Whitham theory for perturbed Korteweg-de Vries equation
NASA Astrophysics Data System (ADS)
Kamchatnov, A. M.
2016-10-01
Original Whitham's method of derivation of modulation equations is applied to systems whose dynamics is described by a perturbed Korteweg-de Vries equation. Two situations are distinguished: (i) the perturbation leads to appearance of right-hand sides in the modulation equations so that they become non-uniform; (ii) the perturbation leads to modification of the matrix of Whitham velocities. General form of Whitham modulation equations is obtained in both cases. The essential difference between them is illustrated by an example of so-called 'generalized Korteweg-de Vries equation'. Method of finding steady-state solutions of perturbed Whitham equations in the case of dissipative perturbations is considered.
Simple Numerical Schemes for the Korteweg-deVries Equation
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.
Numerical studies of the stochastic Korteweg-de Vries equation
Lin Guang; Grinberg, Leopold; Karniadakis, George Em . E-mail: gk@dam.brown.edu
2006-04-10
We present numerical solutions of the stochastic Korteweg-de Vries equation for three cases corresponding to additive time-dependent noise, multiplicative space-dependent noise and a combination of the two. We employ polynomial chaos for discretization in random space, and discontinuous Galerkin and finite difference for discretization in physical space. The accuracy of the stochastic solutions is investigated by comparing the first two moments against analytical and Monte Carlo simulation results. Of particular interest is the interplay of spatial discretization error with the stochastic approximation error, which is examined for different orders of spatial and stochastic approximation.
The transformations between N = 2 supersymmetric Korteweg-de Vries and Harry Dym equations
NASA Astrophysics Data System (ADS)
Tian, Kai; Liu, Q. P.
2012-05-01
The N = 2 supercomformal transformations are employed to study supersymmetric integrable systems. It is proved that two known N = 2 supersymmetric Harry Dym equations are transformed into two N = 2 supersymmetric modified Korteweg-de Vries equations, thus are connected with two N = 2 supersymmetric Korteweg-de Vries equations.
Mixed problems for the Korteweg-de Vries equation
Faminskii, A V
1999-06-30
Results are established concerning the non-local solubility and wellposedness in various function spaces of the mixed problem for the Korteweg-de Vries equation u{sub t}+u{sub xxx}+au{sub x}+uu{sub x}=f(t,x) in the half-strip (0,T)x(-{infinity},0). Some a priori estimates of the solutions are obtained using a special solution J(t,x) of the linearized KdV equation of boundary potential type. Properties of J are studied which differ essentially as x{yields}+{infinity} or x{yields}-{infinity}. Application of this boundary potential enables us in particular to prove the existence of generalized solutions with non-regular boundary values.
Hamiltonian structure of the higher-order corrections to the Korteweg-de Vries equation
NASA Astrophysics Data System (ADS)
Menyuk, C. R.; Chen, H.-H.
1985-10-01
Higher-order corrections to the Korteweg-de Vries equation are examined by Hamiltonian methods. Starting from the underlying Hamiltonian systems (e.g., the two-fluid equations in the case of ion-acoustic waves), one finds that the corrected equations have the same Poisson bracket as the Korteweg-de Vries equation at every order. One also finds that the underlying equations become nonlocal at sufficiently high order.
On exact traveling-wave solutions for local fractional Korteweg-de Vries equation.
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
Negative-order Korteweg-de Vries equations.
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
Negative-order Korteweg-de Vries equations.
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.
Soliton fractals in the Korteweg-de Vries equation.
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
Refinement of the Korteweg-de Vries equation from the Fermi-Pasta-Ulam model
NASA Astrophysics Data System (ADS)
Kudryashov, Nikolay A.
2015-10-01
We study a generalization of the Korteweg-de Vries equation obtained from the Fermi-Pasta-Ulam problem. We get the fifth-order nonlinear evolution equation for description of perturbations in the mass chain. Using the Painlevé test, we analyze this equation and show that it does not pass the Painlevé test in the general case. However, the necessary condition for existence of the meromorphic solution is carried out and some exact solutions can be found. We present a new approach to look for traveling wave solutions of the generalization of the Korteweg-de Vries equation. Solitary wave and elliptic solutions of the equation are found and discussed, compared to the Korteweg-de Vries soliton.
Cylindrical nonlinear Schroedinger equation versus cylindrical Korteweg-de Vries equation
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.
Darboux transformation for a generalized Hirota-Satsuma coupled Korteweg-de Vries equation
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.
The zero dispersion limit for the Korteweg-deVries KdV equation.
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
Darboux transformation for a generalized Hirota-Satsuma coupled Korteweg-de Vries equation.
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
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.
Asymptotic stability of a nonlinear Korteweg-de Vries equation with critical lengths
NASA Astrophysics Data System (ADS)
Chu, Jixun; Coron, Jean-Michel; Shang, Peipei
2015-10-01
We study an initial-boundary-value problem of a nonlinear Korteweg-de Vries equation posed on the finite interval (0, 2 kπ) where k is a positive integer. The whole system has Dirichlet boundary condition at the left end-point, and both of Dirichlet and Neumann homogeneous boundary conditions at the right end-point. It is known that the origin is not asymptotically stable for the linearized system around the origin. We prove that the origin is (locally) asymptotically stable for the nonlinear system if the integer k is such that the kernel of the linear Korteweg-de Vries stationary equation is of dimension 1. This is for example the case if k = 1.
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
Similarity reduction, nonlocal and master symmetries of sixth order Korteweg-deVries equation
NASA Astrophysics Data System (ADS)
Sahadevan, R.; Nalinidevi, L.
2009-05-01
A systematic investigation to derive the Lie point symmetries, nonlocal and master symmetries of sixth order Korteweg-de Vries equation (KdV6) is presented. Using the obtained point symmetries, similarity reductions are derived and constructed their particular solutions wherever possible. It is shown that KdV6 admits infinitely many nonlocal and master symmetries. The existence of infinitely many master symmetries ensures that KdV6 is completely integrable.
Error analysis for spectral approximation of the Korteweg-De Vries equation
NASA Technical Reports Server (NTRS)
Maday, Y.; recent years.
1987-01-01
The conservation and convergence properties of spectral Fourier methods for the numerical approximation of the Korteweg-de Vries equation are analyzed. It is proved that the (aliased) collocation pseudospectral method enjoys the same convergence properties as the spectral Galerkin method, which is less effective from the computational point of view. This result provides a precise mathematical answer to a question raised by several authors in recent years.
Similarity solutions to nonlinear heat conduction and Burgers/Korteweg-deVries fractional equations
NASA Astrophysics Data System (ADS)
Djordjevic, Vladan D.; Atanackovic, Teodor M.
2008-12-01
We analyze self-similar solutions to a nonlinear fractional diffusion equation and fractional Burgers/Korteweg-deVries equation in one spatial variable. By using Lie-group scaling transformation, we determined the similarity solutions. After the introduction of the similarity variables, both problems are reduced to ordinary nonlinear fractional differential equations. In two special cases exact solutions to the ordinary fractional differential equation, which is derived from the diffusion equation, are presented. In several other cases the ordinary fractional differential equations are solved numerically, for several values of governing parameters. In formulating the numerical procedure, we use special representation of a fractional derivative that is recently obtained.
Exact Travelling Wave Solutions of the Schamel-Korteweg-de Vries Equation
NASA Astrophysics Data System (ADS)
Lee, Jonu; Sakthivel, Rathinasamy
2011-12-01
The Schamel-Korteweg-de Vries (S-KdV) equation containing a square root nonlinearity is a very attractive model for the study of ion-acoustic waves in plasma and dusty plasma. In this work, we obtain exact travelling wave solutions of the S-KdV equation by employing the exp function method. In general, the exact travelling wave solutions will be helpful in the theoretical and numerical study of the nonlinear evolution equations. The work emphasizes the power of the method in providing distinct solutions of different physical problems.
NASA Astrophysics Data System (ADS)
Korkmaz, Alper; Dağ, İdris
2009-09-01
Complex Modified Korteweg-deVries Equation is solved numerically using differential quadrature method based on cosine expansion. Three test problems, motion of single solitary wave, interaction of solitary waves and wave generation, are simulated. The accuracy of the method is measured via the discrete root mean square error norm L, maximum error norm L for the motion of single solitary wave since it has an analytical solution. A rate of convergency analysis for motion of single solitary wave containing both real and imaginary parts is also given. Lowest three conserved quantities are computed for all test problems. A comparison with some earlier works is given.
Exact solutions of unsteady Korteweg-de Vries and time regularized long wave equations.
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.
Exact solutions of unsteady Korteweg-de Vries and time regularized long wave equations.
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
NASA Astrophysics Data System (ADS)
Smith, Warren R.
2007-04-01
Original explicit modulation equations are determined for cnoidal waves of the Korteweg-deVries (KdV)-Burgers equation. This formal asymptotic analysis is used to demonstrate that there is no single partial differential equation for the leading-order mean velocity. The technique of Reynolds averaging is also employed to determine an equation for the mean velocity with the familiar closure problem being encountered. The Reynolds-averaged KdV-Burgers equation is shown to be a counterexample to the existence of a closure associated with a convective nonlinearity.
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.
Decay of Solutions to Damped Korteweg-de Vries Type Equation
Cavalcanti, Marcelo M. Domingos Cavalcanti, Valeria N.; Faminskii, Andrei; Natali, Fabio
2012-04-15
In the present paper we establish results concerning the decay of the energy related to the damped Korteweg-de Vries equation posed on infinite domains. We prove the exponential decay rates of the energy when a initial value problem and a localized dissipative mechanism are in place. If this mechanism is effective in the whole line, we get a similar result in H{sup k}-level, k Element-Of Double-Struck-Capital-N . In addition, the decay of the energy regarding a initial boundary value problem posed on the right half-line, is obtained considering convenient a smallness condition on the initial data but a more general dissipative effect.
Compacton solutions in a class of generalized fifth-order Korteweg--de Vries equations
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.
Compacton solutions in a class of generalized fifth-order Korteweg-de Vries equations.
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
Soliton evolution and radiation loss for the Korteweg--de Vries equation
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.
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.
NASA Astrophysics Data System (ADS)
Yesmakhanova, K.; Bekova, G.; Shaikhova, G.; Myrzakulov, R.
2016-08-01
In this paper, we consider the (2+1)-dimensional complex modified Korteweg-de Vries and Maxwell-Bloch (cmKdVMB) equations. Lax pairs of cmKdVMB equations are presented. Using the Lax pair, we construct a Darboux transformation and namely one-fold transformations. The soliton solutions are obtained from the different “seeds” by using this Darboux transformation.
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.
Shallow-water soliton dynamics beyond the Korteweg-de Vries equation.
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
Small-dispersion limit of the Korteweg-deVries equations
Lax, P.D.; Levermore, C.D.
1982-05-01
The scattering transform method is used to study the weak limit of solutions to the initial-value problem for the Korteweg-deVries (KdV) equation as the dispersion tends to zero. In that limit the associated Schroedinger operator becomes semiclassical, so the exact scattering data is replaced by its corresponding WKB expressions. Only nonpositive initial data are considered; in that case the limiting reflection coefficient vanishes. The explicit solution of Kay and Moses for the reflectionless inverse transform is then analyzed, and the weak limit, valid for all time, is characterized by a quadratic minimum problem with constraints. With the aid of function theoretical methods, solutions of this minimum problem are constructed in terms of solutions to an initial value problem for some auxiliary functions. The weak limit satisfies the KdV equation with the dispersive term dropped until the finite time at which its derivatives become infinite. Up to that time the weak limit is a strong L/sup 2/ limit. At later times the weak limit is locally described by Whitham's averaged equations or, more generally, by the equations found by Flaschka et al. using multiphase averaging. For large times, behavior of the weak limit is studied directly from the minimum problem.
Derivation of electrostatic Korteweg-deVries equation in fully relativistic two-fluid plasmas
NASA Astrophysics Data System (ADS)
Lee, Nam C.
2008-08-01
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.
Derivation of electrostatic Korteweg-deVries equation in fully relativistic two-fluid plasmas
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.
NASA Astrophysics Data System (ADS)
Wang, Jianyong; Hu, Hanwei; Yu, Jun
2011-10-01
Starting from the nonlinear version of bilinear negative Kadomtsev-Petviashvili system, a new (2+1)-dimensional generalization of the modified Korteweg-deVries equation is obtained. For this new system, a set of infinitely many generalized symmetries is found by applying a formal series symmetry approach. And these symmetries constitute a closed infinite-dimensional Lie algebra which is a generalization of w∞ type algebra.
Rare-event Simulation for Stochastic Korteweg-de Vries Equation
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.
An operator method for finding exact solutions to vector Korteweg-de Vries equations
NASA Astrophysics Data System (ADS)
Huang, Sen-Zhong
2003-03-01
We develop an operator method which helps finding exact solutions to nonlinear evolution equations (NLEs). Our working schema goes as follows: First we translate the given (NLE) into an appropriate operator version (ONLE). Second, we look for solutions to (ONLE) of the form U=(I+L)-1M, where both L and M are operator-valued functions of the space-time variables and the range of M locates in some appropriate Banach algebras which admits a functional φ that preserves the squares [i.e., φ(A2)=φ(A)2]. Finally, a solution u of the given (NLE) can be obtained by setting u≔φ(U). This method is named by the LM method. Using the LM method, we have rederived the famous Cole-Hopf transformation which reduces the nonlinear Burgers equation into the linear heat equation. The main part of this article is to use the LM method to study the vector Korteweg-de Vries (KdV) equations ut=uxxx+3(u2)x settled in finite-dimensional unital Banach algebras J. It is shown that these vector KdV equations admit soliton solutions. Specially, we have carried out a thorough study of the quaternionic KdV equation (i.e., the vector KdV equation settled in the Hamilton quaternion algebra H) and shown many interesting and surprising aspects of the quaternionic KdV solitons. Two of them read as follows. (a) The paradoxical energy symmetry breaking phenomenon: Two quaternionic KdV solitons with different energies can annihilate each other. (b) The surprising low-dimensional phenomenon: The interaction of any finitely many quaternionic KdV solitons which live in a unital three-dimensional subspace Π of H does not yield any effect to the part outside that subspace Π and thus their interaction behaves as if it were linear although the interaction between quaternionic KdV solitons is really nonlinear. The LM method can be thought as a complement to the famous bilinear operator method of Hirota. Hirota's method works very powerful for solving scalar equation but has difficulty with vector equations
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
NASA Astrophysics Data System (ADS)
Schuch, Dieter
2015-06-01
It is shown that a nonlinear reformulation of time-dependent and time-independent quantum mechanics in terms of Riccati equations not only provides additional information about the physical system, but also allows for formal comparison with other nonlinear theories. This is demonstrated for the nonlinear Burgers and Korteweg-de Vries equations with soliton solutions. As Riccati equations can be linearized to corresponding Schrödinger equations, this also applies to the Riccati equations that can be obtained by integrating the nonlinear soliton equations, resulting in a time-independent Schrödinger equation with Rosen-Morse potential and its supersymmetric partner. Because both soliton equations lead to the same Riccati equation, relations between the Burgers and Korteweg-de Vries equations can be established. Finally, a connection with the inverse scattering method is mentioned.
On a hierarchy of nonlinearly dispersive generalized Korteweg - de Vries evolution equations
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.
Supersymmetric quantum mechanics and the Korteweg--de Vries hierarchy
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.
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.
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.
Spontaneous soliton generation in the higher order Korteweg-de Vries equations on the half-line.
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
Korteweg-deVries solitons and helium films
Condat, C.A.; Guyer, R.A.
1982-03-01
The possibility of propagating Korteweg-deVries solitons in a superfluid /sup 4/He film and in a superfluid /sup 4/He films overlayed by a /sup 3/He film is discussed. Various dispersive and nonlinear contribution tot he equation for the nonlinear modes of the films are analyzed. Conditions depending on the thickness of the films are obtained for the propagation of troughlike and bumplike solitons.
Explicit solutions from eigenfunction symmetry of the Korteweg-de Vries equation.
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
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.
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.
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.
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.
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.
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.
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.
Capillary Korteweg-de Vries solitons on a levitated cylinder
NASA Astrophysics Data System (ADS)
Pham, Chi-Tuong; Perrard, Stephane; Duchene, Charles; Deike, Luc
2014-11-01
A water cylinder is deposited on a straight channel heated far above boiling temperature so that the water levitates above its own vapor owing to Leidenfrost effect. Our setup allows us to study the one-dimensional propagation of surface waves. We show that the dispersion relation of linear waves follows that of gravity-capillary waves under a dramatically reduced gravity (up to a factor 30), yielding an effective capillary length larger than one centimeter. Nonlinear capillary depression solitary waves propagate without deformation and undergo mutual collisions and reflections at the boundaries of the domain. Their typical width and their amplitude-dependent velocity are in very good agreement with theoretical predictions based on Korteweg-de Vries equation. Supported by ANR-11-BS04-001-01 (FREEFLOW project).
NASA Astrophysics Data System (ADS)
Zhang, Ya-Xing; Zhang, Hai-Qiang; Li, Juan; Xu, Tao; Zhang, Chun-Yi; Tian, Bo
2008-04-01
In this paper, we put our focus on a variable-coefficient fifth-order Korteweg-de Vries (fKdV) equation, which possesses a great number of excellent properties and is of current importance in physical and engineering fields. Certain constraints are worked out, which make sure the integrability of such an equation. Under those constraints, some integrable properties are derived, such as the Lax pair and Darboux transformation. Via the Darboux transformation, which is an exercisable way to generate solutions in a recursive manner, the one- and two-solitonic solutions are presented and the relevant physical applications of these solitonic structures in some fields are also pointed out.
Extended Wronskian formula for solutions to the Korteweg-deVries equation
NASA Astrophysics Data System (ADS)
Ge, J.-Y.; Zhang, Y.; Chen, D.-Y.
2008-02-01
A matrix extension is presented for constructing a much broader class of exact solutions to the KdV equation through the Wronskian formulation. The present method can be applied to other soliton equations.
Compactons in PT-symmetric generalized Korteweg-de Vries equations
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.
Asymptotic behavior of solutions of the Korteweg-de Vries equation
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.
Asymptotic behavior of solutions of the Korteweg-de Vries equation for large times
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.
Long-time asymptotic behavior of the solutions of the Korteweg-De Vries equations
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.
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.
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.
NASA Astrophysics Data System (ADS)
Deng, Guo; Biondini, Gino; Trillo, Stefano
2016-10-01
We study the small dispersion limit of the Korteweg-de Vries (KdV) equation with periodic boundary conditions and we apply the results to the Zabusky-Kruskal experiment. In particular, we employ a WKB approximation for the solution of the scattering problem for the KdV equation [i.e., the time-independent Schrödinger equation] to obtain an asymptotic expression for the trace of the monodromy matrix and thereby of the spectrum of the problem. We then perform a detailed analysis of the structure of said spectrum (i.e., band widths, gap widths and relative band widths) as a function of the dispersion smallness parameter ɛ. We then formulate explicit approximations for the number of solitons and corresponding soliton amplitudes as a function of ɛ. Finally, by performing an appropriate rescaling, we compare our results to those in the famous Zabusky and Kruskal's paper, showing very good agreement with the numerical results.
Symmetry breaking in linearly coupled Korteweg-de Vries systems.
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
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.
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
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.
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
Boyd, J.P.
1996-03-01
We numerically calculate bions, which are bound states of two solitary waves which travel together as a single coherent structure with a fixed peak-to-peak separation, for the fifth-order Korteweg-deVries equation. R.H.J. Grimshaw and B.A. Malomed predicted such bions using perturbation theory. We find that the nearly singular quasi-translational eigen-mode which is the heart of the theory is also numerically important in the sense that later iterations are approximately proportional to this eigenmode. However, the near-singularity does not create any serious probelms for our Fourier pseudospectral/Newton-Kantorovich/pseudoarclength continuation algorithms. This type of theory for weakly overlapping solitary waves has been previously developed by Gorshkov, Ostrovskii, Papko, and others. However, Grimshaw and Malomed`s work and our own are the first on bions which are {open_quotes}weakly nonlocal,{close_quotes} that is, decay for large {vert_bar}x{vert_bar} to small amplitude oscillations rather than to zero. Our numerical calculations confirm the main assertions of Grimshaw and Malomed. However, thre are other features, such as a complicated branch structure with multiple turning points and the existence of bions with narrow peak-to-peak separation, which are not predicted by the theory. 20 refs., 15 figs., 2 tabs.
NASA Astrophysics Data System (ADS)
Feng, Zhaosheng
Many physical phenomena can be described by nonlinear models. The last few decades have seen an enormous growth of the applicability of nonlinear models and of the development of related nonlinear concepts. This has been driven by modern computer power as well as by the discovery of new mathematical techniques, which include two contrasting themes: (i) the theory of dynamical systems, most popularly associated with the study of chaos, and (ii) the theory of integrable systems associated, among other things, with the study of solitons. In this dissertation, we study two nonlinear models. One is the 1-dimensional vibrating string satisfying wtt - wxx = 0 with van der Pol boundary conditions. We formulate the problem into an equivalent first order Hyperbolic system, and use the method of characteristics to derive a nonlinear reflection relation caused by the nonlinear boundary conditions. Thus, the problem is reduced to the discrete iteration problem of the type un+1 = F( un). Periodic solutions are investigated, an invariant interval for the Abel equation is studied, and numerical simulations and visualizations with different coefficients are illustrated. The other model is the Korteweg-de Vries-Burgers (KdVB) equation. In this dissertation, we proposed two new approaches: One is what we currently call First Integral Method, which is based on the ring theory of commutative algebra. Applying the Hilbert-Nullstellensatz, we reduce the KdVB equation to a first-order integrable ordinary differential equation. The other approach is called the Coordinate Transformation Method, which involves a series of variable transformations. Some new results on the traveling wave solution are established by using these two methods, which not only are more general than the existing ones in the previous literature, but also indicate that some corresponding solutions presented in the literature contain errors. We clarify the errors and instead give a refined result.
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.
NASA Astrophysics Data System (ADS)
Ghorui, Malay Kumar; Samanta, Utpal Kumar; Chatterjee, Prasanta
2013-06-01
The head-on collisions of ion-acoustic solitary waves (IASWs) in a dense magnetized quantum plasma are investigated. The two-sided Korteweg-de Vries (KdV) equations in generic case as well as the two-sided modified Korteweg-de Vries (mKdV) equations in a special case are obtained, the analytical phase shifts and the trajectories after the head-on collisions of two IASWs in a three species quantum plasma are derived by using the extended version of Poincaré-Lighthill-Kuo (PLK) method for both the situations. We provide the theoretical predictions about the existence of compressive and rarefactive IASWs in the model. We observe that in generic case collisions are possible among the same polarity solitons, whereas in the special case collisions are possible among the same or opposite polarities solitons. Moreover the colliding phase shifts are significantly affected by the quantum diffraction parameter, by the square of the ratio of ion gyrofrequency to ion plasma frequency and by obliqueness of propagation. The important observations of this manuscript are that the waves reach a maximum amplitude which is the superposition of the initial amplitudes and they suffer a time delay during their collision. The plasma parameter values for white dwarfs are taken for discussion.
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
Anomalous autoresonance threshold for chirped-driven Korteweg-de-Vries waves.
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
Electrostatic Korteweg-deVries solitary waves in a plasma with Kappa-distributed electrons
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.
Modified Korteweg--deVries solitons in a warm plasma with negative ions
Kalita, B.C. , India ) Kalita, M.K. )
1990-03-01
The propagation of ion-acoustic solitons in a warm plasma in the presence of negative ions has been investigated theoretically through the modified Korteweg--deVries (KdV) equation. In the case of the first-order velocity perturbation of the positive ions bearing a constant ratio to that of the negative ions, the existence of both compressive and rarefactive solitons at different critical densities for different temperature ratios has been established when the mass ratio is greater than unity. It is also demonstrated in this case that no modified KdV soliton exists at the critical density in a warm plasma with negative ions when the mass ratio is less than unity.
Electrostatic Korteweg-deVries solitary waves in a plasma with Kappa-distributed electrons
NASA Astrophysics Data System (ADS)
Choi, C.-R.; Min, K.-W.; Rhee, T.-N.
2011-09-01
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 κ (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.
Static algebraic solitons in Korteweg-de Vries type systems and the Hirota transformation.
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
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.
NASA Astrophysics Data System (ADS)
Wei, Guang-Mei; Gao, Yi-Tian; Hu, Wei; Zhang, Chun-Yi
2006-10-01
There has been considerable interest in the study on the variable-coefficient nonlinear evolution equations in recent years, since they can describe the real situations in many fields of physical and engineering sciences. In this paper, a generalized variable-coefficient KdV (GvcKdV) equation with the external-force and perturbed/dissipative terms is investigated, which can describe the various real situations, including large-amplitude internal waves, blood vessels, Bose-Einstein condensates, rods and positons. The Painlevé analysis leads to the explicit constraint on the variable coefficients for such a equation to pass the Painlevé test. An auto-Bäcklund transformation is provided by use of the truncated Painlevé expansion and symbolic computation. Via the given auto-Bäcklund transformation, three families of analytic solutions are obtained, including the solitonic and periodic solutions.
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.
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.
NASA Astrophysics Data System (ADS)
Aminmansoor, F.; Abbasi, H.
2015-08-01
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.
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.
NASA Astrophysics Data System (ADS)
Singh, Dhananjay K.; Malik, Hitendra K.
2007-06-01
Soliton propagation at critical density of negative ions is studied for weakly inhomogeneous magnetized cold plasma having positive ions, negative ions, and electrons. A general phase velocity relation is obtained and possible modes are studied for different cases involving different constituents of the plasma. Two types of modes (fast and slow) are found to propagate for the equal mass of the positive and negative ions. However, a limit on the obliqueness of magnetic field is obtained for the propagation of slow mode. For both types of modes, a variable coefficient modified Korteweg-deVries equation with an additional term arisen due to the density gradient is realized, which admits solutions for compressive solitons and rarefactive solitons of the same amplitudes at critical negative ion density. The propagation characteristics of these solitons are studied under the effect of densities of ions, magnetic field, and its obliqueness. The amplitudes of fast and slow wave solitons show their opposite behavior with the negative ion concentration, which is consistent with the variation of phase velocities with the negative ion density.
Singh, Dhananjay K.; Malik, Hitendra K.
2007-06-15
Soliton propagation at critical density of negative ions is studied for weakly inhomogeneous magnetized cold plasma having positive ions, negative ions, and electrons. A general phase velocity relation is obtained and possible modes are studied for different cases involving different constituents of the plasma. Two types of modes (fast and slow) are found to propagate for the equal mass of the positive and negative ions. However, a limit on the obliqueness of magnetic field is obtained for the propagation of slow mode. For both types of modes, a variable coefficient modified Korteweg-deVries equation with an additional term arisen due to the density gradient is realized, which admits solutions for compressive solitons and rarefactive solitons of the same amplitudes at critical negative ion density. The propagation characteristics of these solitons are studied under the effect of densities of ions, magnetic field, and its obliqueness. The amplitudes of fast and slow wave solitons show their opposite behavior with the negative ion concentration, which is consistent with the variation of phase velocities with the negative ion density.
NASA Astrophysics Data System (ADS)
Bustamante, Miguel D.; Hojman, Sergio A.
2003-10-01
We present an approach to the construction of action principles (the inverse problem of the calculus of variations), for first order (in time derivatives) differential equations, and generalize it to field theory in order to construct systematically, for integrable equations which are based on the existence of a Nijenhuis (or hereditary) operator, a (multi-Lagrangian) ladder of action principles which is complementary to the well-known multi-Hamiltonian formulation. We work out results for the Korteweg-de Vries (KdV) equation, which is a member of the positive hierarchy related to a hereditary operator. Three negative hierarchies of (negative) evolution equations are defined naturally from the hereditary operator as well, in a concise way, suitable for field theory. The Euler-Lagrange equations arising from the action principles are equivalent to deformations of the original evolution equation, and the deformations are obtained explicitly in terms of the positive and negative evolution vectors. We recognize, after appropriate coordinate transformations, the Liouville, Sinh-Gordon, Hunter-Zheng, and Camassa-Holm equations as negative evolution equations. The multi-Lagrangian ladder for KdV is directly mappable to a ladder for any of these negative equations and other positive evolution equations (e.g., the Harry-Dym and a special case of the Krichever-Novikov equations). For example, several nonequivalent, nonlocal time-reparametrization invariant action principles for KdV are constructed, and a new nonlocal action principle for the deformed system Sinh-Gordon+spatial translation vector is presented. Local and nonlocal Hamiltonian operators are obtained in factorized form as the inverses of all the nonequivalent symplectic two-forms in the ladder. Alternative Lax pairs for all negative evolution vectors are constructed, using the negative vectors and the hereditary operator as only input. This result leads us to conclude that, basically, all positive and negative
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 → ∞.
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.
Similarity solutions of some two-space-dimensional nonlinear wave evolution equations
NASA Technical Reports Server (NTRS)
Redekopp, L. G.
1980-01-01
Similarity reductions of the two-space-dimensional versions of the Korteweg-de Vries, modified Korteweg-de Vries, Benjamin-Davis-Ono, and nonlinear Schroedinger equations are presented, and some solutions of the reduced equations are discussed. Exact dispersive solutions of the two-dimensional Korteweg-de Vries equation are obtained, and the similarity solution of this equation is shown to be reducible to the second Painleve transcendent.
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.
Adhikary, N. C.; Deka, M. K.; Dev, A. N.; Sarmah, J.
2014-08-15
In this report, the investigation of the properties of dust acoustic (DA) solitary wave propagation in an adiabatic dusty plasma including the effect of the non-thermal ions and trapped electrons is presented. The reductive perturbation method has been employed to derive the modified Korteweg–de Vries (mK-dV) equation for dust acoustic solitary waves in a homogeneous, unmagnetized, and collisionless plasma whose constituents are electrons, singly charged positive ions, singly charged negative ions, and massive charged dust particles. The stationary analytical solution of the mK-dV equation is numerically analyzed and where the effect of various dusty plasma constituents DA solitary wave propagation is taken into account. It is observed that both the ions in dusty plasma play as a key role for the formation of both rarefactive as well as the compressive DA solitary waves and also the ion concentration controls the transformation of negative to positive potentials of the waves.
Deriving average soliton equations with a perturbative method
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.
Optimal error estimates for high order Runge-Kutta methods applied to evolutionary equations
McKinney, W.R.
1989-01-01
Fully discrete approximations to 1-periodic solutions of the Generalized Korteweg de-Vries and the Cahn-Hilliard equations are analyzed. These approximations are generated by an Implicit Runge-Kutta method for the temporal discretization and a Galerkin Finite Element method for the spatial discretization. Furthermore, these approximations may be of arbitrarily high order. In particular, it is shown that the well-known order reduction phenomenon afflicting Implicit Runge Kutta methods does not occur. Numerical results supporting these optimal error estimates for the Korteweg-de Vries equation and indicating the existence of a slow motion manifold for the Cahn-Hilliard equation are also provided.
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.
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.
Solitons and nonlinear wave equations
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.
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:
Bilinear approach to the supersymmetric Gardner equation
NASA Astrophysics Data System (ADS)
Babalic, C. N.; Carstea, A. S.
2016-08-01
We study a supersymmetric version of the Gardner equation (both focusing and defocusing) using the superbilinear formalism. This equation is new and cannot be obtained from the supersymmetric modified Korteweg-de Vries equation with a nonzero boundary condition. We construct supersymmetric solitons and then by passing to the long-wave limit in the focusing case obtain rational nonsingular solutions. We also discuss the supersymmetric version of the defocusing equation and the dynamics of its solutions.
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.
Quelques modèles diffusifs capillaires de type Korteweg
NASA Astrophysics Data System (ADS)
Bresch, Didier; Desjardins, Benoît
2004-11-01
The purpose of this Note is to propose new diffusive capillary models of Korteweg type and discuss their mathematical properties. More precisely, we introduce viscous models which provide some additional information on the behavior of the density close to vacuum. We actually prove that if some compatibility conditions between diffusion and capillarity are satisfied, some extra regularity information on a quantity involving the density is available. We obtain a non-trivial equality deduced from the special structure of the momentum equation. This Note generalizes to some extent the authors' previous works on the Korteweg model (with constant capillary coefficient) and on the shallow water equation. To cite this article: D. Bresch, B. Desjardins, C. R. Mecanique 332 (2004).
Boyd, J.P.
1995-05-01
By performing multiple precision pseudospectral calculations using two different basis sets, we compute the radiation coefficient {alpha}({epsilon}) for very small {epsilon} to resolve discrepancies between earlier numerical work of the author`s and a small-{epsilon} perturbation theory of Grimshaw and Joshi. Multiple precision is needed because {alpha} is asymptotically proportional to exp({minus}{pi}/2{epsilon}), and is therefore below the single precision roundoff threshold when {epsilon}{lt}1/25. Because {alpha} decreases exponentially with 1/{epsilon}, we use a numerical method whose error decreases exponentially fast with the number of grid points {ital N}: a pseudospectral method or finite differences of as high as twenty-fourth order. Richardson iteration, preconditioning by high order finite differences, parity symmetry, Aitken and Richardson extrapolation, and the fast Fourier transform are all crucial in reducing our longest runs to about 24 h on a Unix workstation. Although preconditioning by second order differences is the norm, we find that high order preconditioning---as large as 14th order---is more efficient for our one-dimensional problem. We find that the discrepancies are mostly due to differences in convention for (i) definition of the parameter {epsilon} and (ii) choice of the far field phase. When these are accounted for, we obtain very good agreement with Grimshaw and Joshi`s first order term. However, their second order term, which is predicted to be {pi}{sup 2}/2{approx}4.94, is about {ital O}(0.0 to {minus}0.2) in our computations. The reason for this difference is still a mystery.
Integrability of the Kruskal--Zabusky Discrete Equation by Multiscale Expansion
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.
Linear superposition in nonlinear equations.
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
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.
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.
Fast Neural Solution Of A Nonlinear Wave Equation
NASA Technical Reports Server (NTRS)
Barhen, Jacob; Toomarian, Nikzad
1996-01-01
Neural algorithm for simulation of class of nonlinear wave phenomena devised. Numerically solves special one-dimensional case of Korteweg-deVries equation. Intended to be executed rapidly by neural network implemented as charge-coupled-device/charge-injection device, very-large-scale integrated-circuit analog data processor of type described in "CCD/CID Processors Would Offer Greater Precision" (NPO-18972).
Two-component coupled KdV equations and its connection with the generalized Harry Dym equations
NASA Astrophysics Data System (ADS)
Popowicz, Ziemowit
2014-01-01
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.
Two-component coupled KdV equations and its connection with the generalized Harry Dym equations
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.
DeVry Institute of Technology: A Model for the 21st Century.
ERIC Educational Resources Information Center
Hallongren, Eugene G.
This presentation describes the DeVry Institute of Technology, a four-year, regionally accredited baccalaureate degree-granting institution that provides career-oriented degrees in business and technology to a diverse student population. DeVry has filled this niche for 70 years and now has 18 Institutes in the United States and Canada educating…
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].
Topological and non-topological exact soliton solution of the power law KdV equation
NASA Astrophysics Data System (ADS)
Biswas, Anjan; Petković, Marko D.; Milović, Daniela
2010-11-01
This paper obtains the exact 1-soliton solution of the perturbed Korteweg-de Vries equation with power law nonlinearity. Both topological as well as non-topological soliton solutions are obtained. The solitary wave ansatz is used to carry out this integration. The domain restrictions are identified in the process and the parameter constraints are also obtained. Finally, the numerical simulations are implemented in the paper.
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).
Islam, Md Shafiqul; Khan, Kamruzzaman; Akbar, M Ali; Mastroberardino, Antonio
2014-10-01
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.
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
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.
An integrable shallow water equation with linear and nonlinear dispersion.
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
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.
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.
From the Fermi-Pasta-Ulam Model to Higher-Order Nonlinear Evolution Equations
NASA Astrophysics Data System (ADS)
Kudryashov, Nikolay A.
2016-02-01
We consider generalizations of the Korteweg-de Vries equation of the fifth and seventh order obtained from the Fermi-Pasta-Ulam problem. Analytical properties of the equation are investigated taking into account the Painlevé test. It is shown that the equations of the fifth and seventh order do not have the Painlevé property. We demonstrate that there are expansions of the solution in the Laurent series and as a consequence we can find exact solutions of the equations. Solitary wave and elliptic solutions of the fifth and seventh order equations are presented.
NASA Astrophysics Data System (ADS)
Hay, Mike; Hietarinta, Jarmo; Joshi, Nalini; Nijhoff, Frank
2007-01-01
We present a new, nonautonomous Lax pair for a lattice nonautomous modified Korteweg deVries equation and show that it can be consistently extended multi-dimensionally, a property commonly referred to as being consistent around a cube. This nonautonomous equation is reduced to a series of q-discrete Painlevé equations, and Lax pairs for the reduced equations are found. A 2 × 2 Lax pair is given for a \\qth with multiple parameters and, also, for versions of \\qtw and \\qfi , all for the first time.
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.
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.
Evolution equation for bidirectional surface waves in a convecting fluid
NASA Astrophysics Data System (ADS)
Depassier, M. C.
2006-10-01
Surface waves in a heated viscous fluid exhibit a long-wave oscillatory instability. The non-linear evolution of unidirectional waves is known to be described by a modified Korteweg-deVries-Kuramoto-Sivashinsky equation. In the present work, we eliminate the restriction of unidirectional waves and find that the evolution of the wave is governed by a modified Boussinesq system. A perturbed Boussinesq equation of the form ytt-yxx-ɛ2[yxxtt+(y2)xx]+ɛ3[yxxt+yxxxxt+(y2)xxt]=0, which includes instability and dissipation, can be derived from this system.
Dynamical systems and probabilistic methods in partial differential equations
Deift, P.; Levermore, C.D.; Wayne, C.E.
1996-12-31
This publication covers material presented at the American Mathematical Society summer seminar in June, 1994. This seminar sought to provide participants exposure to a wide range of interesting and ongoing work on dynamic systems and the application of probabilistic methods in applied mathematics. Topics discussed include: the application of dynamical systems theory to the solution of partial differential equations; specific work with the complex Ginzburg-Landau, nonlinear Schroedinger, and Korteweg-deVries equations; applications in the area of fluid mechanics; turbulence studies from the perspective of probabilistic methods. Separate abstracts have been indexed into the database from articles in this proceedings.
NASA Astrophysics Data System (ADS)
Matsuno, Yoshimasa
2004-12-01
We present the new representations of the multiperiodic and multisoliton solutions of the Benjamin-Ono and nonlocal nonlinear Schrödinger equations. The key idea in the analysis is to explore the structure of the determinantal expressions of the solutions. After providing a direct verification of the multiperiodic solution by means of an elementary theory of determinants, we show that the solution admits a representation in terms of solutions for a system of nonlinear algebraic equations. This representation is found to be an analog of the multiperiodic solution of the Korteweg-de Vries equation. We also discuss the long-wave limit of the results associated with the multiperiodic solutions.
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.
Complex PT-symmetric nonlinear Schrödinger equation and Burgers equation.
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
Song, Qingxiang; Bogner, Andreas; Giesselmann, Frank; Lemieux, Robert P
2013-09-25
Smectic liquid crystals with 'de Vries-like' properties are characterized by a maximum layer contraction of ≤1% upon transition from the orthogonal SmA phase to the tilted SmC phase. We show that binary mixtures of 'de Vries-like' and conventional SmC mesogens with a molecular length ratio of 1.34 undergo a SmA-SmC phase transition with a maximum layer contraction ranging from 1.0 to 1.9% depending on the mixture composition.
Undular bore theory for the Gardner equation.
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
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…
The Linear KdV Equation with an Interface
NASA Astrophysics Data System (ADS)
Deconinck, Bernard; Sheils, Natalie E.; Smith, David A.
2016-10-01
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.
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.
Absent bystanders and cognitive dissonance: a comment on Timmins & de Vries.
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'.
Numerical simulation for treatment of dispersive shallow water waves with Rosenau-KdV equation
NASA Astrophysics Data System (ADS)
Ak, Turgut; Battal Gazi Karakoc, S.; Triki, Houria
2016-10-01
In this paper, numerical solutions for the Rosenau-Korteweg-de Vries equation are studied by using the subdomain method based on the sextic B-spline basis functions. Numerical results for five test problems including the motion of single solitary wave, interaction of two and three well-separated solitary waves of different amplitudes, evolution of solitons with Gaussian and undular bore initial conditions are obtained. Stability and a priori error estimate of the scheme are discussed. A comparison of the values of the obtained invariants and error norms for single solitary wave with earlier results is also made. The results show that the present method is efficient and reliable.
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.
NASA Astrophysics Data System (ADS)
Fedotov, I. A.; Polyanin, A. D.
2011-09-01
Broad classes of nonlinear equations of mathematical physics are described that admit order reduction by applying the von Mises transformation (with the unknown function used as a new independent variable and with a suitable partial derivative used as a new dependent variable) and by applying the Crocco transformation (with the first and second partial derivatives used as new independent and dependent variables, respectively). Associated Bäcklund transformations are constructed that connect evolution equations of general form (their special cases include Burgers, Korteweg-de Vries, and Harry Dym type equations and many other nonlinear equations of mathematical physics). Transformations are indicated that reduce the order of hydrodynamic-type equations of higher orders. The generalized Calogero equation and a number of other new integrable nonlinear equations, reducible to linear equations, are considered.
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.
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…
The Novikov-Veselov equation and the inverse scattering method: II. Computation
NASA Astrophysics Data System (ADS)
Lassas, M.; Mueller, J. L.; Siltanen, S.; Stahel, A.
2012-06-01
The Novikov-Veselov (NV) equation is a (2 + 1)-dimensional nonlinear evolution equation generalizing the (1 + 1)-dimensional Korteweg-deVries equation. The inverse scattering method (ISM) is applied for numerical solution of the NV equation. It is the first time the ISM is used as a computational tool for computing evolutions of a (2 + 1)-dimensional integrable system. In addition, a semi-implicit method is given for the numerical solution of the NV equation using finite differences in the spatial variables, Crank-Nicolson in time, and fast Fourier transforms for the auxiliary equation. Evolutions of initial data satisfying the hypotheses of part I of this paper are computed by the two methods and are observed to coincide with significant accuracy.
NASA Astrophysics Data System (ADS)
Ehrnström, Mats; Groves, Mark D.; Wahlén, Erik
2012-10-01
We consider a class of pseudodifferential evolution equations of the form \\begin{equation*} u_t + ( n(u) + Lu )_x = 0, \\end{equation*} in which L is a linear smoothing operator and n is at least quadratic near the origin; this class includes in particular the Whitham equation. A family of solitary-wave solutions is found using a constrained minimization principle and concentration-compactness methods for noncoercive functionals. The solitary waves are approximated by (scalings of) the corresponding solutions to partial differential equations arising as weakly nonlinear approximations; in the case of the Whitham equation the approximation is the Korteweg-deVries equation. We also demonstrate that the family of solitary-wave solutions is conditionally energetically stable.
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.
The reactions on Hugo de Vries's Intracellular pangenesis: the discussion with August Weismann.
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
Hugo De Vries: from the theory of intracellular pangenesis to the rediscovery of Mendel.
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
Hugo De Vries: from the theory of intracellular pangenesis to the rediscovery of Mendel.
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.
YCF1: A Green TIC: Response to the de Vries et al. Commentary
Nakai, Masato
2015-01-01
This response to a recent Commentary article by de Vries et al. highlights critical errors in the annotation and identification of Ycf1 homologs in the sequenced chloroplast genomes. Contrary to what is reported by de Vries et al., the majority of chloroplast genomes sequenced to date appear to have retained a typical Ycf1 sequence (i.e., including the N-terminal 6TM domain and a variable hydrophilic C-terminal domain) as my group previously reported. Our evidence continues to support the model that Ycf1 forms an essential component of a “green TIC” that is largely conserved among the Chlorophyta and land plants. Since the establishment of this green TIC with Tic20 as the core component, some cases of loss of Ycf1 during the evolution of the green lineages might be regarded as modifications or alterations of the complex. Here, I discuss our working model that the presence of an alternative “nonphotosynthetic-type” or “ancestral-type” TIC might explain other (or specific) cases of the lack of Ycf1, not only in early lineages, including Glaucophyta and Rhodophyta, but also in the grasses. PMID:26071422
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.
Krishna Prasad, S; Shankar Rao, D S; Sridevi, S; Naciri, Jawad; Ratna, B R
2011-03-16
Dielectric measurements have been made on three organosiloxane liquid crystal compounds exhibiting a smectic A (SmA) to smectic C* (SmC*) transition, the SmA phase being of the de Vries type. The electroclinic response of the molecules in the de Vries phase of these compounds exhibits a double-peak profile, and is thus different from the conventional chiral SmA phase, a feature explained on the basis of an antiferroelectric (AF) block model (Krishna Prasad et al 2009 Phys. Rev. Lett. 102 147802). The differential interactions arising from the different molecular ends of these siloxane-based compounds, which are the basis for the AF block model, can also be expected to enhance the layer translational order. We present x-ray integrated intensity data that show a high (~0.9) translational order in the SmA phase. Dielectric relaxation spectra bring out the fact that the magnitude of the soft mode relaxation parameters is dependent on the number of siloxane groups in the terminal part of the molecule. A range-shrinking analysis of the temperature-dependent dielectric relaxation strength has been carried out, using a power-law expression. The characteristic exponent shows a systematic growth with range shrinking and reaches limiting values comparable to that predicted for the 2D Ising universality class.
The zero dispersion limits of nonlinear wave equations
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.
Evolution equation for infinitesimal rotational discontinuities
NASA Technical Reports Server (NTRS)
Sonnerup, B. U. O.; Qian, S.; Wang, D.-J.
1990-01-01
An evolution equation in the form of a modified Korteweg-de Vries equation is developed which describes the small-amplitude version of the infinitesimal rotational discontinuity (RD) studied by Wang and Sonnerup (1984). It is shown that the small-amplitude version of the equilibrium pulse solution obtained by Wang and Sonnerup is metastable and thus unlikely to arise spontaneously. When the initial pulse amplitude is smaller than and/or the initial pulse width is greater than the equilibrium value, the pulse decays. When the reverse is the case, the pulse is converted to an infinitesimal intermediate-mode solitary wave having greater pulse amplitude and speed. A simulation experiment is performed in which one of the equilibrium intermediate-mode solitary waves overtakes another, less rapidly moving version of the same wave. The existence of multipeaked intermediate-mode solitary pulses is demonstrated.
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.
ERIC Educational Resources Information Center
Goodman, Joan F.
2002-01-01
Presents points of agreement with DeVries, Zan, and Hildebrandt: overall educational philosophy, the developmental path from egocentrism to reciprocity, and educational approaches when fundamental ethical principles are at stake. Examines the substantial differences in perspectives regarding the substance of morality, the process of teaching…
NASA Astrophysics Data System (ADS)
Batool, Nazia; Masood, W.; Siddiq, M.; Jahangir, R.
2016-08-01
In the present investigation, cylindrical Kadomstev-Petviashvili (CKP) equation is derived in pair-ion-electron plasmas to study the propagation and interaction of two solitons. Using a novel gauge transformation, two soliton solutions of CKP equation are found analytically by using Hirota's method and to the best of our knowledge have been used in plasma physics for the first time. Interestingly, it is observed that unlike the planar Kadomstev-Petviashvili (KP) equation, the CKP equation admits horseshoe-like solitary structures. Another non-trivial feature of CKP solitary solution is that the interaction parameter gets modified by the plasma parameters contrary to the one obtained for Korteweg-de Vries equation. The importance of the present investigation to understand the formation and interaction of solitons in laboratory produced pair plasmas is also highlighted.
Evolution of higher order nonlinear equation for the dust ion-acoustic waves in nonextensive plasma
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).
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.
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.
Molecular tilt near nanoparticles in the smectic-A phase of a de Vries liquid-crystalline compound.
Lejček, L; Novotná, V; Glogarová, M
2014-01-01
We show how the inclusions of the nanoparticles or the clusters of nanoparticles in the liquid-crystalline smectic-A phase lead to layer deformations and may create a tilt in their vicinity, thus inducing locally a smectic-A-smectic-C transition. We have studied a freestanding film of "de Vries" compound, which exhibits the smectic-A-smectic-C transition without layer shrinkage, mixed with functionalized gold nanoparticles. The tilt induced by nanoparticle clusters, which decorate the edge dislocations, has been observed in the smectic-A phase. The tilt of liquid-crystal molecules near nanoparticles is a consequence of interaction of liquid-crystalline molecules with the surface of nanoparticles. The observed tilt may prove the concept of existence of a disordered tilt in the smectic-A phase of de Vries compounds. The tilt distribution near nanoparticles is discussed using both the smectic-A elasticity and local smectic-A-smectic-C transition.
Pretend model of traveling wave solution of two-dimensional K-dV equation
NASA Astrophysics Data System (ADS)
Karim, Md Rezaul; Alim, Md Abdul; Andallah, Laek Sazzad
2013-11-01
Traveling wave resolution of Korteweg-de Vries (K-dV) solitary and numerical estimation of analytic solutions have been studied in this paper for imaginary concept. Pretend model of traveling wave deals with giant waves or series of waves created by an undersea earthquake, volcanic eruption or landslide. The concept of traveling wave is frequently used by mariners and in coastal, ocean and naval engineering. We have found some exact traveling wave solutions with relevant physical parameters using new auxiliary equation method introduced by Pang et al. (Appl. Math. Mech-Engl. Ed 31(7):929-936, 2010). We have solved the imaginary part of exact traveling wave equations analytically, and numerical results of time-dependent wave solutions have been presented graphically. This procedure has a potential to be used in more complex system for other types of K-dV equations.
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
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.
Origin of weak layer contraction in de Vries smectic liquid crystals.
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.
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.
Nonlinear disintegration of sine wave in the framework of the Gardner equation
NASA Astrophysics Data System (ADS)
Kurkina, Oxana; Rouvinskaya, Ekaterina; Talipova, Tatiana; Kurkin, Andrey; Pelinovsky, Efim
2016-10-01
Internal tidal wave entering shallow waters transforms into an undular bore and this process can be described in the framework of the Gardner equation (extended version of the Korteweg-de Vries equation with both quadratic and cubic nonlinear terms). Our numerical computations demonstrate the features of undular bore developing for different signs of the cubic nonlinear term. If cubic nonlinear term is negative, and initial wave amplitude is large enough, two undular bores are generated from the two breaking points formed on both crest slopes (within dispersionless Gardner equation). Undular bore consists of one table-top soliton and a group of small soliton-like waves passing through the table-top soliton. If the cubic nonlinear term is positive and again the wave amplitude is large enough, the breaking points appear on crest and trough generating groups of positive and negative soliton-like pulses. This is the main difference with respect to the classic Korteweg-de Vries equation, where the breaking point is single. It is shown also that nonlinear interaction of waves happens similarly to one of scenarios of two-soliton interaction of "exchange" or "overtake" types with a phase shift. If small-amplitude pulses interact with large-amplitude soliton-like pulses, their speed in average is negative in the case when "free" velocity is positive. Nonlinear interaction leads to the generation of higher harmonics and spectrum width increases with amplitude increase independently of the sign of cubic nonlinear term. The breaking asymptotic k 4 / 3 predicted within the dispersionless Gardner equation emerges during the process of undular bore development. The formation of soliton-like perturbations leads to appearance of several spectral peaks which are downshifting with time.
Analytic study on the Sawada-Kotera equation with a nonvanishing boundary condition in fluids
NASA Astrophysics Data System (ADS)
Shan, Wen-Rui; Yan, Tian-Zhong; Lü, Xing; Li, Min; Tian, Bo
2013-07-01
Under investigation in this paper is the Sawada-Kotera equation with a nonvanishing boundary condition, which describes the evolution of steeper waves of shorter wavelength than those described by the Korteweg-de Vries equation does. With the binary-Bell-polynomial, Hirota method and symbolic computation, the bilinear form and N-soliton solutions for this model are derived. Meanwhile, propagation characteristics and interaction behaviors of the solitons are discussed through the graphical analysis. Via Bell-polynomial approach, the Bäcklund transformation is constructed in both the binary-Bell-polynomial and bilinear forms. Based on the binary-Bell-polynomial-type Bäcklund transformation, we obtain the Lax pair and conservation laws associated.
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.
Roles of mutation and selection in speciation: from Hugo de Vries to the modern genomic era.
Nei, Masatoshi; Nozawa, Masafumi
2011-01-01
One of the most important problems in evolutionary biology is to understand how new species are generated in nature. In the past, it was difficult to study this problem because our lifetime is too short to observe the entire process of speciation. In recent years, however, molecular and genomic techniques have been developed for identifying and studying the genes involved in speciation. Using these techniques, many investigators have already obtained new findings. At present, however, the results obtained are complex and quite confusing. We have therefore attempted to understand these findings coherently with a historical perspective and clarify the roles of mutation and natural selection in speciation. We have first indicated that the root of the currently burgeoning field of plant genomics goes back to Hugo de Vries, who proposed the mutation theory of evolution more than a century ago and that he unknowingly found the importance of polyploidy and chromosomal rearrangements in plant speciation. We have then shown that the currently popular Dobzhansky-Muller model of evolution of reproductive isolation is only one of many possible mechanisms. Some of them are Oka's model of duplicate gene mutations, multiallelic speciation, mutation-rescue model, segregation-distorter gene model, heterochromatin-associated speciation, single-locus model, etc. The occurrence of speciation also depends on the reproductive system, population size, bottleneck effects, and environmental factors, such as temperature and day length. Some authors emphasized the importance of natural selection to speed up speciation, but mutation is crucial in speciation because reproductive barriers cannot be generated without mutations.
Kets de Vries, Manfred F
2004-01-01
Much of the business literature on leadership starts with the assumption that leaders are rational beings. But irrationality is integral to human nature, and inner conflict often contributes to the drive to succeed. Although a number of business scholars have explored the psychology of executives, Manfred F.R Kets de Vries has made the analysis of CEOs his life's work. In this article, Kets de Vries, a psychoanalyst, author, and instead professor, draws on three decades of study to describe the psychological profile of successful CEOs. He explores senior executives' vulnerabilities, which are often intensified by followers' attempts to manipulate their leaders. Leaders, he says, have an uncanny ability to awaken transferential processes--in which people transfer the dynamics of past relationships onto present interactions--among their employees and even in themselves. These processes can present themselves in a number of ways, sometimes negatively. What's more, many top executives, being middle-aged, suffer from depression. Mid-life prompts a reappraisal of career identity, and by the time a leader is a CEO, an existential crisis is often imminent. This can happen with anyone, but the probability is higher with CEOs, and senior executives because so many have devoted themselves exclusively to work. Not all CEOs are psychologically unhealthy, of course. Healthy leaders are talented in self-observation and self-analysis, Kets de Vries says. The best are highly motivated to spend time on self-reflection. Their lives are in balance, they can play, they are creative and inventive, and they have the capacity to be nonconformist. "Those who accept the madness in themselves may be the healthiest leaders of all," he concludes. PMID:14723178
Kets de Vries, Manfred F
2004-01-01
Much of the business literature on leadership starts with the assumption that leaders are rational beings. But irrationality is integral to human nature, and inner conflict often contributes to the drive to succeed. Although a number of business scholars have explored the psychology of executives, Manfred F.R Kets de Vries has made the analysis of CEOs his life's work. In this article, Kets de Vries, a psychoanalyst, author, and instead professor, draws on three decades of study to describe the psychological profile of successful CEOs. He explores senior executives' vulnerabilities, which are often intensified by followers' attempts to manipulate their leaders. Leaders, he says, have an uncanny ability to awaken transferential processes--in which people transfer the dynamics of past relationships onto present interactions--among their employees and even in themselves. These processes can present themselves in a number of ways, sometimes negatively. What's more, many top executives, being middle-aged, suffer from depression. Mid-life prompts a reappraisal of career identity, and by the time a leader is a CEO, an existential crisis is often imminent. This can happen with anyone, but the probability is higher with CEOs, and senior executives because so many have devoted themselves exclusively to work. Not all CEOs are psychologically unhealthy, of course. Healthy leaders are talented in self-observation and self-analysis, Kets de Vries says. The best are highly motivated to spend time on self-reflection. Their lives are in balance, they can play, they are creative and inventive, and they have the capacity to be nonconformist. "Those who accept the madness in themselves may be the healthiest leaders of all," he concludes.
NASA Astrophysics Data System (ADS)
Prasad, S. Krishna; Rao, D. S. Shankar; Sridevi, S.; Lobo, Chethan V.; Ratna, B. R.; Naciri, Jawad; Shashidhar, R.
2009-04-01
X-ray, electrical, electro-optical, and dielectric studies in the de Vries smectic A (SmA) phase of organosiloxane derivatives exhibit features surprisingly different from that of a conventional SmA phase. The switching data show a double peak profile, characteristic of an antiferroelectric (AF) structure. A model with the adjacent smectic layers having an AF-like arrangement and no global tilt correlation is proposed. Observed in molecules with differential interactions between the two termini, these findings have wide ramifications in understanding the minimum layer shrinkage of such systems.
NASA Astrophysics Data System (ADS)
De Matteis, Giovanni; Martina, Luigi
2012-03-01
A system of partial differential equations, describing one-dimensional nematic liquid crystals is studied by Lie group analysis. These equations are the Euler-Lagrange equations associated with a free energy functional that depends on the mass density and the gradient of the mass density. The group analysis is an algorithmic approach that allows us to show all the point symmetries of the system, to determine all possible symmetry reductions and, finally, to obtain invariant solutions in the form of travelling waves. The Hamiltonian formulation of the dynamical equations is also considered and the conservation laws found by exploiting the local symmetries.
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.
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.
Dispersive shock waves in the Kadomtsev-Petviashvili and two dimensional Benjamin-Ono equations
NASA Astrophysics Data System (ADS)
Ablowitz, Mark J.; Demirci, Ali; Ma, Yi-Ping
2016-10-01
Dispersive shock waves (DSWs) in the Kadomtsev-Petviashvili (KP) equation and two dimensional Benjamin-Ono (2DBO) equation are considered using step like initial data along a parabolic front. Employing a parabolic similarity reduction exactly reduces the study of such DSWs in two space one time (2 + 1) dimensions to finding DSW solutions of (1 + 1) dimensional equations. With this ansatz, the KP and 2DBO equations can be exactly reduced to the cylindrical Korteweg-de Vries (cKdV) and cylindrical Benjamin-Ono (cBO) equations, respectively. Whitham modulation equations which describe DSW evolution in the cKdV and cBO equations are derived and Riemann type variables are introduced. DSWs obtained from the numerical solutions of the corresponding Whitham systems and direct numerical simulations of the cKdV and cBO equations are compared with very good agreement obtained. In turn, DSWs obtained from direct numerical simulations of the KP and 2DBO equations are compared with the cKdV and cBO equations, again with good agreement. It is concluded that the (2 + 1) DSW behavior along self similar parabolic fronts can be effectively described by the DSW solutions of the reduced (1 + 1) dimensional equations.
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).
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.
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).
A new perturbative approach to nonlinear partial differential equations
Bender, C.M.; Boettcher, S. ); Milton, K.A. )
1991-11-01
This paper shows how to solve some nonlinear wave equations as perturbation expansions in powers of a parameter that expresses the degree of nonlinearity. For the case of the Burgers equation {ital u}{sub {ital t}}+{ital uu}{sub {ital x}}={ital u}{sub {ital xx}}, the general nonlinear equation {ital u}{sub {ital t}}+{ital u}{sup {delta}}{ital u}{sub {ital x}}={ital u}{sub {ital xx}} is considered and expanded in powers of {delta}. The coefficients of the {delta} series to sixth order in powers of {delta} is determined and Pade summation is used to evaluate the perturbation series for large values of {delta}. The numerical results are accurate and the method is very general; it applies to other well-studied partial differential equations such as the Korteweg--de Vries equation, {ital u}{sub {ital t}}+{ital uu}{sub {ital x}} ={ital u}{sub {ital xxx}}.
Nonnenmacher, Dorothee; Jagiella, Stefan; Song, Qingxiang; Lemieux, Robert P; Giesselmann, Frank
2013-09-16
On the basis of thorough analysis of 2D X-ray diffraction patterns from smectic monodomains, we examine the influence of orientational fluctuations on the weakly first-order smectic A (SmA) to smectic C (SmC) transitions in two nonchiral organosiloxane "de Vries"-type liquid crystals. We find that these materials exhibit very large molecular tilt fluctuations with magnitudes of up to 35°--thus larger than the average tilt itself. This is essential to understand the underlying molecular mechanism behind the practical absence of smectic layer contraction in these materials: in the SmA phase, the nematic order parameter is very low (molecular fluctuations correspondingly high), and the expected layer shrinkage at the SmA to SmC transition is almost fully compensated by the increase in orientational order, as the fluctuations diminish with decreasing temperature. In addition to the general tilt fluctuations, we observe intrinsic soft-mode fluctuations. They have a λ-shaped temperature dependence that peaks at the SmA-SmC transition with a maximum amplitude of about 2°.
The frequency-dependent electrooptic response of the electroclinic effect in deVries SmA materials
NASA Astrophysics Data System (ADS)
Jones, Christopher D.; Dawin, Ute; Giesselmann, Frank; Clark, Noel; Rudquist, Per
2007-03-01
It is well established that electroclinic switching in standard SmA* materials relates to a reorientation of the molecules in a plane normal to the layers, and thus there is no corresponding change in birefringence due to reorientation about a cone, as is the case in the SmC* phase. When the electrooptic response is then analyzed via lock-in amplifier, the signal at the driving frequency is strong, while the second harmonic response, is non-existent [1]. Using this method we have investigated deVries materials W530 and TSiKN65, and show that there is a frequency-dependent second order response -- implying an electroclinic switching that corresponds to a change in birefringence, suggesting a reorientation of the molecule about a cone. We will present our findings and a model for the type of electroclinic switching that occurs in these two materials. Work supported by NSF MRSEC Grant DMR-0213918 and The Swedish Foundation for Strategic Research 2002/0388. [1] W. Kuczynski, et. al., Ferroelectics, 244, [491]/191, (2000)
Manna, U; Song, Jang-Kun; Panarin, Yu P; Fukuda, Atsuo; Vij, J K
2008-04-01
Mixtures of different compositions of an antiferroelectric liquid crystal compound that exhibits direct smectic-A*(Sm-A*)-smectic-C*(A) (Sm-C*(A)) transition with a ferroelectric liquid crystal compound that exhibits Sm-A*-smectic-C*(Sm-C*) transition are studied using electro-optics and dielectric spectroscopy. The results of optical texture, birefringence, and the tilt angle suggest that a part of the Sm-A* phase is of de Vries type, since an increase in the tilt angle with decreasing temperature results in a reduction in the value of the birefringence in the Sm-A* phase, whereas the birefringence at Sm-A* to Sm-C* transition goes up by 12.7%. The soft mode relaxation strength, the Landau coefficient of the temperature dependent term, and the other related parameters of the de Vries-type Sm-A-Sm-C*(A) and Sm-A*-Sm-C* transitions are determined using the Landau theory of the second-order phase transition. For the Sm-A*-Sm-C* transition, we find that the soft mode relaxation strength decreases, the Landau coefficient increases, and the Curie-Weiss temperature range decreases with an increased ferroelectric composition in the mixture. These observations can be explained by assuming that with increased ferroelectric composition in the mixture, the layer shrinkage at the de Vries Sm-A*-Sm-C* transition increases. On comparing the results of de Vries-type Sm-A* to Sm-C*(A) and Sm-C* transitions, we find that the soft mode dielectric strength and the other related Landau parameters of the de Vries Sm-A* phase are of the same order of magnitude for transitions from Sm-A* to Sm-C* and to Sm-C*(A) except for the composition of the mixture where both Sm-C* and Sm-C*(A) transitions are stable and the phase diagram shows phase sequence Sm-A* to Sm-C* to Sm-C*(A).
Nonlinear evolution-type equations and their exact solutions using inverse variational methods
NASA Astrophysics Data System (ADS)
Kara, A. H.; Khalique, C. M.
2005-05-01
We present the role of invariants in obtaining exact solutions of differential equations. Firstly, conserved vectors of a partial differential equation (p.d.e.) allow us to obtain reduced forms of the p.d.e. for which some of the Lie point symmetries (in vector field form) are easily concluded and, therefore, provide a mechanism for further reduction. Secondly, invariants of reduced forms of a p.d.e. are obtainable from a variational principle even though the p.d.e. itself does not admit a Lagrangian. In this latter case, the reductions carry all the usual advantages regarding Noether symmetries and double reductions. The examples we consider are nonlinear evolution-type equations such as the Korteweg-deVries equation, but a detailed analysis is made on the Fisher equation (which describes reaction-diffusion waves in biology, inter alia). Other diffusion-type equations lend themselves well to the method we describe (e.g., the Fitzhugh Nagumo equation, which is briefly discussed). Some aspects of Painlevé properties are also suggested.
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.
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.
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.
Wave-packet formation at the zero-dispersion point in the Gardner-Ostrovsky equation
NASA Astrophysics Data System (ADS)
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.
Wave-packet formation at the zero-dispersion point in the Gardner-Ostrovsky equation.
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
On the Hamiltonian structure of ion-acoustic plasma waves and water waves in channels
NASA Astrophysics Data System (ADS)
Menyuk, C. R.; Chen, H.-H.
1986-04-01
It is shown that the Hamiltonian structure of ion-acoustic waves and channel waves may be used to derive the Hamiltonian structure of the Korteweg-de Vries equation and its higher-order corrections. The Hamiltonian approach used here is more systematic and less laborious than standard methods for deriving the Korteweg-de Vries equation. It is also more revealing. In particular, it is shown that the Poisson bracket of the corrected equations equals the Korteweg-de Vries Poisson bracket at every order. It is also shown that the corrected equations become nonlocal at sufficiently high order.
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.
NASA Astrophysics Data System (ADS)
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
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
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.
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.
Analytical integrability and physical solutions of d-KdV equation
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.
Saunders, Karl
2014-04-01
Critical behavior near the smectic A-C tricritical point is studied using renormalization group techniques. Critical fluctuations induce a singular softening of the smectic bulk modulus in the A phase. At the tricritical point, the quasi-long-range positional order of the smectic layers is destroyed. Despite this loss of order, dislocations remain bound so that smectic elasticity is retained but becomes anomalous, i.e., length scale dependent. The critically induced large layer fluctuations lead to negative thermal expansion of the layers in the A phase and may explain the origin of de Vries behavior. Experimental predictions are given for the temperature dependence of the smectic bulk modulus, x-ray structure factor, and layer spacing in the A phase.
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
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.
Dust acoustic shock waves in two temperatures charged dusty grains
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.
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 B A
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
Vember, V V; Zhdanov, N N; Tugaĭ, T I
1999-01-01
The influence of the low-intensity gamma-irradiation on the process of lipid peroxidation and the activities of the antioxidant glutathione-dependent system (catalase, glutathione-transferase) has been investigated in a number of Cladosporium cladosporioides (Fres.) de Vries strains. The dark-pigmented strains isolated from the habitats with different degree of radionuclide contamination, and the nonpigmented alb-mutant of the same species have been used in our work. The studied properties have been analyzed with the respect of the radiotropism property and of the presence of melanin pigment in the cell wall of these strains. The lipid perioxidation level under the effect of the low-intensity gamma-irradiation was greatly increased in Cladosporium cladosporioides 396 strain only. This strain was isolated from the radiation-pure soil. Catalase activity in a number of the studies strains correlated neither with their pigmentation, nor with the property of positive radiotropism. The correlation between the strain pigmentation and activity of glutathione transferase has been found.
Vember, V V; Tugaĭ, T I; Zhadanov, N N
1998-01-01
Phenomena of melanization of radioactively polluted soils, due to prevalence of melanin-containing species and positive radiotropism of some micromycetes have been found during monitoring of mycobiota of the 30-km alienation zone of the Chernobyl NPP for 10 years. To elucidate the contribution of the melanin system to the cell protection against irradiation, the influence of gamma-irradiation on the activity of protein synthesis in four Cladosporium cladosporioides (Fres.) de Vries strains has been investigated. Two strains isolated from radioactively polluted substrates were characterised by the presence of positive radiotropism. Laboratory strain 396 and its alb-mutant (with blocked melanin synthesis), did not possess this feature. The protein synthesizing activity was assayed by incorporation of 14C-leucine in the protein fraction of mycelium, grown during 7 days under continuous gamma-irradiation of low intensity and without it. The protein synthesis was activated in the radioactively treated mycelium of dark-pigmented C. cladosporioides strains and it was suppressed in similarly treated mycelium of alb-mutant of C. cladosporioides. The rate of 14C-leucine incorporation into biomass of investigated strains correlated with positive radiotropism. The dependence between protein synthesis intensity and the availability of melanin protection system in micromycetes is assumed.
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 B A
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.
{PT}-symmetry breaking in complex nonlinear wave equations and their deformations
NASA Astrophysics Data System (ADS)
Cavaglia, Andrea; Fring, Andreas; Bagchi, Bijan
2011-08-01
We investigate complex versions of the Korteweg-deVries equations and an Ito-type nonlinear system with two coupled nonlinear fields. We systematically construct rational, trigonometric/hyperbolic and elliptic solutions for these models including those which are physically feasible in an obvious sense, that is those with real energies, but also those with complex energy spectra. The reality of the energy is usually attributed to different realizations of an antilinear symmetry, as for instance {PT}-symmetry. It is shown that the symmetry can be spontaneously broken in two alternative ways either by specific choices of the domain or by manipulating the parameters in the solutions of the model, thus leading to complex energies. Surprisingly, the reality of the energies can be regained in some cases by a further breaking of the symmetry on the level of the Hamiltonian. In many examples, some of the fixed points in the complex solution for the field undergo a Hopf bifurcation in the {PT}-symmetry breaking process. By employing several different variants of the symmetries we propose many classes of new invariant extensions of these models and study their properties. The reduction of some of these models yields complex quantum mechanical models previously studied.
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.
Nonlinear disintegration of sine wave in the framework of the Gardner equation
NASA Astrophysics Data System (ADS)
Kurkin, Andrey; Talipova, Tatiana; Kurkina, Oxana; Rouvinskaya, Ekaterina; Pelinovsky, Efim
2016-04-01
Nonlinear disintegration of sine wave is studied in the framework of the Gardner equation (extended version of the Korteweg - de Vries equation with both quadratic and cubic nonlinear terms). Undular bores appear here as an intermediate stage of wave evolution. Our numerical computations demonstrate the features of undular bore developing for different signs of the cubic nonlinear term. If cubic nonlinear term is negative, and initial wave amplitude is large enough, two undular bores are generated from the two breaking points formed on both crest slopes (within dispersionless Gardner equation). Undular bore consists of one table-top soliton and a group of small soliton-like waves passing through the table-top soliton. If the cubic nonlinear term is positive and again the wave amplitude is large enough, the breaking points appear on crest and trough generating groups of positive and negative solitary-like pulses. It is shown that nonlinear interaction of waves happens according to one of scenarios of two-soliton interaction of "exchange" or "overtake" types with a phase shift. If small-amplitude pulses interact with large-amplitude soliton-like pulses, their speed in average is negative in the case when "free" velocity is positive. Nonlinear interaction leads to the generation of higher harmonics and spectrum width increases with amplitude increase independently of the sign of cubic nonlinear term. The breaking asymptotic k4/3 predicted within the dispersionless Gardner equation emerges during the process of undular bore development. The formation of soliton-like perturbations leads to appearance of several spectral peaks which are downshifting with time.
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,…
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
Solitons in nucleon-nucleus collisions
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.
Quantum positron acoustic waves
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.
Shen, Yongqiang; Wang, Lixing; Shao, Renfan; Gong, Tao; Zhu, Chenhui; Yang, Hong; Maclennan, Joseph E; Walba, David M; Clark, Noel A
2013-12-01
In chiral smectic-A (Sm-A) liquid crystals, an applied electric field induces a tilt of the optic axis from the layer normal. When these materials are of the de Vries type, the electroclinic tilt susceptibility is unusually large, with the field-induced director reorientation accompanied by a substantial increase in optical birefringence with essentially no change in the smectic layer spacing. In order to account for the observed electro-optic behavior, we assume that the molecular orientation distribution in the Sm-A has two degrees of freedom: azimuthal orientation and tilt of the molecular long axis from the layer normal, with the tilt confined to a narrow range of angles. We present a generalized Langevin-Debye model of the response of this orientational distribution to applied field that gives a field-induced optic axis tilt, birefringence, and polarization dependence that agrees well with experimental measurements and reproduces the double-peaked polarization current response characteristic of a first-order Sm-A(*)-Sm-C(*) transition. Additionally, we find that the measured field-induced polarization and the Langevin-Debye model predictions can be quantitatively described as pre-transitional behavior near the tricritical point of a recently published generalized 3D XY model of interacting hard rods confined to reorient on a cone in the presence of an applied field.
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.
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.
Modified ion-acoustic solitary waves in plasmas with field-aligned shear flows
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.
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.
Dissipative effects on nonlinear waves in rotating fluids.
NASA Technical Reports Server (NTRS)
Leibovich, S.; Randall, J. D.
1971-01-01
Modifications to the existing inviscid theory of long-wave propagation in rotating fluids are studied. A modification to the Korteweg-deVries equation is found to describe weak dissipation in long waves in a swirling fluid. General features of solutions are discussed, and a solution for the damping of solitary waves is presented.
Modified electron acoustic field and energy applied to observation data
NASA Astrophysics Data System (ADS)
Abdelwahed, H. G.; El-Shewy, E. K.
2016-08-01
Improved electrostatic acoustic field and energy have been debated in vortex trapped hot electrons and fluid of cold electrons with pressure term plasmas. The perturbed higher-order modified-Korteweg-de Vries equation (PhomKdV) has been worked out. The effect of trapping and electron temperatures on the electro-field and energy properties in auroral plasmas has been inspected.
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)]—especially for the roles played therein by the diffuse volume flux j v and the rate of production of volume πν 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)], 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)]. Furthermore, we provide not only what we believe to be the correct constitutive equation for the Korteweg stress in the class of fluids that are constitutively Newtonian in their rheological response
NASA Astrophysics Data System (ADS)
Grigorov, Igor V.
2009-12-01
In article the algorithm of numerical modelling of the nonlinear equation of Korteweg-de Vrieze which generates nonlinear algorithm of digital processing of signals is considered. For realisation of the specified algorithm it is offered to use a inverse scattering method (ISM). Algorithms of direct and return spectral problems, and also problems of evolution of the spectral data are in detail considered. Results of modelling are resulted.
NASA Astrophysics Data System (ADS)
Yang, Yun-Qing; Wang, Yun-Hu; Li, Xin; Cheng, Xue-Ping
2014-03-01
We extend the method of constructing Bäcklund transformations for integrable equations through Riccati equations to the nonisospectral and the variable-coefficient equations. By taking nonisospectral and generalized variable-coefficient Korteweg—de Vries (KdV) equations as examples, their Bäcklund transformations are obtained under a more generalized constrain condition. In addition, the Lax pairs and infinite numbers of conservation laws of these equations are given. Especially, some classical equations such as the cylindrical KdV equation are just the special cases of the constrain condition.
Solving Differential Equations in R: Package deSolve
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...
Phase-modulated solitary waves controlled by a boundary condition at the bottom.
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
Dressed soliton in quantum dusty pair-ion plasma
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)].
Propagation of Long Extensional Nonlinear Waves in a Hyper-Elastic Layer
NASA Astrophysics Data System (ADS)
Teymür, Mevlüt
Propagation of small but finite amplitude waves in a nonlinear hyper-elastic plate of uniform thickness is considered. By employing a perturbation expansion, extensional waves are examined under the long wave limit. It is shown that the asymptotic wave field is governed by a Korteweg-DeVries (K-dV) equation. Then the propagation characteristics of the asymptotic waves are discussed via the well known solutions of the K-dV equation.
Ion-acoustic solitary waves in relativistic plasmas
Das, G.C.; Paul, S.N.
1985-03-01
This is a sequel to our earlier study on ion-acoustic waves studied through the augmentation to a modified Korteweg--deVries (K--dV) equation. We have derived a K--dV equation in a plasma, taking account of weakly relativistic effects, and the result shows that the solitary wave does exhibit the relativistic effect in the presence of ion streaming.
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.
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.
Robustness of de Saint Venant equations for simulating unsteady flows
Baltzer, Robert A.; Schaffranek, Raymond W.; Lai, Chintu; ,
1995-01-01
Long-wave motion in open channels can be expressed mathematically by the one-dimensional de Saint Venant equations describing conservation of fluid mass and momentum. Numerical simulation models, based on either depth/velocity or water-level/discharge dependent-variable formulations of these equations, are typically used to simulate unsteady open-channel flow. However, the implications and significance of selecting either dependent-variable form - on model development, discretization and numerical solution processes, and ultimately on the range-of-application and simulation utility of resulting models - are not well known. Results obtained from a set of numerical experiments employing two models - one based on depth/velocity and the other on water-level/discharge equation formulations - reveal the sensitivity of the two equation sets to various channel properties and dynamic flow conditions. In particular, the effects of channel gradient, channel width-to-depth ratio, flow-resistance coefficient, and flow unsteadiness are analyzed and discussed.
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.
Nonplanar ion-acoustic solitary waves with superthermal electrons in warm plasma
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.
Eslami, Parvin; Mottaghizadeh, Marzieh; Pakzad, Hamid Reza
2011-10-15
Cylindrical and spherical Korteweg-de Vries equations are derived for dust acoustic solitary waves in an unmagnetized three species plasma system, comprised of negatively charged cold dust, nonextensive ions and nonextensive electrons using standard reductive perturbation method. The effects of q{sub e}-nonextensive electrons, q{sub i}-nonextensive ions, electron-to-ion number density ratio {mu}, and nonplanar geometry on the profiles of the amplitudes of the solitary structures are examined numerically.
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.
NASA Astrophysics Data System (ADS)
Shubina, Maria
2016-09-01
In this paper, we investigate the one-dimensional parabolic-parabolic Patlak-Keller-Segel model of chemotaxis. For the case when the diffusion coefficient of chemical substance is equal to two, in terms of travelling wave variables the reduced system appears integrable and allows the analytical solution. We obtain the exact soliton solutions, one of which is exactly the one-soliton solution of the Korteweg-de Vries equation.
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.
Magnetoacoustic solitons in quantum plasma
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.
Cylindrical and spherical ion acoustic waves in a plasma with nonthermal electrons and warm ions
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.
Evolution of solitons over a randomly rough seabed.
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
Tilted and standard ring solitons in shallow water
NASA Astrophysics Data System (ADS)
Mannan, A.
2015-03-01
The propagation of nonlinear multiring soliton structures in a shallow water is theoretically investigated. To study this problem, we have derived a cylindrical (or concentric) Korteweg-deVries equation (cKdVE) for an incompressible, inviscid, and irrotational fluid. The cKdVE has been solved analytically and numerically to describe, respectively, the localized multiring structures with tilted and standard boundary conditions.
Numerical schemes for a model for nonlinear dispersive waves
NASA Technical Reports Server (NTRS)
Bona, J. L.; Pritchard, W. G.; Scott, L. R.
1985-01-01
A description is given of a number of numerical schemes to solve an evolution equation (Korteweg-deVries) that arises when modelling the propagation of water waves in a channel. The discussion also includes the results of numerical experiments made with each of the schemes. It is suggested, on the basis of these experiments, that one of the schemes may have (discrete) solitary-wave solutions.
A dimension-breaking phenomenon in the theory of steady gravity-capillary water waves.
Groves, M D; Haragus, M; Sun, S M
2002-10-15
The existence of a line solitary-wave solution to the water-wave problem with strong surface-tension effects was predicted on the basis of a model equation in the celebrated 1895 paper by D. J. Korteweg and G. de Vries and rigorously confirmed a century later by C. J. Amick and K. Kirchgässner in 1989. A model equation derived by B. B. Kadomtsev and V. I. Petviashvili in 1970 suggests that the Korteweg-de Vries line solitary wave belongs to a family of periodically modulated solitary waves which have a solitary-wave profile in the direction of motion and are periodic in the transverse direction. This prediction is rigorously confirmed for the full water-wave problem in the present paper. It is shown that the Korteweg-de Vries solitary wave undergoes a dimension-breaking bifurcation that generates a family of periodically modulated solitary waves. The term dimension-breaking phenomenon describes the spontaneous emergence of a spatially inhomogeneous solution of a partial differential equation from a solution which is homogeneous in one or more spatial dimensions.
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
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.
Capillary solitons on a levitated medium.
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.
Capillary solitons on a levitated medium.
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
Capillary solitons on a levitated medium
NASA Astrophysics Data System (ADS)
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.
NASA Astrophysics Data System (ADS)
Ata-ur-Rahman, Ali, S.; Mirza, Arshad M.; Qamar, A.
2013-04-01
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.
Analyses of Lattice Traffic Flow Model on a Gradient Highway
NASA Astrophysics Data System (ADS)
Arvind, Kumar Gupta; Sapna, Sharma; Poonam, Redhu
2014-09-01
The optimal current difference lattice hydrodynamic model is extended to investigate the traffic flow dynamics on a unidirectional single lane gradient highway. The effect of slope on uphill/downhill highway is examined through linear stability analysis and shown that the slope significantly affects the stability region on the phase diagram. Using nonlinear stability analysis, the Burgers, Korteweg-deVries (KdV) and modified Korteweg-deVries (mKdV) equations are derived in stable, metastable and unstable region, respectively. The effect of reaction coefficient is examined and concluded that it plays an important role in suppressing the traffic jams on a gradient highway. The theoretical findings have been verified through numerical simulation which confirm that the slope on a gradient highway significantly influence the traffic dynamics and traffic jam can be suppressed efficiently by considering the optimal current difference effect in the new lattice model.
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.
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.
Wheeler-DeWitt equation for brane gravity
Gusin, Pawel
2008-03-15
We consider gravity in the system consisting of the Bogomol'nyi-Prasad-Sommerfield (BPS) D3-brane embedded in a flat background geometry, produced by the solutions of supergravity. The effective action for this system is represented by the sum of the Hilbert-Einstein and Dirac-Born-Infeld actions. We derive the Wheeler-DeWitt equation for this system and obtain analytical solutions in some special cases. We also calculate the tunneling probability from the Planckian size of the D3-brane to the classical regime.
From Classical Nonlinear Integrable Systems to Quantum Shortcuts to Adiabaticity.
Okuyama, Manaka; Takahashi, Kazutaka
2016-08-12
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 XY spin chains from the Toda equations are studied in detail.
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.
Discrete reductive perturbation technique
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.
A non-standard Lax formulation of the Harry Dym hierarchy and its supersymmetric extension
NASA Astrophysics Data System (ADS)
Tian, Kai; Popowicz, Ziemowit; Liu, Q. P.
2012-03-01
For the Harry Dym hierarchy, a non-standard Lax formulation is deduced from that of the Korteweg-de Vries (KdV) equation through a reciprocal transformation. By supersymmetrizing this Lax operator, a new N = 2 supersymmetric extension of the Harry Dym hierarchy is constructed, and is further shown to be linked to one of the N = 2 supersymmetric KdV equations through the superconformal transformation. The bosonic limit of this new N = 2 supersymmetric Harry Dym equation is related to a coupled system of KdV-MKdV equations.
NASA Astrophysics Data System (ADS)
Quastel, Jeremy; Valkó, Benedek
2008-02-01
It is shown that white noise is an invariant measure for the Korteweg- deVries equation on {mathbb{T}} . This is a consequence of recent results of Kappeler and Topalov establishing the well-posedness of the equation on appropriate negative Sobolev spaces, together with a result of Cambronero and McKean that white noise is the image under the Miura transform (Ricatti map) of the (weighted) Gibbs measure for the modified KdV equation, proven to be invariant for that equation by Bourgain.
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.
NASA Astrophysics Data System (ADS)
Chen, Ching-Yao; Wu, H.-J.
2005-04-01
Interfacial instability of a miscible magnetic droplet in a rotating Hele-Shaw cell is simulated numerically. The influence of magnetic strengths, the Korteweg stresses, and their coupled effects are first discussed qualitatively by fingering patterns and streamlines. Quantitative measurements are evaluated by interfacial length L, number of fingers n, and diameter of gyration Dg. The results confirm with coupling rotational effects more vigorous fingering instability occurs on stronger magnetic strengths and less effective surface tensions (Korteweg stresses). Without the effects of Korteweg stresses, significant nonlinear fingering merges occur which lead to reduction in fingering number, early decay of interfacial length and reversed plane trajectories. Before the occurrence of fingering merges, monotonic growths of interfacial lengths, constant fingering numbers, and nearly linear pattern trajectories are observed. If the significant Korteweg stresses are taken into account, the nonlinear merge is prevented and the features of fingering patterns resemble the immiscible situations remarkably. The fingering behavior can be approximated by a master line of dL /dDg≈0.386n+0.13 within the linear fingering region.
Genetics Home Reference: Koolen-de Vries syndrome
... 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 ...
An Image for Technology: DeVry Institute
ERIC Educational Resources Information Center
Ryder, Sharon Lee
1974-01-01
A fast-tracked technical school in Chicago is another tribute to this method of construction. Related articles are EA 504 766 (American School and University; v46 n7 Mar 74) and EA 504 854 (American School and University; v46 n8 Apr '74). Illustrated. (Author/MLF)
The Birth of Miles Henry DeVries
DeVries, Jennifer
2012-01-01
In this birth story, a second-time mother relates her experience of birthing her son at home after her daughter was born via cesarean surgery. Support from the International Cesarean Awareness Network, as well as a home birth midwife specializing in vaginal birth after cesarean (VBAC), made the dream of a vaginal birth a reality for this mom. This story highlights the importance of having a supportive care provider and laboring in a safe and comfortable environment when pursuing a VBAC. PMID:23277724
A new high-order spectral problem of the mKdV and its associated integrable decomposition
NASA Astrophysics Data System (ADS)
Ji, Jie; Yao, Yu-Qin; Yu, Jing; Liu, Yu-Qing
2007-02-01
A new approach to formulizing a new high-order matrix spectral problem from a normal 2×2 matrix modified Korteweg-de Vries (mKdV) spectral problem is presented. It is found that the isospectral evolution equation hierarchy of this new higher-order matrix spectral problem turns out to be the well-known mKdV equation hierarchy. By using the binary nonlinearization method, a new integrable decomposition of the mKdV equation is obtained in the sense of Liouville. The proof of the integrability shows that r-matrix structure is very interesting.
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.
Dressed solitons in quantum electron-positron-ion plasmas
NASA Astrophysics Data System (ADS)
Chatterjee, Prasanta; Roy, Kaushik; Mondal, Ganesh; Muniandy, S. V.; Yap, S. L.; Wong, C. S.
2009-12-01
Nonlinear propagation of quantum ion acoustic waves in a dense quantum plasma whose constituents are electrons, positrons, and positive ions is investigated using a quantum hydrodynamic model. The Korteweg-de Vries equation is derived using reductive perturbation technique. The higher order inhomogeneous differential equation is obtained for the dressed soliton. The dynamical equation for dressed soliton is solved using the renormalization method. The conditions for the validity of the higher order correction are described. The effects of quantum parameter, positron concentration, electron to positron Fermi temperature ratio, and soliton velocity on the amplitude and width of the dressed soliton are studied.
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.
Monotone-short solutions of the Tolman-Oppenheimer-Volkoff-de Sitter equation
NASA Astrophysics Data System (ADS)
Hsu, Cheng-Hsiung; Makino, Tetu
2016-09-01
It is known that spherically symmetric static solutions of the Einstein equations with a positive cosmological constant for the energy-momentum tensor of a barotropic perfect fluid are governed by the Tolman-Oppenheimer-Volkoff-de Sitter equation. Some sufficient conditions for the existence of monotone-short solutions (with finite radii) of the equation are given in this article. Then we show that the interior metric can extend to the exterior Schwarzschild-de Sitter metric on the exterior vacuum region with twice continuous differentiability. In addition, we investigate the analytic property of the solutions at the vacuum boundary. Our result (Theorem 1) can be considered as the de Sitter version of the result by Rendall and Schmidt [Classical Quantum Gravity 8, 985-1000 (1991)]. Furthermore, one can see that there are different properties of the solutions with those of the Tolman-Oppenheimer-Volkoff equation (with zero cosmological constant) in certain situation.
EMHD theory and observations of electron solitary waves in magnetotail plasmas
NASA Astrophysics Data System (ADS)
Ji, Xiao-Fei; Wang, Xiao-Gang; Sun, Wei-Jie; Xiao, Chi-Jie; Shi, Quan-Qi; Liu, Jiang; Pu, Zu-Yin
2014-06-01
A new approach of electron magnetohydrodynamics (EMHD) is developed by including the anisotropy of the electron pressure tensor to take Biermann battery effect into account. Based on the model, the dispersion relation of slow and fast electron magnetosonic modes are derived. A Korteweg-de Vries equation is then obtained from the wave equation to get a solution of one-dimensional slow-mode soliton. Furthermore, according to measurements of Cluster and Time History of Events and Macroscale Interactions during Substorms, we find a good agreement between the theory and observations of magnetic field depression and perpendicular pressure increase.
Ion acoustic shocks in magneto rotating Lorentzian plasmas
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.
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.
Quantum ion-acoustic double layers in unmagnetized dense electron-positron-ion plasmas
NASA Astrophysics Data System (ADS)
Khan, S. A.; Mahmood, S.; Ali, S.
2009-04-01
The existence of small amplitude quantum ion-acoustic double layers is studied in an unmagnetized dense electron-positron-ion plasma. For this purpose, the quantum hydrodynamic model is employed to derive a deformed Korteweg-de Vries (dKdV) equation. The steady state double layer solution of dKdV equation is obtained and its dependence on various parameters is discussed. It is found that only compressive double layers can exist in such plasmas. The analytical and numerical studies reveal that the quantum ion-acoustic double layer structures strongly depend on quantum diffraction effects and positron number density.
Nonplanar Ion-Acoustic Solitons in Electron-Positron-Ion Quantum Plasmas
NASA Astrophysics Data System (ADS)
Khan A., S.; Mahmood, S.; Arshad, Mirza M.
2009-04-01
The propagation of nonplanar quantum ion-acoustic solitary waves in a dense, unmagnetized electron-positronion (e-p-i) plasma are studied by using the Korteweg-de Vries (KdV) model. The quantum hydrodynamic (QHD) equations are used taking into account the quantum diffraction and quantum statistics corrections. The analytical and numerical solutions of KdV equation reveal that the nonplanar ion-acoustic solitons are modified significantly with quantum corrections and positron concentration, and behave differently in different geometries.
Higher order solutions to ion-acoustic solitons in a weakly relativistic two-fluid plasma
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.
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.
Nonlinear wave propagation in a strongly coupled collisional dusty plasma
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.
Nonlinear wave propagation in a strongly coupled collisional dusty plasma.
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
Shock wave in magnetized dusty plasmas with dust charging and nonthermal ion effects
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.
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.
Effect of trapped electrons on soliton propagation in a plasma having a density gradient
NASA Astrophysics Data System (ADS)
Aziz, Farah; Stroth, Ulrich
2009-03-01
A Korteweg-deVries equation with an additional term due to the density gradient is obtained using reductive perturbation technique in an unmagnetized plasma having a density gradient, finite temperature ions, and two-temperature nonisothermal (trapped) electrons. This equation is solved to get the solitary wave solution using sine-cosine method. The phase velocity, soliton amplitude, and width are examined under the effect of electron and ion temperatures and their concentrations. The effect of ion (electron) temperature is found to be more significant in the presence of larger (smaller) number of trapped electrons in the plasma.
Wakes and precursor soliton excitations by a moving charged object in a plasma
NASA Astrophysics Data System (ADS)
Kumar Tiwari, Sanat; Sen, Abhijit
2016-02-01
We study the evolution of nonlinear ion acoustic wave excitations due to a moving charged source in a plasma. Our numerical investigations of the full set of cold fluid equations go beyond the usual weak nonlinearity approximation and show the existence of a rich variety of solutions including wakes, precursor solitons, and "pinned" solitons that travel with the source velocity. These solutions represent a large amplitude generalization of solutions obtained in the past for the forced Korteweg deVries equation and can find useful applications in a variety of situations in the laboratory and in space, wherever there is a large relative velocity between the plasma and a charged object.
Nonlinear dynamics; Proceedings of the International Conference, New York, NY, December 17-21, 1979
NASA Technical Reports Server (NTRS)
Helleman, R. H. G.
1980-01-01
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.
Effect of trapped electrons on soliton propagation in a plasma having a density gradient
Aziz, Farah; Stroth, Ulrich
2009-03-15
A Korteweg-deVries equation with an additional term due to the density gradient is obtained using reductive perturbation technique in an unmagnetized plasma having a density gradient, finite temperature ions, and two-temperature nonisothermal (trapped) electrons. This equation is solved to get the solitary wave solution using sine-cosine method. The phase velocity, soliton amplitude, and width are examined under the effect of electron and ion temperatures and their concentrations. The effect of ion (electron) temperature is found to be more significant in the presence of larger (smaller) number of trapped electrons in the plasma.
NASA Astrophysics Data System (ADS)
Zhao, Hai-qiong; Zhu, Zuo-nong
2011-02-01
This paper aims to find new explicit solutions including multisoliton, multipositon, multinegaton, and multiperiodic for a coupled Volterra lattice system. This coupled lattice system is an integrable discrete version of the coupled Korteweg-deVries (KdV) equation which has many physical applications. The dynamical properties of these new solutions are discussed in detail. We also prove that the theory of the coupled Volterra lattice system including the Lax pair, the Darboux transformation, and explicit solutions yield the corresponding theory of the coupled KdV equation in the continuous limit.
Ion acoustic shock waves in weakly relativistic multicomponent quantum plasma
NASA Astrophysics Data System (ADS)
Gill, T. S.; Bains, A. S.; Bedi, C.
2010-02-01
Ion acoustic Shock waves (IASWs) are studied in an collisionless unmagnetized relativistic quantum electron-positron-ion(e-p-i) plasma employing the quantum hydro -dynamic(QHD) model. Korteweg-deVries- Burger equation(KdVB) is derived using small amplitude perturbation expansion method to study the nonlinear propagation of the quantum IASWs. It is found that the coefficients of the KdVB equation are significantely modified by the positron density p, relativistic factor(Ur), temperatures σ, kinematic viscosity η and quantum factor(H).
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.
On the possibility of dark energy from corrections to the Wheeler DeWitt equation
NASA Astrophysics Data System (ADS)
Nelson, William; Sakellariadou, Mairi
2008-03-01
We present a method for approximating the effective consequence of generic quantum gravity corrections to the Wheeler DeWitt equation. We show that in many cases these corrections can produce departures from classical physics at large scales and that this behaviour can be interpreted as additional matter components. This opens up the possibility that dark energy (and possible dark matter) could be large scale manifestations of quantum gravity corrections to classical general relativity. As a specific example we examine the first order corrections to the Wheeler DeWitt equation arising from loop quantum cosmology in the absence of lattice refinement and show how the ultimate breakdown in large scale physics occurs.
Dispersive shock waves in nematic liquid crystals
NASA Astrophysics Data System (ADS)
Smyth, Noel F.
2016-10-01
The propagation of coherent light with an initial step intensity profile in a nematic liquid crystal is studied using modulation theory. The propagation of light in a nematic liquid crystal is governed by a coupled system consisting of a nonlinear Schrödinger equation for the light beam and an elliptic equation for the medium response. In general, the intensity step breaks up into a dispersive shock wave, or undular bore, and an expansion fan. In the experimental parameter regime for which the nematic response is highly nonlocal, this nematic bore is found to differ substantially from the standard defocusing nonlinear Schrödinger equation structure due to the effect of the nonlocality of the nematic medium. It is found that the undular bore is of Korteweg-de Vries equation-type, consisting of bright waves, rather than of nonlinear Schrödinger equation-type, consisting of dark waves. In addition, ahead of this Korteweg-de Vries bore there can be a uniform wavetrain with a short front which brings the solution down to the initial level ahead. It is found that this uniform wavetrain does not exist if the initial jump is below a critical value. Analytical solutions for the various parts of the nematic bore are found, with emphasis on the role of the nonlocality of the nematic medium in shaping this structure. Excellent agreement between full numerical solutions of the governing nematicon equations and these analytical solutions is found.
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.
Approximate solutions to the nonlinear Klein-Gordon equation in de Sitter spacetime
NASA Astrophysics Data System (ADS)
Yazici, Muhammet; Şengül, Süleyman
2016-09-01
We consider initial value problems for the nonlinear Klein-Gordon equation in de Sitter spacetime. We use the differential transform method for the solution of the initial value problem. In order to show the accuracy of results for the solutions, we use the variational iteration method with Adomian's polynomials for the nonlinearity. We show that the methods are effective and useful.
Head-on collision of dust-ion-acoustic soliton in quantum pair-ion plasma
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}.
Cylindrical and spherical electron acoustic solitary waves with nonextensive hot electrons
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.
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.
Charging-delay induced dust acoustic collisionless shock wave: Roles of negative ions
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)
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.
NASA Astrophysics Data System (ADS)
Ruan, Shi-Sen; Cheng, Ze
2013-07-01
In this paper, we study the head-on collision between two electron acoustic solitary waves (EASWs) in magnetized quantum electron-positron-ion plasma. Using the extended Poincaré-Lighthill-Kuo perturbation method, we obtain the Korteweg-de Vries equations, the phase shifts and the trajectories after the head-on collision of the two EASWs. It is found that the phase shifts are significantly affected by the values of the quantum parameter H, the ion to electron number density ratio δ, the electron cyclotron to electron plasma frequency ratio α and the obliqueness θ (propagation angle).
Linear and nonlinear ion-acoustic waves in very dense magnetized plasmas
Khan, S. A.; Mahmood, S.; Saleem, H.
2008-08-15
Obliquely propagating linear and weakly nonlinear ion-acoustic waves in a magnetized quantum plasma are investigated by employing the quantum hydrodynamic formulation. A linear dispersion relation is presented and the nonlinear Korteweg-de Vries equation is derived using the reductive perturbative method. The dispersion caused by the quantum diffraction effects is possible only in a very short wavelength regime. The amplitude and width of the solitons formed by the ion-acoustic waves propagating in a magnetized plasma depend upon various parameters. Possible applications of the results to dense plasmas are discussed.
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.
Interaction of fast magnetoacoustic solitons in dense plasmas
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.
NASA Astrophysics Data System (ADS)
Hussain, S.; Akhtar, N.
2016-09-01
Ion acoustic shocks in the electron-hole-ion semiconductor plasmas have been studied. The quantum recoil effects, exchange-correlation effects and degenerate pressure of electrons and holes are included. The ion species are considered classical and their dissipation is taken into account via the dynamic viscosity. The Korteweg de Vries Burgers equation is derived by using reductive perturbation approach. The excitation of shock waves in different semiconductor plasmas is pointed out. For numerical analyses, the plasma parameters of different semiconductors are considered. The impact of variation of the plasma parameters on the strength of the shock wave in the semiconductor plasmas is discussed.
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.
Soliton reflection in a magnetized inhomogeneous warm plasma: effect of ionization
NASA Astrophysics Data System (ADS)
Malik, Hitendra K.; Jyoti; Kumar, Ravinder
2014-04-01
The reflection of nonlinear solitary waves is studied in a plasma under the effect of an external magnetic field and constant ionization along with finite ion temperature. To investigate the reflection of solitary waves, relevant modified Korteweg-deVries equations for the right and left going waves are derived, and coupled at the point of reflection for obtaining the expression of reflection coefficient. The solitary waves are found to shift after their reflection. Variation of reflection coefficient and shift are studied for different plasma parameters like ion temperature, ionization rate and wave propagation angle or the obliqueness of magnetic field.
Interaction for solitary waves in coasting charged particle beams
NASA Astrophysics Data System (ADS)
Liu, Shi-Wei; Qi, Xin; Han, Jiu-Ning; Hong, Xue-Ren; Shi, Yu-Ren; Duan, Wen-shan; Yang, Lei
2014-03-01
By using the extended Poincare-Lighthill-Kuo perturbation method, the collision of solitary waves in a coasting charged particle beams is studied. The results show that the system admits a solution with two solitary waves, which move in opposite directions and can be described by two Korteweg-deVries equation in small-amplitude limit. The collision of two solitary waves is elastic, and after the interaction they preserve their original properties. Then the weak phase shift in traveling direction of collision between two solitary waves is derived explicitly.
Reflection of ion acoustic solitons in a plasma having negative ions
Chauhan, S.S.; Malik, H.K.; Dahiya, R.P.
1996-11-01
Reflection of compressive and rarefactive ion acoustic solitons propagating in an inhomogeneous plasma in the presence of negative ions is investigated. Modified Korteweg{endash}deVries equations for incident and reflected solitons are derived and solved. The amplitude of incident and reflected solitons increases with negative to positive ion density ratio. With increasing density ratio, reflection of rarefactive solitons is reinforced whereas that of compressive solitons weakened. The rarefactive solitons are found to undergo stronger reflection than the compressive ones. {copyright} {ital 1996 American Institute of Physics.}
Weakly dissipative solitons in dense relativistic-degenerate plasma
NASA Astrophysics Data System (ADS)
Ahmad, Saeed; Ata-ur-Rahman; Khan, S. A.
2015-07-01
We investigate the features of weakly nonlinear waves in a collisional dense plasma consisting of ultra-relativistic degenerate electrons and non-relativistic degenerate ions. In weak dissipation limit, the dynamics of low frequency nonlinear ion (solitary) wave is described by solving a damped Korteweg-deVries equation. The analytical and numerical analysis shows the existence of weakly dissipative solitons evolving with time. The characteristics of soliton evolution with plasma number density and slow ion-neutral collision rate are discussed with some detail. The relevance of the study with degenerate plasmas in ultra-dense astrophysical objects, particularly white dwarf stars is also pointed out.
Interaction for solitary waves in coasting charged particle beams
Liu, Shi-Wei; Hong, Xue-Ren; Shi, Yu-Ren; Duan, Wen-shan; Qi, Xin; Yang, Lei; Han, Jiu-Ning
2014-03-15
By using the extended Poincare-Lighthill-Kuo perturbation method, the collision of solitary waves in a coasting charged particle beams is studied. The results show that the system admits a solution with two solitary waves, which move in opposite directions and can be described by two Korteweg-deVries equation in small-amplitude limit. The collision of two solitary waves is elastic, and after the interaction they preserve their original properties. Then the weak phase shift in traveling direction of collision between two solitary waves is derived explicitly.
Interaction of fast magnetoacoustic solitons in dense plasmas
NASA Astrophysics Data System (ADS)
Jahangir, R.; Masood, W.; Siddiq, M.; Batool, Nazia; Saleem, Khalid
2015-09-01
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.
Weakly nonlinear ion-sound waves in inhomogeneous electron temperature, magnetized plasmas
NASA Astrophysics Data System (ADS)
Pecseli, H. L.; Guio, P.
2009-12-01
Low frequency electrostatic waves are studied in magnetized plasmas for the case where the electron temperature varies with position in a direction perpendicular to the magnetic field. We analyze guided waves with characteristic frequencies below the ion cyclotron and ion plasma frequencies. A Korteweg-deVries equation is derived for the weakly nonlinear waves, and the results compared to numerical simulations. We study two different models for the electron distribution: one where the electrons are assumed to be in local Boltzmann equilibrium at all times, while the other model assumes a nonthermal-distribution for the electrons. The nonlinear space-time evolution of the electrostatic potential differs for the two cases.
Weakly nonlinear dust ion-acoustic shock waves in a dusty plasma with nonthermal electrons
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.
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.
Quasi-periodic behavior of ion acoustic solitary waves in electron-ion quantum plasma
NASA Astrophysics Data System (ADS)
Sahu, Biswajit; Poria, Swarup; Narayan Ghosh, Uday; Roychoudhury, Rajkumar
2012-05-01
The ion acoustic solitary waves are investigated in an unmagnetized electron-ion quantum plasmas. The one dimensional quantum hydrodynamic model is used to study small as well as arbitrary amplitude ion acoustic waves in quantum plasmas. It is shown that ion temperature plays a critical role in the dynamics of quantum electron ion plasma, especially for arbitrary amplitude nonlinear waves. In the small amplitude region Korteweg-de Vries equation describes the solitonic nature of the waves. However, for arbitrary amplitude waves, in the fully nonlinear regime, the system exhibits possible existence of quasi-periodic behavior for small values of ion temperature.
Head-on collision of dust-ion-acoustic soliton in quantum pair-ion plasma
NASA Astrophysics Data System (ADS)
Chatterjee, Prasanta; Ghorui, Malay kr.; Wong, C. S.
2011-10-01
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 β and the concentration of the negatively charged dust particles δ.
Electrostatic solitary waves in a quantum plasma with relativistically degenerate electrons
NASA Astrophysics Data System (ADS)
Masood, W.; Eliasson, B.
2011-03-01
A model for nonlinear ion waves in an unmagnetized plasma with relativistically degenerate electrons and cold fluid ions is presented here. The inertia is given here by the ion mass while the restoring force is provided by the relativistic electron degeneracy pressure, and the dispersion is due to the deviation from charge neutrality. A nonlinear Korteweg-de Vries equation is derived for small but finite amplitude waves and is used to study the properties of localized ion acoustic solitons for parameters relevant for dense astrophysical objects such as white dwarf stars. Different degrees of relativistic electron degeneracy are discussed and compared.
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.
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.
Rarefaction solitons initiated by sheath instability
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.
Do the freak waves exist in soliton gas?
NASA Astrophysics Data System (ADS)
Shurgalina, Ekaterina; Pelinovsky, Efim
2016-04-01
The possibility of short-lived anomalous large waves (rogue waves) in soliton gas in the frameworks of integrable models like the Korteweg - de Vries - type equations is studied. It is shown that the dynamics of heteropolar soliton gas differs sufficiently from the dynamics of unipolar soliton fields. In particular, in the wave fields consisting of solitons with different polarities the freak wave appearance is possible. It is shown numerically in [Shurgalina and Pelinovsky, 2015]. Freak waves in the framework of the modified Korteweg-de Vries equation have been studied previously in the case of narrowband initial conditions [Grimshaw et al, 2005, 2010; Talipova, 2011]. In this case, the mechanism of freak wave generation was modulation instability of modulated quasi-sinusoidal wave packets. At the same time the modulation instability of modulated cnoidal waves was studied in the mathematical work [Driscoll & O'Neil, 1976]. Since a sequence of solitary waves can be a special case of cnoidal wave, the modulation instability can be a possible mechanism of freak wave appearance in a soliton gas. Thus, we expect that rogue wave phenomenon in soliton gas appears in nonlinear integrable models admitting an existence of modulation instability of periodic waves (like cnoidal waves). References: 1. Shurgalina E.G., Pelinovsky E.N. Dynamics of irregular wave ensembles in the coastal zone, Nizhny Novgorod State Technical University n.a. R.E. Alekseev. - Nizhny Novgorod, 2015, 179 pp. 2. Grimshaw R., Pelinovsky E., Talipova T., Sergeeva A. Rogue internal waves in the ocean: long wave model. European Physical Journal Special Topics, 2010, 185, 195 - 208. 3. Grimshaw R., Pelinovsky E., Talipova T., Ruderman M. Erdelyi R. Short-lived large-amplitude pulses in the nonlinear long-wave model described by the modified Korteweg-de Vries equation. Studied Applied Mathematics, 2005, 114 (2), 189. 4. Talipova T.G. Mechanisms of internal freak waves, Fundamental and Applied Hydrophysics
Nonlinear shear wave in a non Newtonian visco-elastic medium
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.
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.
Selection rules for the Wheeler-DeWitt equation in quantum cosmology
NASA Astrophysics Data System (ADS)
Barvinsky, A. O.; Kamenshchik, A. Yu.
2014-02-01
The incompleteness of the Dirac quantization scheme leads to a redundant set of solutions of the Wheeler-DeWitt equation for the wave function in the superspace of quantum cosmology. The selection of physically meaningful solutions that match quantum initial data can be attained by a reduction of the theory to the sector of true physical degrees of freedom and their canonical quantization. The resulting physical wave function unitarily evolving in the time variable introduced within this reduction can then be raised to the level of the cosmological wave function in the superspace of 3-metrics to form a needed subset of all solutions of the Wheeler-DeWitt equation. We apply this technique in several simple but nonlinear minisuperspace models and discuss (at both the classical and quantum level) the physical reduction in extrinsic time—the time variable determined in terms of extrinsic curvature (or momentum conjugated to the cosmological scale factor). Only this extrinsic time gauge can be consistently used in the vicinity of turning points and bounces where the scale factor reaches extremum and cannot monotonically parametrize the evolution of the system. Since the 3-metric scale factor is canonically dual to the extrinsic time variable, the transition from the physical wave function to the wave function in superspace represents a kind of generalized Fourier transform. This transformation selects square-integrable solutions of the Wheeler-DeWitt equation, which guarantees the Hermiticity of canonical operators of the Dirac quantization scheme. This makes this scheme consistent, a property that is not guaranteed with general solutions of the Wheeler-DeWitt equation. Semiclassically this means that wave functions are represented by oscillating waves in classically allowed domains of superspace and exponentially fall off in classically forbidden (underbarrier) regions. This is explicitly demonstrated in a flat Friedmann-Robertson-Walker (FRW) model with a scalar
Stability of Viscous St. Venant Roll Waves: From Onset to Infinite Froude Number Limit
NASA Astrophysics Data System (ADS)
Barker, Blake; Johnson, Mathew A.; Noble, Pascal; Rodrigues, L. Miguel; Zumbrun, Kevin
2016-09-01
We study the spectral stability of roll wave solutions of the viscous St. Venant equations modeling inclined shallow water flow, both at onset in the small Froude number or "weakly unstable" limit F→ 2^+ and for general values of the Froude number F, including the limit F→ + ∞. In the former, F→ 2^+ , limit, the shallow water equations are formally approximated by a Korteweg-de Vries/Kuramoto-Sivashinsky (KdV-KS) equation that is a singular perturbation of the standard Korteweg-de Vries (KdV) equation modeling horizontal shallow water flow. Our main analytical result is to rigorously validate this formal limit, showing that stability as F→ 2^+ is equivalent to stability of the corresponding KdV-KS waves in the KdV limit. Together with recent results obtained for KdV-KS by Johnson-Noble-Rodrigues-Zumbrun and Barker, this gives not only the first rigorous verification of stability for any single viscous St. Venant roll wave, but a complete classification of stability in the weakly unstable limit. In the remainder of the paper, we investigate numerically and analytically the evolution of the stability diagram as Froude number increases to infinity. Notably, we find transition at around F=2.3 from weakly unstable to different, large-F behavior, with stability determined by simple power-law relations. The latter stability criteria are potentially useful in hydraulic engineering applications, for which typically 2.5≤ F≤ 6.0.
Averaging and renormalization for the Korteveg–deVries–Burgers equation
Chorin, Alexandre J.
2003-01-01
We consider traveling wave solutions of the Korteveg–deVries–Burgers equation and set up an analogy between the spatial averaging of these traveling waves and real-space renormalization for Hamiltonian systems. The result is an effective equation that reproduces means of the unaveraged, highly oscillatory, solution. The averaging enhances the apparent diffusion, creating an “eddy” (or renormalized) diffusion coefficient; the relation between the eddy diffusion coefficient and the original diffusion coefficient is found numerically to be one of incomplete similarity, setting up an instance of Barenblatt's renormalization group. The results suggest a relation between self-similar solutions of differential equations on one hand and renormalization groups and optimal prediction algorithms on the other. An analogy with hydrodynamics is pointed out. PMID:12913126
Dirac equation in a de Sitter expansion for massive neutrinos from modern Kaluza-Klein theory
NASA Astrophysics Data System (ADS)
Sánchez, Pablo Alejandro; Anabitarte, Mariano; Bellini, Mauricio
2012-03-01
Using the modern Kaluza-Klein theory of gravity (or the Induced Matter theory), we study the Dirac equation for massive neutrinos on a de Sitter background metric from a 5D Riemann-flat (and hence Ricci-flat) extended de Sitter metric, on which is defined the vacuum for test massless 1/2-spin neutral fields minimally coupled to gravity and free of any other interactions. We obtain that the effective 4D masses of the neutrinos can only take three possible values, which are related to the (static) foliation of the fifth and noncompact extra dimension.
Automodelling solutions of the Higgs-field nonlinear wave equation in the de Sitter space.
NASA Astrophysics Data System (ADS)
Dyshko, A. L.; Konyukhova, N. B.; Voronov, N. A.
2000-04-01
The effect of the expansion of the Universe on such classical physical objects as spherical bubbles is studied. The authors look for automodelling solutions to scalar Higgs-field equation in the de Sitter space and compare them with the bubble type solutions in the thin-wall approximation. The automodelling bubbles could be considered as critical or singular ones because they collapse in an infinite time. Multinodal solutions as enclosed bubbles are discovered numerically.
Thermal diffusion of Boussinesq solitons.
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
The propagation of internal undular bores over variable topography
NASA Astrophysics Data System (ADS)
Grimshaw, R.; Yuan, C.
2016-10-01
In the coastal ocean, large amplitude, horizontally propagating internal wave trains are commonly observed. These are long nonlinear waves and can be modelled by equations of the Korteweg-de Vries type. Typically they occur in regions of variable bottom topography when the variable-coefficient Korteweg-de Vries equation is an appropriate model. Of special interest is the situation when the coefficient of the quadratic nonlinear term changes sign at a certain critical point. This case has been widely studied for a solitary wave, which is extinguished at the critical point and replaced by a train of solitary waves of the opposite polarity to the incident wave, riding on a pedestal of the original polarity. Here we examine the same situation for an undular bore, represented by a modulated periodic wave train. Numerical simulations and some asymptotic analysis based on Whitham modulation equations show that the leading solitary waves in the undular bore are destroyed and replaced by a developing rarefaction wave supporting emerging solitary waves of the opposite polarity. In contrast the rear of the undular bore emerges with the same shape, but with reduced wave amplitudes, a shorter overall length scale and moves more slowly.
Head-on collisions of electrostatic solitons in nonthermal plasmas.
Verheest, Frank; Hellberg, Manfred A; Hereman, Willy A
2012-09-01
In contrast to overtaking interactions, head-on collisions between two electrostatic solitons can be dealt with only by use of an approximate method, which limits the range of validity but offers valuable insights. Treatments in the plasma physics literature all use assumptions in the stretching of space and time and in the expansion of the dependent variables that are seldom, if ever, discussed. All models force a separability to lowest order, corresponding to two linear waves with opposite but equally large velocities. A systematic exposition of the underlying hypotheses is illustrated by considering a plasma composed of cold ions and nonthermal electrons. This is general enough to yield critical compositions that lead to modified rather than standard Korteweg-de Vries equations, an aspect not discussed so far. The nonlinear evolution equations for both solitons and their phase shifts due to the collision are established. A Korteweg-de Vries description is the generic conclusion, except when the plasma composition is critical, rendering the nonlinearity in the evolution equations cubic, with concomitant repercussions on the phase shifts. In the latter case, the solitons can have either polarity, so combinations of negative and positive solitons can occur, contrary to the generic case, where both solitons necessarily have the same polarity. PMID:23031029
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.
Dust acoustic solitary and shock excitations in a Thomas-Fermi magnetoplasma
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.
Nonlinear propagation of ion-acoustic waves in electron-positron-ion plasma with trapped electrons
NASA Astrophysics Data System (ADS)
Alinejad, H.; Sobhanian, S.; Mahmoodi, J.
2006-01-01
A theoretical investigation has been made for ion-acoustic waves in an unmagnetized electron-positron-ion plasma. A more realistic situation in which plasma consists of a negatively charged ion fluid, free positrons, and trapped as well as free electrons is considered. The properties of stationary structures are studied by the reductive perturbation method, which is valid for small but finite amplitude limit, and by pseudopotential approach, which is valid for large amplitude. With an appropriate modified form of the electron number density, two new equations for the ion dynamics have been found. When deviations from isothermality are finite, the modified Korteweg-deVries equation has been found, and for the case that deviations from isothermality are small, calculations lead to a generalized Korteweg-deVries equation. It is shown from both weakly and highly nonlinear analysis that the presence of the positrons may allow solitary waves to exist. It is found that the effect of the positron density changes the maximum value of the amplitude and M (Mach number) for which solitary waves can exist. The present theory is applicable to analyze arbitrary amplitude ion-acoustic waves associated with positrons which may occur in space plasma.
Nonlinear propagation of ion-acoustic waves in electron-positron-ion plasma with trapped electrons
Alinejad, H.; Sobhanian, S.; Mahmoodi, J.
2006-01-15
A theoretical investigation has been made for ion-acoustic waves in an unmagnetized electron-positron-ion plasma. A more realistic situation in which plasma consists of a negatively charged ion fluid, free positrons, and trapped as well as free electrons is considered. The properties of stationary structures are studied by the reductive perturbation method, which is valid for small but finite amplitude limit, and by pseudopotential approach, which is valid for large amplitude. With an appropriate modified form of the electron number density, two new equations for the ion dynamics have been found. When deviations from isothermality are finite, the modified Korteweg-deVries equation has been found, and for the case that deviations from isothermality are small, calculations lead to a generalized Korteweg-deVries equation. It is shown from both weakly and highly nonlinear analysis that the presence of the positrons may allow solitary waves to exist. It is found that the effect of the positron density changes the maximum value of the amplitude and M (Mach number) for which solitary waves can exist. The present theory is applicable to analyze arbitrary amplitude ion-acoustic waves associated with positrons which may occur in space plasma.
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.
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.
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.
NASA Astrophysics Data System (ADS)
Kanai, Masahiro; Isojima, Shin; Nishinari, Katsuhiro; Tokihiro, Tetsuji
2009-05-01
In this paper, we propose the ultradiscrete optimal velocity model, a cellular-automaton model for traffic flow, by applying the ultradiscrete method for the optimal velocity model. The optimal velocity model, defined by a differential equation, is one of the most important models; in particular, it successfully reproduces the instability of high-flux traffic. It is often pointed out that there is a close relation between the optimal velocity model and the modified Korteweg-de Vries (mkdV) equation, a soliton equation. Meanwhile, the ultradiscrete method enables one to reduce soliton equations to cellular automata which inherit the solitonic nature, such as an infinite number of conservation laws, and soliton solutions. We find that the theory of soliton equations is available for generic differential equations and the simulation results reveal that the model obtained reproduces both absolutely unstable and convectively unstable flows as well as the optimal velocity model.
From Classical Nonlinear Integrable Systems to Quantum Shortcuts to Adiabaticity.
Okuyama, Manaka; Takahashi, Kazutaka
2016-08-12
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 XY spin chains from the Toda equations are studied in detail. PMID:27563938
Schrödinger Wheeler DeWitt Equation in Chaplygin Gas FRW Cosmological Model
NASA Astrophysics Data System (ADS)
Pedram, P.; Jalalzadeh, S.; Gousheh, S. S.
2007-12-01
We present a Chaplygin gas Friedmann Robertson Walker quantum cosmological model. In this work the Schutz’s variational formalism is applied with positive, negative, and zero constant spatial curvature. In this approach the notion of time can be recovered. These give rise to Schrödinger Wheeler DeWitt equation for the scale factor. We use the eigenfunctions in order to construct wave packets for each case. We study the time dependent behavior of the expectation value of the scale factor, using the many-worlds interpretations of quantum mechanics.
Exact solutions of the Wheeler–DeWitt equation and the Yamabe construction
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.
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.
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.
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.
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
Solitons at the critical density of negative ions in multicomponent plasmas
Ibohanbi Singh, K.H.; Das, G.C. )
1989-12-01
The derivation of solitary waves in generalized multicomponent plasmas shows that the negative ion introduces a critical density at which the characteristics of the solitons are studied. The soliton's behavior deriving through the Korteweg-deVries (K-dV) equation at the critical density shows that the nonlinearity of the wave vanishes, due to which the mode of study is augmented through a modified K-dV equation. Employing a higher order equation involving quadratic and cubic nonlinearities, the transition of the K-dV equation to a modified K-dV equation along with the conservation of the Sagdeev potential, which is not affected by the negative ions, is studied in detail. The results are compared with experimental observations.
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.
Soliton turbulence in shallow water ocean surface waves.
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.
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.
Solitary wave dynamics in shallow water over periodic topography.
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
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.
NASA Astrophysics Data System (ADS)
Singh, Dhananjay K.; Malik, Hitendra K.
2007-11-01
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.
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.
Soliton turbulence in shallow water ocean surface waves.
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
Planar and non-planar dust ion-acoustic solitary waves in a quantum dusty electronegative plasma
NASA Astrophysics Data System (ADS)
Tasnim, S.; Islam, S.; Mamun, A. A.
2012-03-01
A theoretical investigation has been made on nonlinear propagation of planar and non-planar solitary waves in a quantum dusty electronegative plasma, whose constituents are quantum electrons, positive ions, negative ions, and arbitrarily charged stationary dust. The reductive perturbation method has been used to derive the Korteweg-de Vries and modified Korteweg-de Vries equations for studying the basic features of solitary waves, which are associated with both positive and negative ion dynamics. The effects of quantum parameter (H), positive and negative ion mass ratio (μin), as well as dust and positive ion number densities (β) on the basic features (polarity, height, and width) of planar solitary waves have been studied. It has been also found that the properties of dust ion-acoustic solitary waves in non-planar cylindrical or spherical geometry differ from those in planar one-dimensional geometry. The implications of our results in space (viz., interstellar compact objects like neutron stars) and laboratory experiments (e.g., intense laser solid density plasma experiments) have been briefly discussed.
Higher-order corrections to dust ion-acoustic soliton in a quantum dusty plasma
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.
NASA Astrophysics Data System (ADS)
Dimitrova, Zlatinka I.
2015-12-01
We investigate flow of incompressible fluid in a cylindrical tube with elastic walls. The radius of the tube may change along its length. The discussed problem is connected to the fluid-structure interaction in large human arteries and especially to nonlinear effects. The long-wave approximation is applied to solve model equations. The obtained model Korteweg-deVries equation possessing a variable coefficient is reduced to a nonlinear dynamical system of three first order differential equations. The low probability of a solitary wave arising is shown. Periodic wave solutions of the model system of equations are studied and it is shown that the waves, that are consequence of the irregular heart pulsations may be modelled by a sequence of parts of such periodic wave solutions.
Linear and nonlinear ion-acoustic waves in an unmagnetized electron-positron-ion quantum plasma
NASA Astrophysics Data System (ADS)
Ali, S.; Moslem, W. M.; Shukla, P. K.; Schlickeiser, R.
2007-08-01
The linear and nonlinear properties of the ion-acoustic waves (IAWs) are investigated by using the quantum hydrodynamic equations together with the Poisson equation in a three-component quantum electron-positron-ion plasma. For this purpose, a linear dispersion relation, a Korteweg-de Vries equation and an energy equation containing quantum corrections are derived. Computational investigations have been performed to examine the quantum mechanical effects on the linear and nonlinear waves. It is found that both the linear and nonlinear properties of the IAWs are significantly affected by the inclusion of the quantum corrections. The relevance of the present investigation to dense white dwarfs (where the electron-positron annihilation can be unimportant) is discussed.
Head on collision of multi-solitons in an electron-positron-ion plasma having superthermal electrons
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.
Dust acoustic dressed soliton with dust charge fluctuations
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.
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…
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.
Collisionless damping of dust-acoustic waves in a charge varying dusty plasma with nonextensive ions
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.
Modulational instability of co-propagating internal wavetrains under rotation.
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.
NASA Astrophysics Data System (ADS)
Akbari-Moghanjoughi, M.
2010-11-01
Recently, Li [Phys. Plasmas 17, 082307 (2010)] has studied the effects of Bohm potential on interaction of nonplanar ion-acoustic solitary waves in an unmagnetized electron-positron-ion quantum plasma. In his work the extended reductive perturbation technique has been employed to reduce the basic quantum hydrodynamics plasma equations to Korteweg-de Vries evolution equations (one for each wave) as well as other coupled differential equations describing the phase variation of the resulting solitary waves. The calculated collisional phase-shifts are then numerically evaluated in terms of plasma parameters such as the fractional positron to ion number-density p, relative electron to positron Fermi-temperature σ and the quantum diffraction parameter H. We show that in the chosen plasma model, the parameters p and σ are not independent quantum plasma parameters which has important consequences on the graphical interpretations presented in the mentioned article.
Akbari-Moghanjoughi, M.
2010-11-15
Recently, Li [Phys. Plasmas 17, 082307 (2010)] has studied the effects of Bohm potential on interaction of nonplanar ion-acoustic solitary waves in an unmagnetized electron-positron-ion quantum plasma. In his work the extended reductive perturbation technique has been employed to reduce the basic quantum hydrodynamics plasma equations to Korteweg-de Vries evolution equations (one for each wave) as well as other coupled differential equations describing the phase variation of the resulting solitary waves. The calculated collisional phase-shifts are then numerically evaluated in terms of plasma parameters such as the fractional positron to ion number-density p, relative electron to positron Fermi-temperature {sigma} and the quantum diffraction parameter H. We show that in the chosen plasma model, the parameters p and {sigma} are not independent quantum plasma parameters which has important consequences on the graphical interpretations presented in the mentioned article.
Ion acoustic kinetic Alfvén rogue waves in two temperature electrons superthermal plasmas
NASA Astrophysics Data System (ADS)
Kaur, Nimardeep; Saini, N. S.
2016-10-01
The propagation properties of ion acoustic kinetic Alfvén (IAKA) solitary and rogue waves have been investigated in two temperature electrons magnetized superthermal plasma in the presence of dust impurity. A nonlinear analysis is carried out to derive the Korteweg-de Vries (KdV) equation using the reductive perturbation method (RPM) describing the evolution of solitary waves. The effect of various plasma parameters on the characteristics of the IAKA solitary waves is studied. The dynamics of ion acoustic kinetic Alfvén rogue waves (IAKARWs) are also studied by transforming the KdV equation into nonlinear Schrödinger (NLS) equation. The characteristics of rogue wave profile under the influence of various plasma parameters (κc, μc, σ , θ) are examined numerically by using the data of Saturn's magnetosphere (Schippers et al. 2008; Sakai et al. 2013).
Solitary and freak waves in a dusty plasma with negative ions
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.
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.
Dressed ion-acoustic solitons in magnetized dusty plasmas
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)].
Traffic jams, granular flow, and soliton selection
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.
Modulational instability of co-propagating internal wavetrains under rotation.
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
Semiclassical solitons in strongly correlated systems of ultracold bosonic atoms in optical lattices
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.
Nonlinear compressional waves in a two-dimensional Yukawa lattice.
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
Fast magnetoacoustic solitary waves in dense magnetoplasmas in a cylindrical geometry
NASA Astrophysics Data System (ADS)
Masood, W.; Mahmood, A.; Rizvi, H.
2013-01-01
Nonlinear properties of the quantum magnetoacoustic wave are studied in electron-ion magnetoplasmas. In this regard, cylindrical Korteweg deVries (CKdV) equation is derived for small amplitude perturbations. The solution of the planar KdV equation is obtained using the tanh method and is subsequently used as an initial profile to solve the CKdV equation. It is found that the system under consideration admits compressive solitary structures. Finally, it is found that the amplitude as well as the width of the nonplanar magnetosonic solitary structure increases with the increase in the magnetic field whereas a decrease is observed with the increase in number density of the system. The present study may be beneficial to understand the nonlinear wave propagation in nonplanar geometries in dense plasmas.
Soliton Reflection in a Magnetized Cold Plasma having Dust Grains and Trapped Electrons
NASA Astrophysics Data System (ADS)
Malik, Hitendra K.; Singh, Omveer; Dahiya, Raj P.
2012-10-01
A solitary wave is said to be a soliton if it retains its shape after collision with another solitary wave. The solitons get reflected from a boundary or the density gradient present in the plasma. In the present work, the reflection of a soliton is studied in a magnetized cold plasma having dust grains and trapped electrons. Considering the density inhomogeneity in the plasma, we derive relevant modified Korteweg-deVries (mKdV) equations for the right and left going solitary waves and then after coupling these equations at the point of reflection we solve the coupled equation for obtaining the expression for the reflection coefficient based on which the soliton reflection is examined under the effect of magnetic field, dust grain density, and the temperature of trapped electrons. Specifically the role of trapped electrons and dust grains is uncovered for the excitation of solitary waves and their reflection.
Beyond the KdV: Post-explosion development.
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
From weak discontinuities to nondissipative shock waves
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}.
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.
NASA Astrophysics Data System (ADS)
Kraniotis, G. V.
2016-11-01
Exact solutions of the Klein–Gordon–Fock (KGF) general relativistic equation that describe the dynamics of a massive, electrically charged scalar particle in the curved spacetime geometry of an electrically charged, rotating Kerr–Newman–(anti) de Sitter black hole are investigated. In the general case of a rotating, charged, cosmological black hole the solution of the KGF equation with the method of separation of variables results in Fuchsian differential equations for the radial and angular parts which for most of the parameter space contain more than three finite singularities and thereby generalise the Heun differential equations. For particular values of the physical parameters (i.e. mass of the scalar particle) these Fuchsian equations reduce to the case of the Heun equation and the closed form analytic solutions we derive are expressed in terms of Heun functions. For other values of the parameters some of the extra singular points are false singular points. We derive the conditions on the coefficients of the generalised Fuchsian equation such that a singular point is a false point. In such a case the exact solution of the Fuchsian equation can in principle be simplified and expressed in terms of Heun functions. This is the generalisation of the case of a Heun equation with a false singular point in which the exact solution of Heun’s differential equation is expressed in terms of Gauß hypergeometric function. We also derive the exact solutions of the radial and angular equations for a charged massive scalar particle in the Kerr–Newman spacetime. The analytic solutions are expressed in terms of confluent Heun functions. Moreover, we derived the constraints on the parameters of the theory such that the solution simplifies and expressed in terms of confluent Kummer hypergeometric functions. We also investigate the radial solutions in the KN case in the regions near the event horizon and far from the black hole. Finally, we construct several
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.
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].
Dust acoustic shock wave in electronegative dusty plasma: Roles of weak magnetic field
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.
On shallow water waves in a medium with time-dependent dispersion and nonlinearity coefficients.
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.
General formulation for acoustic solitons in three-component nonthermal plasmas
Chuang, S.-H.; Hau, L.-N.
2011-06-15
A generalized formulation is developed for nonlinear acoustic solitons in three-component such as dust-ion-electron and electron-positron-ion plasmas with the charge of each species being unspecified. The heavy, cold charged particles (ions or dust particles) are treated as a fluid while the light, hot components are described by the kinetic Vlasov equation with separate velocity distributions which can be of {kappa} function or highly nonthermal (non-monotonic) distributions. The model is also applicable for two-component such as ion-electron plasmas with two different temperatures for electrons. The generalized dispersion relation for acoustic waves and the Korteweg-de Vries equations as well as the Sagdeev potential are derived for various models with different combinations of velocity distributions. The parameter regimes for the existence of acoustic solitons are analyzed and examples of nonlinear solutions are illustrated. The polarity of electric potential is found to exhibit anomaly for highly nonthermal cases.
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.
Fate of classical solitons in one-dimensional quantum systems.
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.
Electrostatic Solitary Waves in Pair-ion Plasmas with Trapped Electrons
NASA Astrophysics Data System (ADS)
Mushtaq, A.; Ikram, M.; Clark, R. E. H.
2014-09-01
Electrostatic solitons in an unmagnetized pair-ion plasma comprising adiabatic fluid positive and negative ions and non-isothermal electrons are investigated using both arbitrary and small amplitude techniques. An energy integral equation involving the Sagdeev potential is derived, and the basic properties of large amplitude solitary structures are investigated. Various features of solitons differ in different existence domains. The effects of ion adiabaticity, particle concentration, and resonant electrons on the profiles of Sagdeev potential and corresponding solitary waves are investigated. The generalized Korteweg-de Vries equation with mixed-nonlinearity is derived by expanding the Sagdeev potential. Asymptotic solutions for different orders of nonlinearity are discussed for solitary waves. The present work is applicable to understanding the wave phenomena and associated nonlinear electrostatic perturbations in pair/bi-ion plasmas which may occur in space and laboratory plasmas.
Electrostatic Solitary Waves in Pair-ion Plasmas with Trapped Electrons
NASA Astrophysics Data System (ADS)
Mushtaq, A.; Ikram, M.; Clark, R. E. H.
2014-12-01
Electrostatic solitons in an unmagnetized pair-ion plasma comprising adiabatic fluid positive and negative ions and non-isothermal electrons are investigated using both arbitrary and small amplitude techniques. An energy integral equation involving the Sagdeev potential is derived, and the basic properties of large amplitude solitary structures are investigated. Various features of solitons differ in different existence domains. The effects of ion adiabaticity, particle concentration, and resonant electrons on the profiles of Sagdeev potential and corresponding solitary waves are investigated. The generalized Korteweg-de Vries equation with mixed-nonlinearity is derived by expanding the Sagdeev potential. Asymptotic solutions for different orders of nonlinearity are discussed for solitary waves. The present work is applicable to understanding the wave phenomena and associated nonlinear electrostatic perturbations in pair/bi-ion plasmas which may occur in space and laboratory plasmas.
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.
Kink antikink density wave of an extended car-following model in a cooperative driving system
NASA Astrophysics Data System (ADS)
Yu, Lei; Shi, Zhongke; Zhou, Bingchang
2008-12-01
We propose an extended optimal velocity model applicable to cooperative driving control system by considering the headway of arbitrary number of cars that precede and the relative velocity. The stability condition of the extended model is obtained by using the linear stability theory. The modified Korteweg-de Vries (mKdV) equation is derived to describe the traffic behavior near the critical point by applying the nonlinear analysis. Thus the traffic jams can be described by the kink-antikink density wave which is the solution of the mKdV equation. The simulation results confirm the analytical results and show that the traffic jams are suppressed more efficiently with considering not only the headway of more vehicles ahead but also the relative velocity.
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.
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.
Regularized degenerate multi-solitons
NASA Astrophysics Data System (ADS)
Correa, Francisco; Fring, Andreas
2016-09-01
We report complex PT-symmetric multi-soliton solutions to the Korteweg de-Vries equation that asymptotically contain one-soliton solutions, with each of them possessing the same amount of finite real energy. We demonstrate how these solutions originate from degenerate energy solutions of the Schrödinger equation. Technically this is achieved by the application of Darboux-Crum transformations involving Jordan states with suitable regularizing shifts. Alternatively they may be constructed from a limiting process within the context Hirota's direct method or on a nonlinear superposition obtained from multiple Bäcklund transformations. The proposed procedure is completely generic and also applicable to other types of nonlinear integrable systems.
Spin solitons in magnetized pair plasmas
Brodin, G.; Marklund, M.
2007-11-15
A set of fluid equations, taking into account the spin properties of the electrons and positrons in a magnetoplasma, are derived. The magnetohydrodynamic limit of the pair plasma is investigated. It is shown that the microscopic spin properties of the electrons and positrons can lead to interesting macroscopic and collective effects in strongly magnetized plasmas. In particular, it is found that new Alfvenic solitary structures, governed by a modified Korteweg-de Vries equation, are allowed in such plasmas. These solitary structures vanish if the quantum spin effects are neglected. Our results should be of relevance for astrophysical plasmas, e.g., in pulsar magnetospheres, as well as for low-temperature laboratory plasmas.
Head-on collisions of electrostatic solitons in multi-ion plasmas
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.
Dust ion-acoustic cnoidal waves in a plasma with two temperature superthermal electrons
NASA Astrophysics Data System (ADS)
Saini, N. S.; Sethi, Papihra
2016-10-01
An investigation of dust ion-acoustic (DIA) cnoidal waves in unmagnetized collisionless plasma consisting of two temperature superthermal electrons, inertial warm ions, and negatively charged dust grains is presented. Reductive perturbation technique has been used to derive the modified Korteweg-de Vries (mKdV) equation for the study of nonlinear periodic waves. Further, applying the Sagdeev potential approach, energy balance equation is derived. Using the expression for Sagdeev potential in expanded form, the cnoidal wave solution is determined. Both positive and negative potential (compressive and rarefactive) nonlinear DIA cnoidal structures are observed. The effects of parameters like the number density of cold electrons, superthermality of hot and cold electrons, ions to hot electrons temperature ratio, and dust to ion density ratio on the characteristics of DIA cnoidal waves are analyzed.
Nonlinear ion-acoustic waves in a degenerate plasma with nuclei of heavy elements
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.
Nonlinear ion-acoustic structures in dusty plasma with superthermal electrons and positrons
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.
Regularized degenerate multi-solitons
NASA Astrophysics Data System (ADS)
Correa, Francisco; Fring, Andreas
2016-09-01
We report complex {P}{T} -symmetric multi-soliton solutions to the Korteweg de-Vries equation that asymptotically contain one-soliton solutions, with each of them possessing the same amount of finite real energy. We demonstrate how these solutions originate from degenerate energy solutions of the Schrödinger equation. Technically this is achieved by the application of Darboux-Crum transformations involving Jordan states with suitable regularizing shifts. Alternatively they may be constructed from a limiting process within the context Hirota's direct method or on a nonlinear superposition obtained from multiple Bäcklund transformations. The proposed procedure is completely generic and also applicable to other types of nonlinear integrable systems.
Observation of dispersive shock waves developing from initial depressions in shallow water
NASA Astrophysics Data System (ADS)
Trillo, S.; Klein, M.; Clauss, G. F.; Onorato, M.
2016-10-01
We investigate surface gravity waves in a shallow water tank, in the limit of long wavelengths. We report the observation of non-stationary dispersive shock waves rapidly expanding over a 90 m flume. They are excited by means of a wave maker that allows us to launch a controlled smooth (single well) depression with respect to the unperturbed surface of the still water, a case that contains no solitons. The dynamics of the shock waves are observed at different levels of nonlinearity equivalent to a different relative smallness of the dispersive effect. The observed undulatory behavior is found to be in good agreement with the dynamics described in terms of a Korteweg-de Vries equation with evolution in space, though in the most nonlinear cases the description turns out to be improved over the quasi linear trailing edge of the shock by modeling the evolution in terms of the integro-differential (nonlocal) Whitham equation.
Nonlinear features of ion acoustic shock waves in dissipative magnetized dusty plasma
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.
Dust acoustic solitary wave with variable dust charge: Role of negative ions
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.
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.
Ion-acoustic compressive and rarefactive solitons in an electron-beam plasma system
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.
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.
Soliton and kink jams in traffic flow with open boundaries.
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
Nonlinear waves in nonplanar and nonuniform dusty plasmas
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.
On shallow water waves in a medium with time-dependent dispersion and nonlinearity coefficients.
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
Dispersive shock wave interactions and asymptotics.
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
Solitary waves in particle beams
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.
Evolution of nonlinear dust-ion-acoustic waves in an inhomogeneous plasma
NASA Astrophysics Data System (ADS)
Xiao, De-long; Ma, J. X.; Li, Yang-fang; Xia, Yinhua; Yu, M. Y.
2006-05-01
The propagation of nonlinear dust-ion-acoustic waves in an inhomogeneous dusty plasma is studied. At small but finite amplitudes, the wave evolution is governed by a modified Korteweg-deVries Burgers equation, whose coefficients are space dependent. The properties of the evolution equation are analyzed and the behavior of the corresponding shock and soliton solutions is numerically studied. If dust-charge perturbation is neglected, there exists a zero-nonlinearity point where the coefficient of the nonlinear term changes from negative to positive. At that point the nonlinear wave also undergoes structural deformation. If the dust-charge perturbation is taken into account, the zero-nonlinearity point may not appear and the soliton or shock wave will retain its form during the propagation.
Evolution of nonlinear dust-ion-acoustic waves in an inhomogeneous plasma
Xiao Delong; Ma, J.X.; Li Yangfang; Xia Yinhua; Yu, M.Y.
2006-05-15
The propagation of nonlinear dust-ion-acoustic waves in an inhomogeneous dusty plasma is studied. At small but finite amplitudes, the wave evolution is governed by a modified Korteweg-deVries Burgers equation, whose coefficients are space dependent. The properties of the evolution equation are analyzed and the behavior of the corresponding shock and soliton solutions is numerically studied. If dust-charge perturbation is neglected, there exists a zero-nonlinearity point where the coefficient of the nonlinear term changes from negative to positive. At that point the nonlinear wave also undergoes structural deformation. If the dust-charge perturbation is taken into account, the zero-nonlinearity point may not appear and the soliton or shock wave will retain its form during the propagation.
Ion acoustic solitons in a relativistic warm plasma with density gradient
Malik, H.K.
1995-10-01
Modified Korteweg-deVries equation (mK-dV), which governs the behavior of ion acoustic solitons in a relativistic warm plasma with density gradient, is derived. The electron inertia is also taken into account which is important when the streaming ions are present in the plasma. A solution of the mK-dV equation is obtained for the constant density gradient. When the ion acoustic soliton propagates into the lower plasma density region, its amplitude and energy increase, but the width decreases; the same is the case for the stronger density gradients. Plasmas with high-energy streaming ions are found, for example, in the plasma sheet boundary layer of the earth`s magnetosphere and in the Van Allen radiation belts.
A nonlinear approach for two-dimensional bubbly flows around a thin body
Al Assa`ad, A.
1994-12-31
This paper deals with the study of the flow of a liquid containing small gas bubbles around a thin body. For the sake of simplicity, attention is focused on plane-parallel flow, with the aim of assessing the dynamic effects of the bubble growth. Limiting themselves to the case of supersonic flows, the original system of field equations obtained in their previous work is treated by the reductive pertubation method. Its shown that when the flow around the body takes place at zero angle of incidence, the flow is determined by the solutions of a Korteweg-deVries equation. The boundary value problem in velocity potential is presented. To determine the general qualitative nature of the flow behind the body, self-similar solutions are considered and similarity conditions are specified. It is seen that soliton-like solutions can be found under some conditions, and their typical features are outlined.
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.
NASA Astrophysics Data System (ADS)
Masood, W.; Rizvi, H.
2011-04-01
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.
Multiple optimal current difference effect in the lattice traffic flow model
NASA Astrophysics Data System (ADS)
Sun, D. H.; Zhang, M.; Chuan, T.
2014-05-01
Kerner and Konhäuser study moving jam dynamics first discovered in 1993 in Ref. 1. In light of their previous work, a new lattice hydrodynamic model is presented with consideration of the effect of multiple optimal current difference. To investigate the influences of new consideration on traffic jams, the linear stability analysis of the new model is conducted by employing the linear stability theory. Theoretical analysis result shows that the new consideration can stabilize traffic flow. By means of nonlinear analysis method, a modified Korteweg-deVries (mKdV) equation near the critical point is constructed and solved. The propagation behavior of traffic jam can thus be described by the kink-antikink soliton solution for the mKdV equation. Numerical simulation result shows that the effect of the multiple optimal current differences can suppress the emergence of traffic jams and the result is in good agreement with the analytical results.
Super integrable four-dimensional autonomous mappings
NASA Astrophysics Data System (ADS)
Capel, H. W.; Sahadevan, R.; Rajakumar, S.
2007-05-01
A systematic investigation of the complete integrability of a fourth-order autonomous difference equation of the type w(n + 4) = w(n)F(w(n + 1), w(n + 2), w(n + 3)) is presented. We identify seven distinct families of four-dimensional mappings which are super integrable and have three (independent) integrals via a duality relation as introduced in a recent paper by Quispel, Capel and Roberts (2005 J. Phys. A: Math. Gen. 38 3965-80). It is observed that these seven families can be related to the four-dimensional symplectic mappings with two integrals including all the four-dimensional periodic reductions of the integrable double-discrete modified Korteweg-deVries and sine-Gordon equations treated in an earlier paper by two of us (Capel and Sahadevan 2001 Physica A 289 86-106).
New experimental capabilities and theoretical insights of high pressure compression waves
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.
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.
NASA Astrophysics Data System (ADS)
Singh, S. V.; Devanandhan, S.; Lakhina, G. S.; Bharuthram, R.
2016-08-01
A theoretical investigation is carried out to study the obliquely propagating electron acoustic solitary waves having nonthermal hot electrons, cold and beam electrons, and ions in a magnetized plasma. We have employed reductive perturbation theory to derive the Korteweg-de-Vries-Zakharov-Kuznetsov (KdV-ZK) equation describing the nonlinear evolution of these waves. The two-dimensional plane wave solution of KdV-ZK equation is analyzed to study the effects of nonthermal and beam electrons on the characteristics of the solitons. Theoretical results predict negative potential solitary structures. We emphasize that the inclusion of finite temperature effects reduces the soliton amplitudes and the width of the solitons increases by an increase in the obliquity of the wave propagation. The numerical analysis is presented for the parameters corresponding to the observations of "burst a" event by Viking satellite on the auroral field lines.
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…
Sign inversion of the spontaneous polarization in a "de Vries"-type ferroelectric liquid crystal.
Nonnenmacher, Dorothee; Lemieux, Robert P; Osipov, Mikhail A; Giesselmann, Frank
2014-05-19
In contrast to common ferroelectric smectic C* liquid crystals, the siloxane-terminated smectic mesogen E6 is characterized by an unusual temperature variation of the spontaneous polarization. The polarization starts to grow from nearly zero despite the first-order SmA*-SmC* transition, and increases faster than linearly over a large temperature interval while the tilt angle rapidly saturates. To study this behavior in more detail, binary mixtures of different concentrations of E6 in the achiral SmC material C8Cl, which has a similar chemical structure, were investigated. Surprisingly, all mixtures show a temperature dependent polarization sign inversion, which shifts towards the SmC*-SmA* transition with increasing E6 concentration. For the pure E6 the inversion temperature meets the SmA*-SmC* phase transition temperature. In a second binary mixture with E6 and a conventional material C9-2PhP we found out, that the dependence of the inversion temperature on the concentration of E6 changes qualitatively when the nanosegregation is partially destroyed. A molecular theory of the polarization sign inversion in smectics C* with strong polar intermolecular interactions is developed which enables one to explain the concentration dependence of the inversion temperature in both mixtures.
[The first isolation of Cladosporium cladosporioides (Fres.) de Vries from dental granulomas].
Pepe, R R; Bertolotto, C
1991-12-01
Thirteen Cladosporium have been isolated from 221 dental granulomas. Cases have been observed of cerebral lesions both in man and cats. Also various types of lesions, encapsulated abscesses, etc. to be classified under the group of pheoifomycoses. Cutaneous allergies and cases of keratitis and chromoblastomycosis have been observed, too Cladosporium cladosporioides is very resistant to mercuric and phenolic compounds and radiations. The systematic position and morphology of Cladosporium have been fully examined in accordance to the latest scientific views.
[Destruction of radioactive particles by strains of Cladosporium cladosporoides (FRES.) de Vries].
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.
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…
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.
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
Mass transport theory for the Toda lattices, dispersive and dissipative
NASA Astrophysics Data System (ADS)
Horii, Zene
2005-05-01
To establish mass transport theory on nonlinear lattices, we formulate the Korteweg-deVries (KdV) equation and the Burgers equation using the flow variable representation so as to facilitate comparison with the Boltzmann equation and with the Cahn-Hilliard equation in classical statistical mechanics. We also study Toda lattice microdynamics using the Flaschka representation, and compare with the Liouville equation. Like the linear diffusion equation, the Boltzmann equation and the Liouville equation are to be solved for a distribution function, which is intrinsically probabilistic. Transport theory in linear systems is governed by the isotropic motions of the kinetic equations. In contrast, the KdV perturbation equation derived from the Toda lattice microdynamics expresses hydrodynamic mass transport. The KdV equation in hydrodynamics and the Burgers equation in thermodynamics do not involve a probability distribution function. The nonlinear lattices do not retain isotropy of the mass transport equations. In consequence, it is proposed that in the presence of hydrodynamic flows to the left, KdV wave propagation proceeds to the right. This basic property of the KdV system is extended to thermodynamics in the Burgers system. These features arise because linear systems are driven towards an equilibrium by molecular collisions, whereas the inhomogeneities of the nonlinear lattices are generated by the potential energy of interaction. Diffusion as expressed by the Burgers equation is governed not only by a chemical potential, but also by the Toda lattice potential energy.
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.
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.
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.
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.
Magnetosonic waves interactions in a spin-1/2 degenerate quantum plasma
Li, Sheng-Chang; Han, Jiu-Ning
2014-03-15
We investigate the magnetosonic waves and their interactions in a spin-1/2 degenerate quantum plasma. With the help of the extended Poincaré-Lighthill-Kuo perturbation method, we derive two Korteweg-de Vries-Burgers equations to describe the magnetosonic waves. The parameter region where exists magnetosonic waves and the phase diagram of the compressive and rarefactive solitary waves with different plasma parameters are shown. We further explore the effects of quantum diffraction, quantum statistics, and electron spin magnetization on the head-on collisions of magnetosonic solitary waves. We obtain the collision-induced phase shifts (trajectory changes) analytically. Both for the compressive and rarefactive solitary waves, it is found that the collisions only lead to negative phase shifts. Our present study should be useful to understand the collective phenomena related to the magnetosonic wave collisions in degenerate plasmas like those in the outer shell of massive white dwarfs as well as to the potential applications of plasmas.
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.
Plasma Approach to Describing the Electric Dynamics of a Neuron
Berezin, A. A.
2002-07-15
The electric excitation of a neuron is interpreted as the formation of a nonlinear solitary ion acoustic wave of the charge density of sodium and hydrogen ions in an electrolytic intracellular fluid, which is treated as a dense plasma. It is shown that such a wave can be described by the coupled sine-Gordon and Korteweg-de Vries equations, having a solution in the form of a soliton whose internal vibrational structure is described by the Fermi-Pasta-Ulam spectrum. It is concluded that a nerve impulse can be interpreted as a low-frequency solitary wave of the charge density of sodium ions with a trapped high-frequency charge density wave of protons.
Interactions of nonlinear electron-acoustic solitary waves with vortex electron distribution
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.
Ion-acoustic cnoidal waves in a quantum plasma
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.
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.
Electron inertia effect on small amplitude solitons in a weakly relativistic two-fluid plasma
Singh, Khushvant; Kumar, Vinod; Malik, Hitendra K.
2005-05-15
One-dimensional evolution of solitons in a two-fluid plasma having weakly relativistic streaming ions and electrons is studied through usual Korteweg-de Vries equation under the effect of electron inertia. Although fast and slow ion acoustic modes are possible in such a plasma, only the fast mode corresponds to the soliton propagation for a particular range of velocity difference of ions and electrons. This range depends upon the ratios of mass and temperature of the ions and electrons. The effect of electron inertia on the propagation characteristics of the soliton is studied for typical values of the speed and temperature of the ions and electrons and it is found that this effect is dominant over the relativistic effect and the effect of ion temperature.
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.
Nonlinear dust-acoustic solitary waves in strongly coupled dusty plasmas.
Cousens, S E; Sultana, S; Kourakis, I; Yaroshenko, V V; Verheest, F; Hellberg, M A
2012-12-01
Dust-acoustic waves are investigated in a three-component plasma consisting of strongly coupled dust particles and Maxwellian electrons and ions. A fluid model approach is used, with the effects of strong coupling being accounted for by an effective electrostatic "pressure" which is a function of the dust number density and the electrostatic potential. Both linear and weakly nonlinear cases are considered by derivation and analysis of the linear dispersion relation and the Korteweg-de Vries equation, respectively. In contrast to previous studies using this model, this paper presents the results arising from an expansion of the dynamical form of the electrostatic pressure, accounting for the variations in its value in the vicinity of the wave. PMID:23368056
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.
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.
Observation of dust acoustic multi-solitons in a strongly coupled dusty plasma
NASA Astrophysics Data System (ADS)
Boruah, A.; Sharma, S. K.; Nakamura, Y.; Bailung, H.
2016-09-01
The excitation and propagation of low frequency dust acoustic multi-solitons are investigated in an unmagnetized strongly coupled dusty plasma. A floating 2D dusty medium is produced in an RF discharge Ar plasma with silica micro-particles. Dust acoustic perturbations are excited by applying a negative sinusoidal pulse of frequency 1-2 Hz and amplitude 4-20 V to an exciter grid. An initial large amplitude dust density compression breaks into a number of solitary pulses which are identified as dust acoustic solitons. The observed multi-soliton evolution is compared with numerical simulations of modified Korteweg de Vries (KdV)-Burger equation. The characteristics of the generated solitons are in good agreement with the theory.
Dissipative kinetic Alfvén solitary waves resulting from viscosity
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.
Small amplitude Kinetic Alfven waves in a superthermal electron-positron-ion plasma
NASA Astrophysics Data System (ADS)
Adnan, Muhammad; Mahmood, Sahahzad; Qamar, Anisa; Tribeche, Mouloud
2016-11-01
We are investigating the propagating properties of coupled Kinetic Alfven-acoustic waves in a low beta plasma having superthermal electrons and positrons. Using the standard reductive perturbation method, a nonlinear Korteweg-de Vries (KdV) type equation is derived which describes the evolution of Kinetic Alfven waves. It is found that nonlinearity and Larmor radius effects can compromise and give rise to solitary structures. The parametric role of superthermality and positron content on the characteristics of solitary wave structures is also investigated. It is found that only sub-Alfvenic and compressive solitons are supported in the present model. The present study may find applications in a low β electron-positron-ion plasma having superthermal electrons and positrons.
Heavy-Ion-Acoustic Solitary and Shock Waves in an Adiabatic Multi-Ion Plasma
NASA Astrophysics Data System (ADS)
Hossen, M. A.; Rahman, M. M.; Hossen, M. R.; Mamun, A. A.
2015-08-01
The standard reductive perturbation method has been employed to derive the Korteweg-deVries (K-dV) and Burgers (BG) equations to investigate the basic properties of heavy-ion-acoustic (HIA) waves in a plasma system which is supposed to be composed of nonthermal electrons, Boltzmann distributed light ions, and adiabatic positively charged inertial heavy ions. The HIA solitary and shock structures are found to exist with either positive or negative potential. It is found that the effects of adiabaticity of inertial heavy ions, nonthermality of electrons, and number densities of plasma components significantly modify the basic properties of the HIA solitary and shock waves. The implications of our results may be helpful in understanding the electrostatic perturbations in various laboratory and astrophysical plasma environments.
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.
Magnetoacoustic shock waves in dissipative degenerate plasmas
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.
Nonlinear electrostatic drift waves in dense electron-positron-ion plasmas
NASA Astrophysics Data System (ADS)
Haque, Q.; Mahmood, S.; Mushtaq, A.
2008-08-01
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.
Nonlinear electrostatic drift waves in dense electron-positron-ion plasmas
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.
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.
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).
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.
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.
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.
On the problem of periodicity and hidden solitons for the KdV model.
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
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
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.
Acoustic solitons in inhomogeneous pair-ion plasmas
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.
Linear and nonlinear dust ion acoustic waves using the two-fluid quantum hydrodynamic model
NASA Astrophysics Data System (ADS)
Masood, W.; Mushtaq, A.; Khan, R.
2007-12-01
The linear and nonlinear properties of a dust ion acoustic wave (DIAW) propagating in an electron-dust-ion plasma are investigated from both analytical and numerical perspectives by employing the two-fluid quantum hydrodynamic model. Ions and dust are assumed to be mobile while electrons are considered to be inertialess. Furthermore, quantum effects (diffraction as well as statistic) due to ions and electrons are incorporated. It is emphasized that the linear dispersion characteristics of the DIAW depend on the quantum diffraction effects of both ions and electrons as well as on the dust concentration. The one-dimensional Korteweg-deVries equation is derived for the quantum DIAW using the reductive perturbative technique. It is observed that the quantum electron diffraction term shrinks the width while the dust concentration enhances both the amplitude and width of the soliton.
Ion acoustic solitary waves in magneto-rotating plasmas
NASA Astrophysics Data System (ADS)
Mushtaq, A.
2010-08-01
Propagation of an ion acoustic wave (IAW) in a magnetized electron-ion plasma, which is rotating around an axis at an angle θ with the direction of magnetic field, is studied by incorporating the effects of trapped and untrapped electron distributions. Employing the perturbation scheme, Korteweg-deVries and Schamel's modified KdV equations are derived for the small angle θ which may support the nonlinear IAW on a slow time scale of ion motion. The amplitude and width of the solitary wave in both cases (trapped and untrapped electrons) have been discussed with the effects of oblique rotation and external magnetic field. It is shown that the nonlinear effects considerably influence the propagation of waves in rotating plasmas.
Linear and nonlinear dust ion acoustic waves using the two-fluid quantum hydrodynamic model
Masood, W.; Mushtaq, A.; Khan, R.
2007-12-15
The linear and nonlinear properties of a dust ion acoustic wave (DIAW) propagating in an electron-dust-ion plasma are investigated from both analytical and numerical perspectives by employing the two-fluid quantum hydrodynamic model. Ions and dust are assumed to be mobile while electrons are considered to be inertialess. Furthermore, quantum effects (diffraction as well as statistic) due to ions and electrons are incorporated. It is emphasized that the linear dispersion characteristics of the DIAW depend on the quantum diffraction effects of both ions and electrons as well as on the dust concentration. The one-dimensional Korteweg-deVries equation is derived for the quantum DIAW using the reductive perturbative technique. It is observed that the quantum electron diffraction term shrinks the width while the dust concentration enhances both the amplitude and width of the soliton.
NASA Astrophysics Data System (ADS)
Hu, Tao; Ma, Li
2010-09-01
An internal wave observation experiment was performed near the south of Hai-Nan Island in the South China Sea in July 2004. Three vertical thermistor arrays were moored to estimate internal wave propagation direction and velocity. A nonlinear internal wave packet was observed in this experiment. It appeared at flood tide time of wee hours. Computation indicated that the nonlinear internal wave packet's velocity was 0.54 m/s and its propagation direction was northwest. From its propagation direction, we estimated that the nonlinear internal wave packet was generated near Xi-Sha Islands. The dnoidal model of KdV(Korteweg-deVries) equation was used to simulate the waveform of thid nonlinear internal wave. Measured data shows the crest interval of nonlinear internal waves was shorter when they propagated. In the last section of this paper we simulate a nonlinear internal wave packet's effect on sound propagation and analyzed mode coupling led by the nonlinear internal wave packet.
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.
NASA Astrophysics Data System (ADS)
Rahman, Ata-Ur; Ali, S.; Mushtaq, A.; Qamar, A.; Qamar
2013-10-01
The dynamics and propagation of ion acoustic (IA) waves are considered in an unmagnetized collisionless plasma, whose constituents are the relativistically degenerate electrons and positrons as well as the inertial cold ions. At a first step, a linear dispersion relation for IA waves is derived and analysed numerically. For nonlinear analysis, the reductive perturbation technique is used to derive a Korteweg-deVries equation, which admits a localized wave solution in the presence of relativistic degenerate electrons and positrons. It is shown that only compressive IA solitary waves can propagate, whose amplitude, width and phase velocity are significantly modified due to the positron concentration. The latter also strongly influences all the relativistic plasma parameters. Our present analysis is aimed to understand collective interactions in dense astrophysical objects, e.g. white dwarfs, where the lighter species electrons and positrons are taken as relativistically degenerate.
Experimental observation of precursor solitons in a flowing complex plasma.
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
Typhoon-induced, highly nonlinear internal solitary waves off the east coast of Korea
NASA Astrophysics Data System (ADS)
Nam, SungHyun; Kim, Duk-jin; Rok Kim, Hyoung; Kim, Young-Gyu
2007-01-01
Highly nonlinear internal solitary waves (ISWs) propagating both onshore and offshore were detected in a SAR image taken approximately 19 hours after typhoon MAEMI's passage across the east coast of Korea. Analysis of ocean buoy data suggests that the ISWs were generated by near-inertial waves in response to typhoon wind. The near-inertial waves can propagate seaward due to a downwelling coastal jet (positive relative vorticity offshore of the jet), and interact with sharply varying topography, producing the ISWs. The area of sharply varying topography approximately 28 km off the coast is suggested as a source region for the ISWs. Simple calculations of wave speed based on the two-layered Korteweg-deVries (KdV) equation with upper layer thickness and densities at both layers fixed indicate that the ISWs were generated 6 hours prior to the time of the acquisition of the SAR image (approximately 13 hours after the typhoon passage), consistent with simultaneous buoy measurements.
NASA Astrophysics Data System (ADS)
Benzekka, Moufida; Tribeche, Mouloud
2016-07-01
The aim of the present communication is to investigate the charge variation induced nonlinear dust acoustic wave damping in a charge varying electronegative dusty plasma with nonthermal ions. 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 equation (dK-dV). The latter is significantly modified by the nonthermal negative ions effects. It may be useful to note that we consider nonthermal negative ions because of the role of their distribution into the formation and dynamics of nonlinear dust acoustic structures. Moreover, the observation of nonthermal ion distributions made by Phobos and Nozomi motivated us to consider non- Maxwellian ions.
Quantum electron-acoustic double layers in a magnetoplasma
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.
Small and arbitrary shock structures in spin 1/2 magnetohydrodynamic quantum plasma
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.
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…
Existence of Global Weak Solution for Compressible Fluid Models of Korteweg Type
NASA Astrophysics Data System (ADS)
Haspot, Boris
2011-06-01
This work is devoted to proving existence of global weak solutions for a general isothermal model of capillary fluids derived by Dunn and Serrin (Arch Rational Mech Anal 88(2):95-133, 1985) which can be used as a phase transition model. We improve the results of Danchin and Desjardins (Annales de l'IHP, Analyse non linéaire 18:97-133, 2001) by showing the existence of global weak solution in dimension two for initial data in the energy space, close to a stable equilibrium and with specific choices on the capillary coefficients. In particular we are interested in capillary coefficients approximating a constant capillarity coefficient κ. To finish we show the existence of global weak solution in dimension one for a specific type of capillary coefficients with large initial data in the energy space.
Some New Aspects of Degenerate Quantum Plasma
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.
Causal theories of evolution and wave propagation in mathematical physics
Kranys, M. )
1989-11-01
There are still many phenomena, especially in continuum physics, that are described by means of parabolic partial differential equations whose solution are not compatible with the causality principle. Compatibility with this principle is required also by the theory of relativity. A general form of hyperbolic operators for the most frequently occurring linear governing equations in mathematical physics is written down. It is then easy to convert any given parabolic equation to the hyperbolic form without necessarily entering into the cause of the inadequacy of the governing equation. The method is verified on the well-known example of Timoshenko's correction of the Bernoulli-Euler-Rayleigh beam equation for flexural motion. The Love-Rayleigh fourth-order differential equations for the longitudinal and torsional wave propagation in the rod is generalized with this method. The hyperbolic version (not to mention others) of the linear Korteweg-deVries equation and of the telegraph equation governing electromagnetic wave propagation through relaxing material are given. Lagrangians of all the equations studied are listed. For all the reasons given the author believes the hyperbolic governing equations to be physically and mathematically more realistic and adequate.
From Euler's elastica to the mKdV hierarchy, through the Faber polynomials
NASA Astrophysics Data System (ADS)
Matsutani, Shigeki; Previato, Emma
2016-08-01
The modified Korteweg-de Vries hierarchy (mKdV) is derived by imposing isometry and isoenergy conditions on a moduli space of plane loops. The conditions are compared to the constraints that define Euler's elastica. Moreover, the conditions are shown to be constraints on the curvature and other invariants of the loops which appear as coefficients of the generating function for the Faber polynomials.
NASA Astrophysics Data System (ADS)
Guha, Partha
Following the work of Ovsienko and Roger ([54]), we study loop Virasoro algebra. Using this algebra, we formulate the Euler-Poincaré flows on the coadjoint orbit of loop Virasoro algebra. We show that the Calogero-Bogoyavlenskii-Schiff equation and various other (2 + 1)-dimensional Korteweg-deVries (KdV) type systems follow from this construction. Using the right invariant H1 inner product on the Lie algebra of loop Bott-Virasoro group, we formulate the Euler-Poincaré framework of the (2 + 1)-dimensional of the Camassa-Holm equation. This equation appears to be the Camassa-Holm analogue of the Calogero-Bogoyavlenskii-Schiff type (2 + 1)-dimensional KdV equation. We also derive the (2 + 1)-dimensional generalization of the Hunter-Saxton equation. Finally, we give an Euler-Poincaré formulation of one-parameter family of (1 + 1)-dimensional partial differential equations, known as the b-field equations. Later, we extend our construction to algebra of loop tensor densities to study the Euler-Poincaré framework of the (2 + 1)-dimensional extension of b-field equations.
NASA Astrophysics Data System (ADS)
Nadjafikhah, Mehdi; Ahangari, Fatemeh
2012-06-01
This paper is devoted to the comprehensive analysis of the problem of symmetries and conservation laws for the geodesic equations of the Reissner-Nordström de Sitter (RNdS) black hole with a global monopole. For this purpose, the system of geodesic equations is determined and the corresponding classical Lie point symmetry operators are obtained. An optimal system of one dimensional subalgebras is constructed and a brief discussion about the algebraic structure of the Lie algebra of symmetries is presented. Also, the Noether symmetries of the geodesic Lagrangian is calculated. Finally, by applying two methods including Noether's theorem and direct method the conservation laws associated to the system of geodesic equations are obtained.
Solitons and kinks in a general car-following model.
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
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.
NASA Astrophysics Data System (ADS)
Demiray, Hilmi
2014-12-01
The basic equations describing the nonlinear electron-acoustic waves in a plasma composed of a cold electron fluid, hot electrons obeying a trapped/vortex-like distribution, and stationary ions, in the long-wave limit, are re-examined through the use of the modified PLK method. Introducing the concept of strained coordinates and expanding the field variables into a power series of the smallness parameter ɛ, a set of evolution equations is obtained for various order terms in the perturbation expansion. The evolution equation for the lowest order term in the perturbation expansion is characterized by the conventional modified Korteweg-deVries (mKdV) equation, whereas the evolution equations for the higher order terms in the expansion are described by the degenerate(linearized) mKdV equation. By studying the localized traveling wave solution to the evolution equations, the strained coordinate for this order is determined so as to remove possible secularities that might occur in the solution. It is observed that the coefficient of the strained coordinate for this order corresponds to the correction term in the wave speed. The numerical results reveal that the contribution of second order term to the wave amplitude is about 20 %, which cannot be ignored.
Structural changes of small amplitude kinetic Alfvén solitary waves due to second-order corrections
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.
NASA Astrophysics Data System (ADS)
Horsley, S. A. R.
2016-08-01
There is a well explored relationship between quantum mechanical scattering from a potential and the Korteweg-de Vries (KdV) equation of fluid dynamics: if the potential is ‘evolved’ according to the KdV equation then it will have the same reflectivity and transmissivity as a function of energy, for each snapshot in time. In this work we explore this connection in optics, where the permittivity plays the role of the potential. We begin by deriving the relationship between the Helmholtz equation and the KdV equation in terms of the current induced in a material when a permittivity profile is changed slightly. It is then shown that the KdV equation can be used to design a plethora of bounded complex potentials that are relfectionless from both sides for all angles of incidence, and planar periodic media that exhibit a real Bloch vector for all angles of propagation. Finally we apply the KdV equation to reduce the reflection of a wave from an interface between two media of differing refractive indices.
Young, C.W.
1997-10-01
In 1967, Sandia National Laboratories published empirical equations to predict penetration into natural earth materials and concrete. Since that time there have been several small changes to the basic equations, and several more additions to the overall technique for predicting penetration into soil, rock, concrete, ice, and frozen soil. The most recent update to the equations was published in 1988, and since that time there have been changes in the equations to better match the expanding data base, especially in concrete penetration. This is a standalone report documenting the latest version of the Young/Sandia penetration equations and related analytical techniques to predict penetration into natural earth materials and concrete. 11 refs., 6 tabs.
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.
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.
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
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.
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).
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.
Complex solitons with real energies
NASA Astrophysics Data System (ADS)
Cen, Julia; Fring, Andreas
2016-09-01
Using Hirota’s direct method and Bäcklund transformations we construct explicit complex one and two-soliton solutions to the complex Korteweg-de Vries (KdV) equation, the complex modified KdV (mKdV) equation and the complex sine-Gordon equation. The one-soliton solutions of trigonometric and elliptic type turn out to be { P }{ T }-symmetric when a constant of integration is chosen to be purely imaginary with one special choice corresponding to solutions recently found by Khare and Saxena. We show that alternatively complex { P }{ T }-symmetric solutions to the KdV equation may also be constructed alternatively from real solutions to the mKdV by means of Miura transformations. The multi-soliton solutions obtained from Hirota’s method break the { P }{ T }-symmetric, whereas those obtained from Bäcklund transformations are { P }{ T }-invariant under certain conditions. Despite the fact that some of the Hamiltonian densities are non-Hermitian, the total energy is found to be positive in all cases, that is irrespective of whether they are { P }{ T }-symmetric or not. The reason is that the symmetry can be restored by suitable shifts in space-time and the fact that any of our N-soliton solutions may be decomposed into N separate { P }{ T }-symmetrizable one-soliton solutions.
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.
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.
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.
Kinetic Alfvén solitary and rogue waves in superthermal plasmas
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.
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.
Dust-acoustic solitary and rogue waves in a Thomas-Fermi degenerate dusty plasma
NASA Astrophysics Data System (ADS)
Irfan, M.; Ali, S.; Mirza, Arshad M.
2014-10-01
The formation and propagation of dust-acoustic (DA) solitary and rogue waves are studied in a non-relativistic degenerate Thomas-Fermi thermal dusty plasma incorporating transverse velocity perturbation effects. The electrons and ions are described by the Thomas-Fermi density distributions, whereas the dust grains are taken as dynamic and classical. By using the reductive perturbation technique, the cylindrical Kadomtsev-Petviashvili (CKP) equation is derived, which is then transformed into a Korteweg-deVries (KdV) equation by using appropriate variable transformations. The latter admits a solitary wave solution. However, when the carrier waves frequency is much smaller than the dust plasma frequency, the DA waves evolve into the nonlinear modulation instability, generating modulated wave packets in the form of Rogue waves. For the study of DA-rogue waves, the KdV equation is transformed into a self-focusing nonlinear Schrödinger equation. The variation of dust temperature and the electron density affects the nonlinearity and dispersion coefficients which suppress the amplitudes of the DA solitary and rogue waves. The present results aim to describe the nonlinear electrostatic excitations in astrophysical degenerate dense plasma.
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.
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
Dust kinetic Alfvén solitary and rogue waves in a superthermal dusty plasma
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.
Landau damping effects on dust-acoustic solitary waves in a dusty negative-ion plasma
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)
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.