. Laminates with different cell size, which controls the internal time scale, impacted by plates with different thicknesses that determine the incoming pulse duration, were investigated. It has been observed that the ratio of the duration of the incoming pulse to the internal characteristic time determines the nature of the high-amplitude dissipative propagating waves—a triangular oscillatory shock-like profile, a train of localized pulses, or a single localized pulse. These localized quasistationary waves resemble solitary waves even in the presence of dissipation: The similar pulses emerged from different initial conditions, indicating that they are inherent properties of the corresponding laminates; their characteristic length scale is determined by the scale of mesostructure, nonlinear properties of materials, and the stress amplitude; and a linear relationship exists between their speed and amplitude. They mostly recover their shapes after collision with phase shift. A theoretical description approximating the shape, length scale, and speed of these high-amplitude dissipative pulses was proposed based on the Korteweg-de Vries equation with a dispersive term determined by the mesostructure and a nonlinear term derived using Hugoniot curves of components.

  5. Dust kinetic Alfvén solitary and rogue waves in a superthermal dusty plasma

    NASA Astrophysics Data System (ADS)

    Saini, N. S.; Singh, Manpreet; Bains, A. S.

    2015-11-01

    Dust kinetic Alfvén solitary waves (DKASWs) have been examined in a low-β dusty plasma comprising of negatively charged dust grains, superthermal electrons, and ions. A nonlinear Korteweg-de Vries (KdV) equation has been derived using the reductive perturbation method. The combined effects of superthermality of charged particles (via κ), plasma β, obliqueness of propagation (θ), and dust concentration (via f) on the shape and size of the DKASWs have been examined. Only negative potential (rarefactive) structures are observed. Further, characteristics of dust kinetic Alfvén rogue waves (DKARWs), by deriving the non-linear Schrödinger equation (NLSE) from the KdV equation, are studied. Rational solutions of NLSE show that rogue wave envelopes are supported by this plasma model. It is observed that the influence of various plasma parameters (superthermality, plasma β, obliqueness, and dust concentration) on the characteristics of the DKARWs is very significant. This fundamental study may be helpful in understanding the formation of coherent nonlinear structures in space and astrophysical plasma environments where superthermal particles are present.

  6. Landau damping effects on dust-acoustic solitary waves in a dusty negative-ion plasma

    NASA Astrophysics Data System (ADS)

    Barman, Arnab; Misra, A. P.

    2014-07-01

    The nonlinear theory of dust-acoustic waves (DAWs) with Landau damping is studied in an unmagnetized dusty negative-ion plasma in the extreme conditions when the free electrons are absent. The cold massive charged dusts are described by fluid equations, whereas the two-species of ions (positive and negative) are described by the kinetic Vlasov equations. A Korteweg-de Vries (KdV) equation with Landau damping, governing the dynamics of weakly nonlinear and weakly dispersive DAWs, is derived following Ott and Sudan [Phys. Fluids 12, 2388 (1969)]. It is shown that for some typical laboratory and space plasmas, the Landau damping (and the nonlinear) effects are more pronounced than the finite Debye length (dispersive) effects for which the KdV soliton theory is not applicable to DAWs in dusty pair-ion plasmas. The properties of the linear phase velocity, solitary wave amplitudes (in presence and absence of the Landau damping) as well as the Landau damping rate are studied with the effects of the positive ion to dust density ratio (μpd) as well as the ratios of positive to negative ion temperatures (σ) and masses (m).

  7. Linear and nonlinear heavy ion-acoustic waves in a strongly coupled plasma

    NASA Astrophysics Data System (ADS)

    Ema, S. A.; Hossen, M. R.; Mamun, A. A.

    2015-09-01

    A theoretical study on the propagation of linear and nonlinear heavy ion-acoustic (HIA) waves in an unmagnetized, collisionless, strongly coupled plasma system has been carried out. The plasma system is assumed to contain adiabatic positively charged inertial heavy ion fluids, nonextensive distributed electrons, and Maxwellian light ions. The normal mode analysis is used to study the linear behaviour. On the other hand, the well-known reductive perturbation technique is used to derive the nonlinear dynamical equations, namely, Burgers equation and Korteweg-de Vries (K-dV) equation. They are also numerically analyzed in order to investigate the basic features of shock and solitary waves. The adiabatic effects on the HIA shock and solitary waves propagating in such a strongly coupled plasma are taken into account. It has been observed that the roles of the adiabatic positively charged heavy ions, nonextensivity of electrons, and other plasma parameters arised in this investigation have significantly modified the basic features (viz., polarity, amplitude, width, etc.) of the HIA solitary/shock waves. The findings of our results obtained from this theoretical investigation may be useful in understanding the linear as well as nonlinear phenomena associated with the HIA waves both in space and laboratory plasmas.

  8. Supersymmetric Structure of two Families of Solitons

    NASA Astrophysics Data System (ADS)

    Koller, Andrew; Olshanii, Maxim

    2012-02-01

    Solitons have generated considerable interest in the cold atoms and condensed matter communities. We demonstrate that two families of n-soliton solutions (with n an integer) -- one for the attractive nonlinear Schr"odinger (NLS) equation, and one for the sine-Gordon (sG) equation -- originate from a quantum-mechanical supersymmetric (QM-SUSY) chain connecting a set of reflectionless operators Hn. The families consist of breather-type solitons for NLSootnotetextD. Schrader, IEEE J. Quantum Electron. 31, 2221 (1995). and multi-(anti)kink solitons with specific velocities for sG. The operators Hn, which we refer to as Akulin`s HamiltoniansootnotetextV. M. Akulin, Coherent Dynamics of Complex Quantum Systems (Springer, Heidelberg, 2006)., form reflectionless direct-scattering initial conditions for the inverse scattering method. Such a QM-SUSY chain is analogous to the known connection between QM-SUSY chains of P"oschl-Teller potentials and solitons of the Korteweg-de Vries (KdV) equationootnotetextSukumar, J. Phys. A 19, 2297 (1986). The existence of QM-SUSY chains connecting soliton solutions, now for three different integrable nonlinear equations, sheds light on the underlying mechanisms responsible for soliton generation.

  9. The local--global analysis of the stimulated Brillouin scattering in the regime of nonlinear sound waves

    SciTech Connect

    Rozmus, W.; Casanova, M.; Pesme, D.; Heron, A.; Adam, J. )

    1992-03-01

    The effect of ion sound wave (ISW) nonlinearities on the stimulated Brillouin scattering (SBS) in long plasmas is investigated within the framework of the Korteweg--de Vries--Maxwell equations. The nonlinear evolution of the driven ISW results in the localization of the ion density on a scale shorter than the wavelength ({lambda}{sub {ital s}}) of the resonant ISW satisfying SBS three-wave matching conditions. Since the transverse wave amplitudes vary on a much longer scale, a local--global modeling of SBS is proposed in which this scale separation is exploited. The local part of the procedure includes a solution to the damped KdV equation with periodic boundary conditions and driven by a constant amplitude ponderomotive force. In the global part of the analysis approximate solutions for the transverse waves in long plasmas are constructed using the results from the local part. Particle-in-cell simulations have been performed in order to investigate the importance of kinetic effects for the local model. Numerical results obtained from the solutions to the KdV--Maxwell equations are well approximated by the local--global modeling. They are also compared with the results of a harmonic decomposition approximation.

  10. Marcus equation

    DOE R&D Accomplishments Database

    1998-09-21

    In the late 1950s to early 1960s Rudolph A. Marcus developed a theory for treating the rates of outer-sphere electron-transfer reactions. Outer-sphere reactions are reactions in which an electron is transferred from a donor to an acceptor without any chemical bonds being made or broken. (Electron-transfer reactions in which bonds are made or broken are referred to as inner-sphere reactions.) Marcus derived several very useful expressions, one of which has come to be known as the Marcus cross-relation or, more simply, as the Marcus equation. It is widely used for correlating and predicting electron-transfer rates. For his contributions to the understanding of electron-transfer reactions, Marcus received the 1992 Nobel Prize in Chemistry. This paper discusses the development and use of the Marcus equation. Topics include self-exchange reactions; net electron-transfer reactions; Marcus cross-relation; and proton, hydride, atom and group transfers.

  11. Marcus equation

    SciTech Connect

    1998-11-01

    In the late 1950s to early 1960s Rudolph A. Marcus developed a theory for treating the rates of outer-sphere electron-transfer reactions. Outer-sphere reactions are reactions in which an electron is transferred from a donor to an acceptor without any chemical bonds being made or broken. (Electron-transfer reactions in which bonds are made or broken are referred to as inner-sphere reactions.) Marcus derived several very useful expressions, one of which has come to be known as the Marcus cross-relation or, more simply, as the Marcus equation. It is widely used for correlating and predicting electron-transfer rates. For his contributions to the understanding of electron-transfer reactions, Marcus received the 1992 Nobel Prize in Chemistry. This paper discusses the development and use of the Marcus equation. Topics include self-exchange reactions; net electron-transfer reactions; Marcus cross-relation; and proton, hydride, atom and group transfers.

  12. The A d S 5 Warp of Spatially Hyperbolic Universes, Spinless Modes and Spectra and the Corresponding Wheeler-DeWitt Schrödinger-Like Equation

    NASA Astrophysics Data System (ADS)

    Dariescu, Ciprian; Dariescu, Marina-Aura; Bodnarescu, Adrian

    2016-02-01

    In this paper, we consider an A d S 5 bulk with k=-1- FRW branes, together with bosons test particles, evolving in the 5D hyperspace. In the first part, we compute the wave function of the scalar fields in the bulk and the allowed mass spectrum for physically relevant cases. Also, an important quantization law, connecting the mass spectrum of the bosons on the brane and the bulk mass parameter is written down. In the second part, in oder to develop a quantization model, we use the Wheeler-DeWitt equation and solve its Schrödinger-like form, obtaining the wave function of the Universe. The solutions describe a universe emerging out of nothing, without tunneling. Lastly, using a mixture of states, we emphasize a smooth universe, with neither Bangs nor Crunches.

  13. Developpement et implementation d'une methode pour resoudre les equations de la couche limite laminaire et turbulente

    NASA Astrophysics Data System (ADS)

    Leuca, Maxim

    CFD (Computational Fluid Dynamics) is a computational tool for studying flow in science and technology. The Aerospace Industry uses increasingly the CFD modeling and design phase of the aircraft, so the precision with which phenomena are simulated boundary layer is very important. The research efforts are focused on optimizing the aerodynamic performance of airfoils to predict the drag and delay the laminar-turbulent transition. CFD codes must be fast and efficient to model complex geometries for aerodynamic flows. The resolution of the boundary layer equations requires a large amount of computing resources for viscous flows. CFD codes are commonly used to simulate aerodynamic flows, require normal meshes to the wall, extremely fine, and, by consequence, the calculations are very expensive. . This thesis proposes a new approach to solve the equations of boundary layer for laminar and turbulent flows using an approach based on the finite difference method. Integrated into a code of panels, this concept allows to solve airfoils avoiding the use of iterative algorithms, usually computing time and often involving convergence problems. The main advantages of panels methods are their simplicity and ability to obtain, with minimal computational effort, solutions in complex flow conditions for relatively complicated configurations. To verify and validate the developed program, experimental data are used as references when available. Xfoil code is used to obtain data as a pseudo references. Pseudo-reference, as in the absence of experimental data, we cannot really compare two software together. Xfoil is a program that has proven to be accurate and inexpensive computing resources. Developed by Drela (1985), this program uses the method with two integral to design and analyze profiles of wings at low speed (Drela et Youngren, 2014), (Drela, 2003). NACA 0012, NACA 4412, and ATR-42 airfoils have been used for this study. For the airfoils NACA 0012 and NACA 4412 the calculations

  14. Generalized Cahn-Hilliard Navier-Stokes equations for numerical simulations of multicomponent immiscible flows

    NASA Astrophysics Data System (ADS)

    Li, Zhaorui; Livescu, Daniel

    2014-11-01

    By using the second-law of thermodynamics and the Onsager reciprocal method for irreversible processes, we have developed a set of physically consistent multicomponent compressible generalized Cahn-Hilliard Navier-Stokes (CGCHNS) equations from basic thermodynamics. The new equations can describe not only flows with pure miscible and pure immiscible materials but also complex flows in which mass diffusion and surface tension or Korteweg stresses effects may coexist. Furthermore, for the first time, the incompressible generalized Cahn-Hilliard Navier-Stokes (IGCHNS) equations are rigorously derived from the incompressible limit of the CGCHNS equations (as the infinite sound speed limit) and applied to the immiscible Rayleigh-Taylor instability problem. Extensive good agreements between numerical results and the linear stability theory (LST) predictions for the Rayleigh-Taylor instability are achieved for a wide range of wavenumber, surface tension, and viscosity values. The late-time results indicate that the IGCHNS equations can naturally capture complex interface topological changes including merging and breaking-up and are free of singularity problems.

  15. Effects of ionization and ion loss on dust ion- acoustic solitary waves in a collisional dusty plasma with suprathermal electrons

    NASA Astrophysics Data System (ADS)

    Tribeche, Mouloud; Mayout, Saliha

    2016-07-01

    The combined effects of ionization, ion loss and electron suprathermality on dust ion- acoustic solitary waves in a collisional dusty plasma are examined. Carrying out a small but finite amplitude analysis, a damped Korteweg- de Vries (dK-- dV) equation is derived. The damping term decreases with the increase of the spectral index and saturates for Maxwellian electrons. Choosing typical plasma parameters, the analytical approximate solution of the dK- dV equation is numerically analyzed. We first neglect the ionization and ion loss effects and account only for collisions to estimate the relative importance between these damping terms which can act concurrently. Interestingly, we found that as the suprathermal character of the electrons becomes important, the strength of the collisions related dissipation becomes more important and causes the DIA solitary wave amplitude to decay more rapidly. Moreover, the collisional damping may largely prevail over the ionization and ion loss related damping. The latter becomes more effective as the electrons evolve far away from their thermal equilibrium. Our results complement and provide new insights into previously published work on this problem.

  16. Linear and nonlinear ion-acoustic waves in nonrelativistic quantum plasmas with arbitrary degeneracy

    NASA Astrophysics Data System (ADS)

    Haas, Fernando; Mahmood, Shahzad

    2015-11-01

    Linear and nonlinear ion-acoustic waves are studied in a fluid model for nonrelativistic, unmagnetized quantum plasma with electrons with an arbitrary degeneracy degree. The equation of state for electrons follows from a local Fermi-Dirac distribution function and applies equally well both to fully degenerate and classical, nondegenerate limits. Ions are assumed to be cold. Quantum diffraction effects through the Bohm potential are also taken into account. A general coupling parameter valid for dilute and dense plasmas is proposed. The linear dispersion relation of the ion-acoustic waves is obtained and the ion-acoustic speed is discussed for the limiting cases of extremely dense or dilute systems. In the long-wavelength limit, the results agree with quantum kinetic theory. Using the reductive perturbation method, the appropriate Korteweg-de Vries equation for weakly nonlinear solutions is obtained and the corresponding soliton propagation is analyzed. It is found that soliton hump and dip structures are formed depending on the value of the quantum parameter for the degenerate electrons, which affect the phase velocities in the dispersive medium.

  17. Ion-acoustic nonlinear periodic waves in electron-positron-ion plasma

    SciTech Connect

    Chawla, J. K.; Mishra, M. K.

    2010-10-15

    Ion-acoustic nonlinear periodic waves, namely, ion-acoustic cnoidal waves have been studied in electron-positron-ion plasma. Using reductive perturbation method and appropriate boundary condition for nonlinear periodic waves, the Korteweg-de Vries (KdV) equation is derived for the system. The cnoidal wave solution of the KdV equation is discussed in detail. It is found that the frequency of the cnoidal wave is a function of its amplitude. It is also found that the positron concentration modifies the properties of the ion-acoustic cnoidal waves. The existence regions for ion-acoustic cnoidal wave in the parameters space (p,{sigma}), where p and {sigma} are the positron concentration and temperature ratio of electron to positron, are discussed in detail. In the limiting case these ion-acoustic cnoidal waves reduce to the ion-acoustic soliton solutions. The effect of other parameters on the characteristics of the nonlinear periodic waves is also discussed.

  18. Compressive and rarefactive DIA solitons beyond the KdV limit

    SciTech Connect

    Mamun, A. A.; Deeba, F.

    2012-04-15

    The modified Gardner equation (MGE), showing the existence of compressive and rarefactive dust-ion-acoustic (DIA) solitons in a nonplanar dusty plasma (containing inertial ions, Boltzmann electrons, and negatively charged stationary dust) beyond the KdV Korteweg-de Vries (KdV) limit, is derived and numerically solved. The basic features of the compressive and rarefactive cylindrical and spherical DIA solitons, which are found to exist beyond the KdV limit, i.e., exist for {mu} {approx} 2/3 (where {mu} = Z{sub n}n{sub d0}/n{sub i0}, z{sub d} is the number of electrons residing onto the dust grain surface, n{sub d0}(n{sub i0}) is the dust (ion) number density at equilibrium, and {mu} {approx} 2/3 means that {mu} is not equal to 2/3, but it is around 2/3) are identified. These solitons (which can be referred to as DIA Gardner solitons (DIA-GSs)) are completely different from the KdV solitons because {mu} = 2/3 corresponds to the vanishing of the nonlinear coefficient of the KdV equation, and {mu} {approx} 2/3 corresponds to extremely large amplitude KdV solitons for which the validity of the reductive perturbation method breaks down. It is also shown that the properties of the nonplanar (cylindrical and spherical) DIA-GSs are significantly different from those of the one dimensional planar ones.

  19. Quasilongitudinal soliton in a two-dimensional strongly coupled complex dusty plasma in the presence of an external magnetic field.

    PubMed

    Ghosh, Samiran

    2014-09-01

    The propagation of a nonlinear low-frequency mode in two-dimensional (2D) monolayer hexagonal dusty plasma crystal in presence of external magnetic field and dust-neutral collision is investigated. The standard perturbative approach leads to a 2D Korteweg-de Vries (KdV) soliton for the well-known dust-lattice mode. However, the Coriolis force due to crystal rotation and Lorentz force due to magnetic field on dust particles introduce a linear forcing term, whereas dust-neutral drag introduce the usual damping term in the 2D KdV equation. This new nonlinear equation is solved both analytically and numerically to show the competition between the linear forcing and damping in the formation of quasilongitudinal soliton in a 2D strongly coupled complex (dusty) plasma. Numerical simulation on the basis of the typical experimental plasma parameters and the analytical solution reveal that the neutral drag force is responsible for the usual exponential decay of the soliton, whereas Coriolis and/or Lorentz force is responsible for the algebraic decay as well as the oscillating tail formation of the soliton. The results are discussed in the context of the plasma crystal experiment. PMID:25314548

  20. Generation of undular bores in the shelves of slowly-varying solitary waves.

    PubMed

    El, G. A.; Grimshaw, R. H. J.

    2002-12-01

    We study the long-time evolution of the trailing shelves that form behind solitary waves moving through an inhomogeneous medium, within the framework of the variable-coefficient Korteweg-de Vries equation. We show that the nonlinear evolution of the shelf leads typically to the generation of an undular bore and an expansion fan, which form apart but start to overlap and nonlinearly interact after a certain time interval. The interaction zone expands with time and asymptotically as time goes to infinity occupies the whole perturbed region. Its oscillatory structure strongly depends on the sign of the inhomogeneity gradient of the variable background medium. We describe the nonlinear evolution of the shelves in terms of exact solutions to the KdV-Whitham equations with natural boundary conditions for the Riemann invariants. These analytic solutions, in particular, describe the generation of small "secondary" solitary waves in the trailing shelves, a process observed earlier in various numerical simulations. (c) 2002 American Institute of Physics. PMID:12779625

  1. Effects Of Relative Strength Of Dispersion On The Formation Of Nonlinear Waves In Dusty Plasmas

    SciTech Connect

    Asgari, H.; Muniandy, S. V.; Wong, C. S.; Yap, S. L.

    2009-07-07

    In this paper, we studied the effect of strength of dispersion on the formation of solitons and shock waves in un-magnetized dusty plasma using the reductive perturbative technique. Different relational forms of strength parameter epsilon were chosen such a way that it altered the stretching of space, x and time, t variables, thereby leading to different nonlinearities. First, we considered the form zeta = sq root(epsilon(x-v{sub 0}t)) and tau = sq root(epsilont), where v{sub 0} is the phase velocity, with 0Korteweg-de Vries (KdV) equation for un-modulated dust acoustic wave with solitary wave-type solution. The effect of dissipation on the wave propagation was analyzed with coordinate transformations zeta epsilon(x-v{sub 0}t) and tau = epsilon{sup 2}t, with 0equation with shock wave-type solution. From this study, we concluded that when the dissipation effect is negligible in comparison with dispersion, dust charge fluctuations can only change the amplitude of solitary wave, as observed in the KdV case. However, when the system is not sufficiently dispersive, the dissipation due to dust charge fluctuations can play dominant role and eventually leads to the formation of dust-acoustic shock wave.

  2. Resolution of a shock in hyperbolic systems modified by weak dispersion.

    PubMed

    El, G A

    2005-09-01

    We present a way to deal with dispersion-dominated "shock-type" transition in the absence of completely integrable structure for the systems that one may characterize as strictly hyperbolic regularized by a small amount of dispersion. The analysis is performed by assuming that the dispersive shock transition between two different constant states can be modeled by an expansion fan solution of the associated modulation (Whitham) system for the short-wavelength nonlinear oscillations in the transition region (the so-called Gurevich-Pitaevskii problem). We consider both single-wave and bidirectional systems. The main mathematical assumption is that of hyperbolicity of the Whitham system for the solutions of our interest. By using general properties of the Whitham averaging for a certain class of nonlinear dispersive systems and specific features of the Cauchy data prescription on characteristics we derive a set of transition conditions for the dispersive shock, actually bypassing full integration of the modulation equations. Along with the Korteweg-de Vries (KdV) and modified KdV (mKdV) equations as model examples, we consider a nonintegrable system describing fully nonlinear ion-acoustic waves in collisionless plasma. In all cases our transition conditions are in complete agreement with previous analytical and numerical results. PMID:16252998

  3. Excitation of solitons by an external resonant wave with a slowly varying phase velocity

    SciTech Connect

    Aranson, I.; Meerson, B. . Racah Inst. of Physics); Tajima, Toshiki )

    1992-02-01

    A novel mechanism is proposed for the excitation of solitons in nonlinear dispersive media. The mechanism employs an external pumping wave with a varying phase velocity, which provides a continuous resonant excitation of a nonlinear wave in the medium. Two different schemes of a continuous resonant growth (continuous phase-locking) of the induced nonlinear wave are suggested. The first of them requires a definite time dependence of the pumping wave phase velocity and is relatively sensitive to the initial wave phase. The second employs the dynamic autoresonance effect and is insensitive to the exact time dependence of the pumping wave phase velocity. It is demonstrated analytically and numerically, for a particular example of a driven Korteweg-de Vries (KdV) equation with periodic boundary conditions, that as the nonlinear wave grows, it transforms into a soliton, which continues growing and accelerating adiabatically. A fully nonlinear perturbation theory is developed for the driven KdV equation to follow the growing wave into the strongly nonlinear regime and describe the soliton formation.

  4. Large amplitude ion-acoustic solitons in dusty plasmas

    SciTech Connect

    Tiwari, R. S.; Jain, S. L.; Mishra, M. K.

    2011-08-15

    Characteristics of ion-acoustic soliton in dusty plasma, including the dynamics of heavily charged massive dust grains, are investigated following the Sagdeev Potential formalism. Retaining fourth order nonlinearities of electric potential in the expansion of the Sagdeev Potential in the energy equation for a pseudo particle and integrating the resulting energy equation, large amplitude soliton solution is determined. Variation of amplitude (A), half width (W) at half maxima and the product P = AW{sup 2} of the Korteweg-deVries (KdV), dressed and large amplitude soliton as a function of wide range of dust concentration are numerically studied for recently observed parameters of dusty plasmas. We have also presented the region of existence of large amplitude ion-acoustic soliton in the dusty plasma by analyzing the structure of the pseudo potential. It is found that in the presence of positively charged dust grains, system supports only compressive solitons, on the other hand, in the presence of negatively charged dust grains, the system supports compressive solitons up to certain critical concentration of dust grains and above this critical concentration, the system can support rarefactive solitons also. The effects of dust concentration, charge, and mass of the dust grains, on the characteristics of KdV, dressed and large amplitude the soliton, i.e., amplitude (A), half width at half maxima (W), and product of amplitude (A) and half width at half maxima (P = AW{sup 2}), are discussed in detail.

  5. Resolution of a shock in hyperbolic systems modified by weak dispersion

    SciTech Connect

    El, G.A.

    2005-09-01

    We present a way to deal with dispersion-dominated 'shock-type' transition in the absence of completely integrable structure for the systems that one may characterize as strictly hyperbolic regularized by a small amount of dispersion. The analysis is performed by assuming that the dispersive shock transition between two different constant states can be modeled by an expansion fan solution of the associated modulation (Whitham) system for the short-wavelength nonlinear oscillations in the transition region (the so-called Gurevich-Pitaevskii problem). We consider both single-wave and bidirectional systems. The main mathematical assumption is that of hyperbolicity of the Whitham system for the solutions of our interest. By using general properties of the Whitham averaging for a certain class of nonlinear dispersive systems and specific features of the Cauchy data prescription on characteristics we derive a set of transition conditions for the dispersive shock, actually bypassing full integration of the modulation equations. Along with the Korteweg-de Vries (KdV) and modified KdV (mKdV) equations as model examples, we consider a nonintegrable system describing fully nonlinear ion-acoustic waves in collisionless plasma. In all cases our transition conditions are in complete agreement with previous analytical and numerical results.

  6. Finite beta effects on low- and high-frequency magnetosonic waves in a two-ion-species plasma

    SciTech Connect

    Toida, Mieko; Aota, Yukio

    2013-08-15

    A magnetosonic wave propagating perpendicular to a magnetic field in a two-ion-species plasma has two branches, high-frequency and low-frequency modes. The finite beta effects on these modes are analyzed theoretically on the basis of the three-fluid model with finite ion and electron pressures. First, it is shown that the Korteweg-de Vries (KdV) equation for the low-frequency mode is valid for amplitudes ε<ε{sub max}, where the upper limit of the amplitude ε{sub max} is given as a function of β (β is the ratio of the kinetic and magnetic energy densities), the density ratio, and the cyclotron frequency ratio of two ion species. Next, the linear dispersion relation and KdV equation for the high-frequency mode are derived, including β as a factor. In addition, the theory for heavy ion acceleration by the high-frequency mode pulse and the pulse damping due to this energy transfer in a finite beta plasma are presented.

  7. Gaussian solitary waves and compactons in Fermi-Pasta-Ulam lattices with Hertzian potentials.

    PubMed

    James, Guillaume; Pelinovsky, Dmitry

    2014-05-01

    We consider a class of fully nonlinear Fermi-Pasta-Ulam (FPU) lattices, consisting of a chain of particles coupled by fractional power nonlinearities of order α>1. This class of systems incorporates a classical Hertzian model describing acoustic wave propagation in chains of touching beads in the absence of precompression. We analyse the propagation of localized waves when α is close to unity. Solutions varying slowly in space and time are searched with an appropriate scaling, and two asymptotic models of the chain of particles are derived consistently. The first one is a logarithmic Korteweg-de Vries (KdV) equation and possesses linearly orbitally stable Gaussian solitary wave solutions. The second model consists of a generalized KdV equation with Hölder-continuous fractional power nonlinearity and admits compacton solutions, i.e. solitary waves with compact support. When [Formula: see text], we numerically establish the asymptotically Gaussian shape of exact FPU solitary waves with near-sonic speed and analytically check the pointwise convergence of compactons towards the limiting Gaussian profile. PMID:24808748

  8. Ion-acoustic dressed solitons in a dusty plasma

    SciTech Connect

    Tiwari, R.S.; Mishra, M.K.

    2006-06-15

    Using the reductive perturbation method, equations for ion-acoustic waves governing the evolution of first- and second-order potentials in a dusty plasma including the dynamics of charged dust grains have been derived. The renormalization procedure of Kodama and Taniuti is used to obtain a steady state nonsecular solution of these equations. The variation of velocity and width of the Korteweg-de Vries (KdV) as well as dressed solitons with amplitude have been studied for different concentrations and charge multiplicity of dust grains. The higher-order perturbation corrections to the KdV soliton description significantly affect the characteristics of the solitons in dusty plasma. It is found that in the presence of positively charged dust grains the system supports only compressive solitons. However, the plasma with negatively charged dust grains can support compressive solitons only up to a certain concentration of dust. Above this critical concentration of negative charge, the dusty plasma can support rarefactive solitons. An expression for the critical concentration of negatively charged dust in terms of charge and mass ratio of dust grains with plasma ions is also derived.

  9. Obliquely propagating cnoidal waves in a magnetized dusty plasma with variable dust charge

    SciTech Connect

    Yadav, L. L.; Sayal, V. K.

    2009-11-15

    We have studied obliquely propagating dust-acoustic nonlinear periodic waves, namely, dust-acoustic cnoidal waves, in a magnetized dusty plasma consisting of electrons, ions, and dust grains with variable dust charge. Using reductive perturbation method and appropriate boundary conditions for nonlinear periodic waves, we have derived Korteweg-de Vries (KdV) equation for the plasma. It is found that the contribution to the dispersion due to the deviation from plasma approximation is dominant for small angles of obliqueness, while for large angles of obliqueness, the dispersion due to magnetic force becomes important. The cnoidal wave solution of the KdV equation is obtained. It is found that the frequency of the cnoidal wave depends on its amplitude. The effects of the magnetic field, the angle of obliqueness, the density of electrons, the dust-charge variation and the ion-temperature on the characteristics of the dust-acoustic cnoidal wave are also discussed. It is found that in the limiting case the cnoidal wave solution reduces to dust-acoustic soliton solution.

  10. Ion-acoustic solitons in negative ion plasma with two-electron temperature distributions

    SciTech Connect

    Mishra, M. K.; Tiwari, R. S.; Chawla, J. K.

    2012-06-15

    Ion-acoustic solitons in a warm positive and negative ion species with different masses, concentrations, and charge states with two electron temperature distributions are studied. Using reductive perturbation method, Korteweg de-Vries (KdV) and modified-KdV (m-KdV) equations are derived for the system. The soliton solution of the KdV and m-KdV equations is discussed in detail. It is found that if the ions have finite temperatures, then there exist two types of modes, namely slow and fast ion-acoustic modes. It is also investigated that the parameter determining the nature of soliton (i.e., whether the system will support compressive or rarefactive solitons) is different for slow and fast modes. For the slow mode, the parameter is the relative temperature of the two ion species; whereas for the fast mode, it is the relative concentration of the two ion species. At a critical concentration of negative ions, both compressive and rarefactive solitons coexist. The amplitude and width of the solitons are discussed in detail at critical concentration for m-KdV solitons. The effect of the relative temperature of the two-electron and cold-electron concentration on the characteristics of the solitons are also discussed.

  11. Effects of strength of dispersion and dust density on the formation of solitons and shocks in unmagnetized dusty plasma

    SciTech Connect

    Asgari, H.; Muniandy, S. V.; Wong, C. S.

    2009-07-15

    The effects of strength of dispersion on the formation of solitons and shock waves in unmagnetized dusty plasma are studied using reductive perturbative technique. Different relational forms of the strength parameter {epsilon} can be chosen to stretch the space and time variables, thereby leading to different types of nonlinearities. The Korteweg-de Vries (KdV) equation for the unmodulated dust acoustic wave is derived and the solitary wave solution is obtained. It is shown that there exists a critical dust density n{sub dc} at which the formation of the dust acoustic solitary waves is not possible. Furthermore, the solution of the KdV represents a rarefactive (compressive) solitary wave if n{sub d}n{sub dc}) where n{sub d} is the dust density. Using another type of coordinate transformation that reduces the strength of dispersion, the Burgers' equation with shock wave solution is obtained. Shocks with negative (positive) potentials are observed when n{sub d}n{sub dc}), respectively.

  12. Ion-acoustic Gardner solitons in a four-component nonextensive multi-ion plasma

    NASA Astrophysics Data System (ADS)

    Jannat, N.; Ferdousi, M.; Mamun, A. A.

    2016-07-01

    The nonlinear propagation of ion-acoustic (IA) solitary waves (SWs) in a four-component non-extensive multi-ion plasma system containing inertial positively charged light ions, negatively charged heavy ions, as well as noninertial nonextensive electrons and positrons has been theoretically investigated. The reductive perturbation method has been employed to derive the nonlinear equations, namely, Korteweg-deVries (KdV), modified KdV (mKdV), and Gardner equations. The basic features (viz. polarity, amplitude, width, etc.) of Gardner solitons are found to exist beyond the KdV limit and these IA Gardner solitons are qualitatively different from the KdV and mKdV solitons. It is observed that the basic features of IA SWs are modified by various plasma parameters (viz. electron and positron nonextensivity, electron number density to ion number density, and electron temperature to positron temperature, etc.) of the considered plasma system. The results obtained from this theoretical investigation may be useful in understanding the basic features of IA SWs propagating in both space and laboratory plasmas.

  13. Nonlinear ion-acoustic cnoidal waves in a dense relativistic degenerate magnetoplasma.

    PubMed

    El-Shamy, E F

    2015-03-01

    The complex pattern and propagation characteristics of nonlinear periodic ion-acoustic waves, namely, ion-acoustic cnoidal waves, in a dense relativistic degenerate magnetoplasma consisting of relativistic degenerate electrons and nondegenerate cold ions are investigated. By means of the reductive perturbation method and appropriate boundary conditions for nonlinear periodic waves, a nonlinear modified Korteweg-de Vries (KdV) equation is derived and its cnoidal wave is analyzed. The various solutions of nonlinear ion-acoustic cnoidal and solitary waves are presented numerically with the Sagdeev potential approach. The analytical solution and numerical simulation of nonlinear ion-acoustic cnoidal waves of the nonlinear modified KdV equation are studied. Clearly, it is found that the features (amplitude and width) of nonlinear ion-acoustic cnoidal waves are proportional to plasma number density, ion cyclotron frequency, and direction cosines. The numerical results are applied to high density astrophysical situations, such as in superdense white dwarfs. This research will be helpful in understanding the properties of compact astrophysical objects containing cold ions with relativistic degenerate electrons. PMID:25871222

  14. Rotation-induced nonlinear wavepackets in internal waves

    SciTech Connect

    Whitfield, A. J. Johnson, E. R.

    2014-05-15

    The long time effect of weak rotation on an internal solitary wave is the decay into inertia-gravity waves and the eventual formation of a localised wavepacket. Here this initial value problem is considered within the context of the Ostrovsky, or the rotation-modified Korteweg-de Vries (KdV), equation and a numerical method for obtaining accurate wavepacket solutions is presented. The flow evolutions are described in the regimes of relatively-strong and relatively-weak rotational effects. When rotational effects are relatively strong a second-order soliton solution of the nonlinear Schrödinger equation accurately predicts the shape, and phase and group velocities of the numerically determined wavepackets. It is suggested that these solitons may form from a local Benjamin-Feir instability in the inertia-gravity wave-train radiated when a KdV solitary wave rapidly adjusts to the presence of strong rotation. When rotational effects are relatively weak the initial KdV solitary wave remains coherent longer, decaying only slowly due to weak radiation and modulational instability is no longer relevant. Wavepacket solutions in this regime appear to consist of a modulated KdV soliton wavetrain propagating on a slowly varying background of finite extent.

  15. Dust-acoustic Gardner solitons and double layers in dusty plasmas with nonthermally distributed ions of two distinct temperatures

    SciTech Connect

    Tasnim, I.; Mamun, A. A.; Masud, M. M.; Asaduzzaman, M.

    2013-03-15

    A rigorous theoretical investigation has been performed on dust-acoustic (DA) solitary structures in an unmagnetized dusty plasma, consisting of negatively charged mobile dust grains, Boltzmann distributed electrons, and nonthermally distributed ions of two distinct temperatures. The Korteweg-de Vries (K-dV), modified K-dV (mK-dV) and Gardner equations, and their solitary waves (SWs) and double layer (DL) (in case of Gardner equation) solutions are derived by using the reductive perturbation technique. The basic features of the DA Gardner solitons (GSs) and DLs are studied analytically as well as numerically. It has been observed that the GSs significantly differ from K-dV and mK-dV solitons, and only positive potential DLs exist in the system. It is also studied that two-temperature nonthermal ions significantly modify the nature and basic properties of the DA SWs. The present investigation can be very effective for understanding and studying the nonlinear characteristics of the DA waves in laboratory and space dusty plasmas.

  16. Formation of undular bores and solitary waves in the Strait of Malacca caused by the 26 December 2004 Indian Ocean tsunami

    NASA Astrophysics Data System (ADS)

    Grue, J.; Pelinovsky, E. N.; Fructus, D.; Talipova, T.; Kharif, C.

    2008-05-01

    Deformation of the Indian Ocean tsunami moving into the shallow Strait of Malacca and formation of undular bores and solitary waves in the strait are simulated in a model study using the fully nonlinear dispersive method (FNDM) and the Korteweg-deVries (KdV) equation. Two different versions of the incoming wave are studied where the waveshape is the same but the amplitude is varied: full amplitude and half amplitude. While moving across three shallow bottom ridges, the back face of the leading depression wave steepens until the wave slope reaches a level of 0.0036-0.0038, when short waves form, resembling an undular bore for both full and half amplitude. The group of short waves has very small amplitude in the beginning, behaving like a linear dispersive wave train, the front moving with the shallow water speed and the tail moving with the linear group velocity. Energy transfer from long to short modes is similar for the two input waves, indicating the fundamental role of the bottom topography to the formation of short waves. The dominant period becomes about 20 s in both cases. The train of short waves, emerging earlier for the larger input wave than for the smaller one, eventually develops into a sequence of rank-ordered solitary waves moving faster than the leading depression wave and resembles a fission of the mother wave. The KdV equation has limited capacity in resolving dispersion compared to FNDM.

  17. Small amplitude electron acoustic solitary waves in a magnetized superthermal plasma

    NASA Astrophysics Data System (ADS)

    Devanandhan, S.; Singh, S. V.; Lakhina, G. S.; Bharuthram, R.

    2015-05-01

    The propagation of electron acoustic solitary waves in a magnetized plasma consisting of fluid cold electrons, electron beam and superthermal hot electrons (obeying kappa velocity distribution function) and ion is investigated in a small amplitude limit using reductive perturbation theory. The Korteweg-de-Vries-Zakharov-Kuznetsov (KdV-ZK) equation governing the dynamics of electron acoustic solitary waves is derived. The solution of the KdV-ZK equation predicts the existence of negative potential solitary structures. The new results are: (1) increase of either the beam speed or temperature of beam electrons tends to reduce both the amplitude and width of the electron acoustic solitons, (2) the inclusion of beam speed and temperature pushes the allowed Mach number regime upwards and (3) the soliton width maximizes at certain angle of propagation (αm) and then decreases for α >αm . In addition, increasing the superthermality of the hot electrons also results in reduction of soliton amplitude and width. For auroral plasma parameters observed by Viking, the obliquely propagating electron-acoustic solitary waves have electric field amplitudes in the range (7.8-45) mV/m and pulse widths (0.29-0.44) ms. The Fourier transform of these electron acoustic solitons would result in a broadband frequency spectra with peaks near 2.3-3.5 kHz, thus providing a possible explanation of the broadband electrostatic noise observed during the Burst a.

  18. Ion temperature gradient mode driven solitons and shocks

    NASA Astrophysics Data System (ADS)

    Zakir, U.; Adnan, Muhammad; Haque, Q.; Qamar, Anisa; Mirza, Arshad M.

    2016-04-01

    Ion temperature gradient (ITG) driven solitons and shocks are studied in a plasma having gradients in the equilibrium number density and equilibrium ion temperature. In the linear regime, it is found that the ion temperature and the ratio of the gradient scale lengths, ηi=Ln/LT , affect both the real frequency and the growth rate of the ITG driven wave instability. In the nonlinear regime, for the first time we derive a Korteweg de Vries-type equation for the ITG mode, which admits solitary wave solution. It is found that the ITG mode supports only compressive solitons. Further, it is noticed that the soliton amplitude and width are sensitive to the parameter ηi=Ln/LT . Second, in the presence of dissipation in the system, we obtain a Burger type equation, which admits the shock wave solution. This work may be useful to understand the low frequency electrostatic modes in inhomogeneous electron-ion plasma having density and ion temperature gradients. For illustration, the model has been applied to tokamak plasma.

  19. Compressive and rarefactive dust-ion-acoustic Gardner solitons in a multi-component dusty plasma

    SciTech Connect

    Ema, S. A.; Ferdousi, M.; Mamun, A. A.

    2015-04-15

    The linear and nonlinear propagations of dust-ion-acoustic solitary waves (DIASWs) in a collisionless four-component unmagnetized dusty plasma system containing nonextensive electrons, inertial negative ions, Maxwellian positive ions, and negatively charged static dust grains have been investigated theoretically. The linear properties are analyzed by using the normal mode analysis and the reductive perturbation method is used to derive the nonlinear equations, namely, the Korteweg-de Vries (K-dV), the modified K-dV (mK-dV), and the Gardner equations. The basic features (viz., polarity, amplitude, width, etc.) of Gardner solitons (GS) are found to exist beyond the K-dV limit and these dust-ion-acoustic GS are qualitatively different from the K-dV and mK-dV solitons. It is observed that the basic features of DIASWs are affected by various plasma parameters (viz., electron nonextensivity, negative-to-positive ion number density ratio, electron-to-positive ion number density ratio, electron-to-positive ion temperature ratio, etc.) of the considered plasma system. The findings of our results obtained from this theoretical investigation may be useful in understanding the nonlinear structures and the characteristics of DIASWs propagating in both space and laboratory plasmas.

  20. Solitary and shock structures in a strongly coupled cryogenic quantum plasma

    SciTech Connect

    Hossen, M. A. Mamun, A. A.

    2015-07-15

    The quantum ion-acoustic (QIA) solitary and shock structures formed in a strongly coupled cryogenic quantum plasma (containing strongly coupled positively charged inertial cold ions and Fermi electrons as well as positrons) have been theoretically investigated. The generalized quantum hydrodynamic model and the reductive perturbation method have been employed to derive the Korteweg-de Vries (K-dV) and Burgers equations. The basic features of the QIA solitary and shock structures are identified by analyzing the stationary solitary and shock wave solutions of the K-dV and Burgers equations. It is found that the basic characteristics (e.g., phase speed, amplitude, and width) of the QIA solitary and shock structures are significantly modified by the effects of the Fermi pressures of electrons and positrons, the ratio of Fermi temperature of positrons to that of electrons, the ratio of effective ion temperature to electron Fermi temperature, etc. It is also observed that the effect of strong correlation among extremely cold ions acts as a source of dissipation, and is responsible for the formation of the QIA shock structures. The results of this theoretical investigation should be useful for understanding the nonlinear features of the localized electrostatic disturbances in laboratory electron-positron-ion plasmas (viz., super-intense laser-dense matter experiments)

  1. Oblique propagation of ion-acoustic solitary waves in a magnetized electron-positron-ion plasma

    SciTech Connect

    Ferdousi, M.; Sultana, S.; Mamun, A. A.

    2015-03-15

    The properties of obliquely propagating ion-acoustic solitary waves in the presence of ambient magnetic field have been investigated theoretically in an electron-positron-ion nonthermal plasma. The plasma nonthermality is introduced via the q-nonextensive distribution of electrons and positrons. The Korteweg-de Vries (K-dV) and modified K-dV (mK-dV) equations are derived by adopting reductive perturbation method. The solution of K-dV and modified K-dV equation, which describes the solitary wave characteristics in the long wavelength limit, is obtained by steady state approach. It is seen that the electron and positron nonextensivity and external magnetic field (obliqueness) have significant effects on the characteristics of solitary waves. A critical value of nonextensivity is found for which solitary structures transit from positive to negative potential. The findings of this investigation may be used in understanding the wave propagation in laboratory and space plasmas where static external magnetic field is present.

  2. Effects of ionization and ion loss on dust ion-acoustic solitary waves in a collisional dusty plasma with suprathermal electrons

    NASA Astrophysics Data System (ADS)

    Mayout, Saliha; Gougam, Leila Ait; Tribeche, Mouloud

    2016-03-01

    The combined effects of ionization, ion loss, and electron suprathermality on dust ion-acoustic solitary waves in a collisional dusty plasma are examined. Carrying out a small but finite amplitude analysis, a damped Korteweg-de Vries (dK-dV) equation is derived. The damping term decreases with the increase of the spectral index and saturates for Maxwellian electrons. Choosing typical plasma parameters, the analytical approximate solution of the dK-dV equation is numerically analyzed. We first neglect the ionization and ion loss effects and account only for collisions to estimate the relative importance between these damping terms which can act concurrently. Interestingly, we found that as the suprathermal character of the electrons becomes important, the strength of the collisions related dissipation becomes more important and causes the dust ion-acoustic solitary wave amplitude to decay more rapidly. Moreover, the collisional damping may largely prevail over the ionization and ion loss related damping. The latter becomes more effective as the electrons evolve far away from their thermal equilibrium. Our results complement and provide new insights into previously published work on this problem.

  3. Linear and nonlinear analysis of dust acoustic waves in dissipative space dusty plasmas with trapped ions

    NASA Astrophysics Data System (ADS)

    El-Hanbaly, A. M.; El-Shewy, E. K.; Sallah, M.; Darweesh, H. F.

    2015-05-01

    The propagation of linear and nonlinear dust acoustic waves in a homogeneous unmagnetized, collisionless and dissipative dusty plasma consisted of extremely massive, micron-sized, negative dust grains has been investigated. The Boltzmann distribution is suggested for electrons whereas vortex-like distribution for ions. In the linear analysis, the dispersion relation is obtained, and the dependence of damping rate of the waves on the carrier wave number , the dust kinematic viscosity coefficient and the ratio of the ions to the electrons temperatures is discussed. In the nonlinear analysis, the modified Korteweg-de Vries-Burgers (mKdV-Burgers) equation is derived via the reductive perturbation method. Bifurcation analysis is discussed for non-dissipative system in the absence of Burgers term. In the case of dissipative system, the tangent hyperbolic method is used to solve mKdV-Burgers equation, and yield the shock wave solution. The obtained results may be helpful in better understanding of waves propagation in the astrophysical plasmas as well as in inertial confinement fusion laboratory plasmas.

  4. Precursors in gas-liquid mixtures

    NASA Astrophysics Data System (ADS)

    Gasenko, V. G.; Gorelik, R. S.; Nakoryakov, V. E.; Timkin, L. S.

    2013-10-01

    Two types of precursors propagating at the speed of sound in a pure liquid have been revealed in the experiments on the evolution of pressure pulses in a gas-liquid mixture; at the same time, the main pressure pulse propagates at a low equilibrium speed of sound and its evolution is described by the Burgers-Korteweg-de Vries equation. The first high-frequency precursor is a complete analog of a classical Sommerfeld precursor, because the resonance dispersion equation for a bubble mixture coincides with that for insulators in the Lorentz model, and oscillates at a frequency close to the "plasma frequency." The second low-frequency precursor has been revealed in this work. The frequency of the low-frequency precursor is close to the resonance frequency of pulsations of bubbles, which is almost an order of magnitude lower than the frequency of the high-frequency precursor. The low-frequency precursor has a much larger amplitude of pulsations and smaller damping and is not described within the homogeneous model of the gas-liquid mixture. The observed phenomenon of low-frequency precursors has been explained within a simple heterogeneous model of a bubble liquid.

  5. Vortexons in axisymmetric Poiseuille pipe flows

    NASA Astrophysics Data System (ADS)

    Fedele, F.; Dutykh, D.

    2013-02-01

    We present a study on the nonlinear dynamics of small long-wave disturbances to the laminar state in non-rotating axisymmetric Poiseuille pipe flows. At high Reynolds numbers, the associated Navier-Stokes equations can be reduced to a set of coupled Korteweg-de Vries-type (KdV) equations that support inviscid and smooth travelling waves numerically computed using the Petviashvili method. In physical space they correspond to localized toroidal vortices concentrated near the pipe boundaries (wall vortexons) or that wrap around the pipe axis (centre vortexons), in agreement with the analytical soliton solutions derived by Fedele (Fluid Dyn. Res., 44 (2012) 45509). The KdV dynamics of a perturbation is also investigated by means of a high accurate Fourier-based numerical scheme. We observe that an initial vortical patch splits into a centre vortexon radiating patches of vorticity near the wall. These can undergo further splitting leading to a proliferation of centre vortexons that eventually decay due to viscous effects. The splitting process originates from a radial flux of azimuthal vorticity from the wall to the pipe axis in agreement with the inverse cascade of cross-stream vorticity identified in channel flows by Eyink (Plysica D, 237 (2008) 1956). The inviscid vortexon most likely is unstable to non-axisymmetric disturbances and may be a precursor to puffs and slug flow formation.

  6. Quantum electron-acoustic double layers in two electron species quantum plasma

    SciTech Connect

    Sah, Om Prakash

    2009-01-15

    The existence and the characteristic properties of electron-acoustic double layers are investigated in three component unmagnetized dense quantum plasmas consisting of stationary background ions and two electron populations: one 'cold' and the other 'hot'. Using the one-dimensional quantum hydrodynamic model and the reductive perturbation technique, a generalized form of nonlinear quantum Korteweg-de Vries equation governing the dynamics of weak electron acoustic double layers is derived. A stationary solution of this equation is obtained to discuss the existence criteria of different types of double layers and their characteristic properties. It is shown that two types of compressive double layers: one in the lower {delta}-parameter region and the other at the higher {delta}-parameter region, along with rarefactive double layers in the intermediate region, may exist, where {delta}=n{sub ec0}/n{sub eh0} is the ratio of unperturbed cold to hot electron densities. The width, the amplitude, and the velocity of these double layers are significantly affected by the {delta}-parameter. The relevance of the present investigation is also discussed.

  7. Asymptotic analysis of surface waves in continuous strip casting processes

    NASA Astrophysics Data System (ADS)

    Kluwick, Alfred; Scheichl, Stefan

    2000-09-01

    This paper presents a two-dimensional analysis of surface waves possibly emerging in a specific open channel flow with continuous solidification, i.e. the fluid consisting of molten material is cooled from below and solidifies. In modern metallurgical engineering such processes are of importance for the strip casting of steel and other metals. The study is based on the assumption that the wavelengths are large compared to the characteristic depth of the melt but small compared to the solidification length. Within the framework of a weakly nonlinear theory the use of the Euler equations supplemented with the appropriate boundary conditions at the solidification front and the free surface yields two Korteweg-de Vries equations with varying coefficients, which govern the propagation of the waves. However, the adopted form of the asymptotic expansions ceases to be valid as the point of complete solidification is approached, where the displacements at the free boundary and the depth of the melt are of the same order. Thus, a separate investigation for this region is carried out in order to describe the further evolution of the surface waves and its influence on the final shape of the fully solidified metal sheet.

  8. Coupled nonlinear drift and ion acoustic waves in dense dissipative electron-positron-ion magnetoplasmas

    SciTech Connect

    Masood, W.; Siddiq, M.; Karim, S.; Shah, H. A.

    2009-11-15

    Linear and nonlinear propagation characteristics of drift ion acoustic waves are investigated in an inhomogeneous electron-positron-ion (e-p-i) quantum magnetoplasma with neutrals in the background using the well known quantum hydrodynamic model. In this regard, Korteweg-de Vries-Burgers (KdVB) and Kadomtsev-Petviashvili-Burgers (KPB) equations are obtained. Furthermore, the solutions of KdVB and KPB equations are presented by using the tangent hyperbolic (tanh) method. The variation in the shock profile with the quantum Bohm potential, collision frequency, and the ratio of drift to shock velocity in the comoving frame, v{sub *}/u, is also investigated. It is found that increasing the positron concentration and collision frequency decreases the strength of the shock. It is also shown that when the localized structure propagates with velocity greater than the diamagnetic drift velocity (i.e., u>v{sub *}), the shock strength decreases. However, the shock strength is observed to increase when the localized structure propagates with velocity less than that of drift velocity (i.e., u

  9. CONDENSED MATTER: STRUCTURE, THERMAL AND MECHANICAL PROPERTIES: Multiple car-following model of traffic flow and numerical simulation

    NASA Astrophysics Data System (ADS)

    Peng, Guang-Han; Sun, Di-Hua

    2009-12-01

    On the basis of the full velocity difference (FVD) model, an improved multiple car-following (MCF) model is proposed by taking into account multiple information inputs from preceding vehicles. The linear stability condition of the model is obtained by using the linear stability theory. Through nonlinear analysis, a modified Korteweg-de Vries equation is constructed and solved. The traffic jam can thus be described by the kink-antikink soliton solution for the mKdV equation. The improvement of this new model over the previous ones lies in the fact that it not only theoretically retains many strong points of the previous ones, but also performs more realistically than others in the dynamical evolution of congestion. Furthermore, numerical simulation of traffic dynamics shows that the proposed model can avoid the disadvantage of negative velocity that occurs at small sensitivity coefficients λ in the FVD model by adjusting the information on the multiple leading vehicles. No collision occurs and no unrealistic deceleration appears in the improved model.

  10. Development of kink jams in traffic flow

    NASA Astrophysics Data System (ADS)

    Kurtze, Douglas

    Near the threshold of absolute stability of uniform, steady traffic flow, car-following models can often be reduced to a modified Korteweg-deVries (mKdV) equation plus small corrections. The mKdV equation has a continuous family of hyperbolic-kink solutions describing boundaries between regions of different traffic densities, i.e. the edges of traffic jams. A solvability calculation picks out the one member of this family which is consistent with the correction terms; this is usually labelled the ``selected'' kink. This identification is problematic, however, since it must be the downstream boundary condition that determines which kink solution is realized. We display a two-parameter family of mKdV solutions which has the kink solutions as one limit and uniform flow as another, and show how the correction terms can lead to kinks developing from initially near-uniform traffic. We then clarify the meaning of the usual solvability calcuation and of the ``selected'' kink.

  11. Asymmetric effect on single-file dense pedestrian flow

    NASA Astrophysics Data System (ADS)

    Kuang, Hua; Cai, Mei-Jing; Li, Xing-Li; Song, Tao

    2015-11-01

    In this paper, an extended optimal velocity model is proposed to simulate single-file dense pedestrian flow by considering asymmetric interaction (i.e. attractive force and repulsive force), which depends on the different distances between pedestrians. The stability condition of this model is obtained by using the linear stability theory. The phase diagram comparison and analysis show that asymmetric effect plays an important role in strengthening the stabilization of system. The modified Korteweg-de Vries (mKdV) equation near the critical point is derived by applying the reductive perturbation method. The pedestrian jam could be described by the kink-antikink soliton solution for the mKdV equation. From the simulation of space-time evolution of the pedestrians distance, it can be found that the asymmetric interaction is more efficient compared to the symmetric interaction in suppressing the pedestrian jam. Furthermore, the simulation results are consistent with the theoretical analysis as well as reproduce experimental phenomena better.

  12. Particle-in-cell simulation of large amplitude ion-acoustic solitons

    SciTech Connect

    Sharma, Sarveshwar Sengupta, Sudip; Sen, Abhijit

    2015-02-15

    The propagation of large amplitude ion-acoustic solitons is studied in the laboratory frame (x, t) using a 1-D particle-in-cell code that evolves the ion dynamics by treating them as particles but assumes the electrons to follow the usual Boltzmann distribution. It is observed that for very low Mach numbers the simulation results closely match the Korteweg-de Vries soliton solutions, obtained in the wave frame, and which propagate without distortion. The collision of two such profiles is observed to exhibit the usual solitonic behaviour. As the Mach number is increased, the given profile initially evolves and then settles down to the exact solution of the full non-linear Poisson equation, which then subsequently propagates without distortion. The fractional change in amplitude is found to increase linearly with Mach number. It is further observed that initial profiles satisfying k{sup 2}λ{sub de}{sup 2}<1 break up into a series of solitons.

  13. Acoustic double layer structures in dense magnetized electron-positron-ion plasmas

    SciTech Connect

    Akhtar, N.; Mahmood, S.

    2011-11-15

    The acoustic double layer structures are studied using quantum hydrodynamic model in dense magnetized electron-positron-ion plasmas. The extended Korteweg-de Vries is derived using reductive perturbation method. It is found that increase in the ion concentration in dense magnetized electron-positron plasmas increases the amplitude as well as the steepness of the double layer structure. However, increase in the magnetic field strength and decrease in the obliqueness of the nonlinear acoustic wave enhances only the steepness of the double layer structures. The numerical results have also been shown by using the data of the outer layer regions of white dwarfs given in the literature.

  14. Oblique Propagation of Ion Acoustic Solitons in Magnetized Superthermal Plasmas

    NASA Astrophysics Data System (ADS)

    Devanandhan, S.; Sreeraj, T.; Singh, S.; Lakhina, G. S.

    2015-12-01

    Small amplitude ion-acoustic solitons are studied in a magnetized plasma consisting of protons, doubly charged helium ions and superthermal electrons. The Korteweg-de-Vries-Zakharov-Kuznetsov (KdV-ZK) is derived to examine the properties of ion acoustic solitary structures observed in space plasmas. Our model is applicable for weakly magnetized plasmas. The results will be applied to the satellite observations in the solar wind at 1 AU where magnetized ion acoustic waves with superthermal electrons can exist. The effects of superthermality, temperature and densities on these solitary structures will be discussed.

  15. Extended rate equations

    SciTech Connect

    Shore, B.W.

    1981-01-30

    The equations of motion are discussed which describe time dependent population flows in an N-level system, reviewing the relationship between incoherent (rate) equations, coherent (Schrodinger) equations, and more general partially coherent (Bloch) equations. Approximations are discussed which replace the elaborate Bloch equations by simpler rate equations whose coefficients incorporate long-time consequences of coherence.

  16. Propagation of sound and supersonic bright solitons in superfluid Fermi gases in BCS-BEC crossover

    NASA Astrophysics Data System (ADS)

    Wen, Wen; Shen, Shun-Qing; Huang, Guoxiang

    2010-01-01

    We investigate the linear and nonlinear sound propagations in a cigar-shaped superfluid Fermi gas with a large particle number. We first solve analytically the eigenvalue problem of linear collective excitations and provide explicit expressions of all eigenvalues and eigenfunctions, which are valid for all superfluid regimes in the Bardeen-Cooper-Schrieffer-Bose-Einstein condensation (BCS-BEC) crossover. The linear sound speed obtained agrees well with that of a recent experimental measurement. We then consider a weak nonlinear excitation and show that the time evolution of the excitation obeys a Korteweg de Vries equation. Different from the result obtained in quasi-one-dimensional case studied previously, where subsonic dark solitons are obtained via the balance between quantum pressure and nonlinear effect, we demonstrate that bright solitons with supersonic propagating velocity can be generated in the present three-dimensional system through the balance between a waveguidelike dispersion and the interparticle interaction. The supersonic bright solitons obtained display different physical properties in different superfluid regimes and hence can be used to characterize superfluid features of the BCS-BEC crossover.

  17. Stringent limitations on reductive perturbation studies of nonplanar acoustic solitons in plasmas

    NASA Astrophysics Data System (ADS)

    Verheest, Frank; Hellberg, Manfred A.

    2016-06-01

    More than fifty years ago, the Korteweg-de Vries equation was shown to describe not only solitary surface waves on shallow water, but also nonlinear ion-acoustic waves. Because of the algorithmic ease of using reductive perturbation theory, intensive research followed on a wide range of wave types. Soon, the formalism was extended to nonplanar modes by introducing a stretching designed to accommodate spherically and cylindrically symmetric ion-acoustic waves. Over the last two decades many authors followed this approach, but almost all have ignored the severe restrictions in parameter space imposed by the Ansatz. In addition, for other steps in the formalism, the justification is often not spelled out, leading to effects that are physically undesirable or ambiguous. Hence, there is a need to critically assess this approach to nonplanar modes and to use it with the utmost care, respecting the restrictions on its validity. Only inward propagation may be meaningfully studied and respect for weak nonlinearities of at most 1/10 implies that one cannot get closer to the axis or centre of symmetry than about 30 Debye lengths. Thus, one is in a regime where the modes are quasi-planar and not particularly interesting. Most papers disregard these constraints and hence reach questionable conclusions.

  18. Nonlinear magnetosonic waves in dense plasmas with non-relativistic and ultra-relativistic degenerate electrons

    SciTech Connect

    Hussain, S.; Mahmood, S.; Rehman, Aman-ur-

    2014-11-15

    Linear and nonlinear propagation of magnetosonic waves in the perpendicular direction to the ambient magnetic field is studied in dense plasmas for non-relativistic and ultra-relativistic degenerate electrons pressure. The sources of nonlinearities are the divergence of the ions and electrons fluxes, Lorentz forces on ions and electrons fluids and the plasma current density in the system. The Korteweg-de Vries equation for magnetosonic waves propagating in the perpendicular direction of the magnetic field is derived by employing reductive perturbation method for non-relativistic as well as ultra-relativistic degenerate electrons pressure cases in dense plasmas. The plots of the magnetosonic wave solitons are also shown using numerical values of the plasma parameters such a plasma density and magnetic field intensity of the white dwarfs from literature. The dependence of plasma density and magnetic field intensity on the magnetosonic wave propagation is also pointed out in dense plasmas for both non-relativistic and ultra-relativistic degenerate electrons pressure cases.

  19. Long-term behavior of granular chains held between walls is really equilibrium

    NASA Astrophysics Data System (ADS)

    Przedborski, Michelle; Sen, Surajit; Harroun, Thad

    Granular chains have been the focus of a number of studies, in part due to their numerous applications, ranging from shock absorption and vibration reduction to energy localization. Force impulses to an unloaded granular chain result in a propagating solitary wave (SW), analogous to a soliton of the Korteweg-de Vries equation. When SWs collide with a boundary or another SW, secondary solitary waves (SSWs) are produced as grains break contact. A consequence of this process is the transition from a non-ergodic, SW dominant, phase to the stable ``quasi-equilibrium'' (QEQ) phase, thought to be distinct from true thermodynamic equilibrium due to the absence of equipartitioning of energy. We show that, in the absence of energy dissipation, when granular systems are allowed to evolve to extremely long times, the number of SSWs becomes sufficiently large that the system actually approaches a true equilibrium phase. In this extreme-time limit, energy in fact becomes equipartitioned among all grains, and we illustrate how the specific heat and kinetic energy fluctuations can be predicted by the generalized equipartition theorem, regardless of the degree of the interaction potential. This opens up the possibility that granular systems should be treated by equilibrium statistical mechanics. This work was supported by a Vanier Canada Graduate Scholarship.

  20. Ion acoustic shock wave in collisional equal mass plasma

    NASA Astrophysics Data System (ADS)

    Adak, Ashish; Ghosh, Samiran; Chakrabarti, Nikhil

    2015-10-01

    The effect of ion-ion collision on the dynamics of nonlinear ion acoustic wave in an unmagnetized pair-ion plasma has been investigated. The two-fluid model has been used to describe the dynamics of both positive and negative ions with equal masses. It is well known that in the dynamics of the weakly nonlinear wave, the viscosity mediates wave dissipation in presence of weak nonlinearity and dispersion. This dissipation is responsible for the shock structures in pair-ion plasma. Here, it has been shown that the ion-ion collision in presence of collective phenomena mediated by the plasma current is the source of dissipation that causes the Burgers' term which is responsible for the shock structures in equal mass pair-ion plasma. The dynamics of the weakly nonlinear wave is governed by the Korteweg-de Vries Burgers equation. The analytical and numerical investigations revealed that the ion acoustic wave exhibits both oscillatory and monotonic shock structures depending on the frequency of ion-ion collision parameter. The results have been discussed in the context of the fullerene pair-ion plasma experiments.