Decay of Kadomtsev-Petviashvili lumps in dissipative media

NASA Astrophysics Data System (ADS)

Clarke, S.; Gorshkov, K.; Grimshaw, R.; Stepanyants, Y.

2018-03-01

The decay of Kadomtsev-Petviashvili lumps is considered for a few typical dissipations-Rayleigh dissipation, Reynolds dissipation, Landau damping, Chezy bottom friction, viscous dissipation in the laminar boundary layer, and radiative losses caused by large-scale dispersion. It is shown that the straight-line motion of lumps is unstable under the influence of dissipation. The lump trajectories are calculated for two most typical models of dissipation-the Rayleigh and Reynolds dissipations. A comparison of analytical results obtained within the framework of asymptotic theory with the direct numerical calculations of the Kadomtsev-Petviashvili equation is presented. Good agreement between the theoretical and numerical results is obtained.

Numerical study of the Kadomtsev-Petviashvili equation and dispersive shock waves

NASA Astrophysics Data System (ADS)

Grava, T.; Klein, C.; Pitton, G.

2018-02-01

A detailed numerical study of the long time behaviour of dispersive shock waves in solutions to the Kadomtsev-Petviashvili (KP) I equation is presented. It is shown that modulated lump solutions emerge from the dispersive shock waves. For the description of dispersive shock waves, Whitham modulation equations for KP are obtained. It is shown that the modulation equations near the soliton line are hyperbolic for the KPII equation while they are elliptic for the KPI equation leading to a focusing effect and the formation of lumps. Such a behaviour is similar to the appearance of breathers for the focusing nonlinear Schrödinger equation in the semiclassical limit.

The Kadomtsev-Petviashvili equation under rapid forcing

NASA Astrophysics Data System (ADS)

Moroz, Irene M.

1997-06-01

We consider the initial value problem for the forced Kadomtsev-Petviashvili equation (KP) when the forcing is assumed to be fast compared to the evolution of the unforced equation. This suggests the introduction of two time scales. Solutions to the forced KP are sought by expanding the dependent variable in powers of a small parameter, which is inversely related to the forcing time scale. The unforced system describes weakly nonlinear, weakly dispersive, weakly two-dimensional wave propagation and is studied in two forms, depending upon whether gravity dominates surface tension or vice versa. We focus on the effect that the forcing has on the one-lump solution to the KPI equation (where surface tension dominates) and on the one- and two-line soliton solutions to the KPII equation (when gravity dominates). Solutions to second order in the expansion are computed analytically for some specific choices of the forcing function, which are related to the choice of initial data.

Fission and fusion interaction phenomena of mixed lump kink solutions for a generalized (3+1)-dimensional B-type Kadomtsev-Petviashvili equation

NASA Astrophysics Data System (ADS)

Liu, Yaqing; Wen, Xiaoyong

2018-05-01

In this paper, a generalized (3+1)-dimensional B-type Kadomtsev-Petviashvili (gBKP) equation is investigated by using the Hirota’s bilinear method. With the aid of symbolic computation, some new lump, mixed lump kink and periodic lump solutions are derived. Based on the derived solutions, some novel interaction phenomena like the fission and fusion interactions between one lump soliton and one kink soliton, the fission and fusion interactions between one lump soliton and a pair of kink solitons and the interactions between two periodic lump solitons are discussed graphically. Results might be helpful for understanding the propagation of the shallow water wave.

The Kadomtsev{endash}Petviashvili equation as a source of integrable model equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Maccari, A.

1996-12-01

A new integrable and nonlinear partial differential equation (PDE) in 2+1 dimensions is obtained, by an asymptotically exact reduction method based on Fourier expansion and spatiotemporal rescaling, from the Kadomtsev{endash}Petviashvili equation. The integrability property is explicitly demonstrated, by exhibiting the corresponding Lax pair, that is obtained by applying the reduction technique to the Lax pair of the Kadomtsev{endash}Petviashvili equation. This model equation is likely to be of applicative relevance, because it may be considered a consistent approximation of a large class of nonlinear evolution PDEs. {copyright} {ital 1996 American Institute of Physics.}

Internal Solitons in the Oceans

DTIC Science & Technology

2006-01-01

stratification and also allow various generalizations of the KdV equa- tion, such as the Kadomtsev - Petviashvili equation shown below. The soliton... Kadomtsev - Petviashvili (KP) equation , which is applicable to a weakly diffracted wave beam, and is based again on adding a small term to the KdV equation ...well-known Boussinesq and Korteweg-de Vries equations . Then certain generalizations are considered, including effects of cubic nonlin- earity, Earth’s

Collapse of ultrashort spatiotemporal pulses described by the cubic generalized Kadomtsev-Petviashvili equation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Leblond, Herve; Kremer, David; Mihalache, Dumitru

2010-03-15

By using a reductive perturbation method, we derive from Maxwell-Bloch equations a cubic generalized Kadomtsev-Petviashvili equation for ultrashort spatiotemporal optical pulse propagation in cubic (Kerr-like) media without the use of the slowly varying envelope approximation. We calculate the collapse threshold for the propagation of few-cycle spatiotemporal pulses described by the generic cubic generalized Kadomtsev-Petviashvili equation by a direct numerical method and compare it to analytic results based on a rigorous virial theorem. Besides, typical evolution of the spectrum (integrated over the transverse spatial coordinate) is given and a strongly asymmetric spectral broadening of ultrashort spatiotemporal pulses during collapse is evidenced.

Quasideterminant solutions of the extended noncommutative Kadomtsev-Petviashvili hierarchy

NASA Astrophysics Data System (ADS)

Wu, Hongxia; Liu, Jingxin; Li, Chunxia

2017-07-01

We construct a nonauto Darboux transformation for the extended noncommutative Kadomtsev-Petviashvili (ncKP) hierarchy and consequently derive its quasi-Wronskian solution. We also obtain the quasi-Wronskian solution of the ncKP equation with self-consistent sources (ncKPESCS) as a by-product. Finally, we use the direct verification method to prove the quasi-Wronskian solution of the ncKPESCS.

Constants and pseudo-constants of the Kadomtsev-Petviashvili equation.

PubMed

Case, K M

1985-08-01

Elucidating earlier work, it is shown that the Kadomtsev-Petviashvili equation has n + 2 constants for all n >/= 0. It also has a pseudo-constant from which the constants can be obtained by differentiation with respect to time. The pseudo-constant can be obtained from a basis functional J(n) ((n+2)) = -1/18 [unk] y(n+2)q by taking repeated Poisson brackets with the Hamiltonian.

Constants and pseudo-constants of the Kadomtsev-Petviashvili equation

PubMed Central

Case, K. M.

1985-01-01

Elucidating earlier work, it is shown that the Kadomtsev-Petviashvili equation has n + 2 constants for all n ≥ 0. It also has a pseudo-constant from which the constants can be obtained by differentiation with respect to time. The pseudo-constant can be obtained from a basis functional Jn(n+2) = -1/18 [unk] yn+2q by taking repeated Poisson brackets with the Hamiltonian. PMID:16593588

Lump waves and breather waves for a (3+1)-dimensional generalized Kadomtsev-Petviashvili Benjamin-Bona-Mahony equation for an offshore structure

NASA Astrophysics Data System (ADS)

Yin, Ying; Tian, Bo; Wu, Xiao-Yu; Yin, Hui-Min; Zhang, Chen-Rong

2018-04-01

In this paper, we investigate a (3+1)-dimensional generalized Kadomtsev-Petviashvili Benjamin-Bona-Mahony equation, which describes the fluid flow in the case of an offshore structure. By virtue of the Hirota method and symbolic computation, bilinear forms, the lump-wave and breather-wave solutions are derived. Propagation characteristics and interaction of lump waves and breather waves are graphically discussed. Amplitudes and locations of the lump waves, amplitudes and periods of the breather waves all vary with the wavelengths in the three spatial directions, ratio of the wave amplitude to the depth of water, or product of the depth of water and the relative wavelength along the main direction of propagation. Of the interactions between the lump waves and solitons, there exist two different cases: (i) the energy is transferred from the lump wave to the soliton; (ii) the energy is transferred from the soliton to the lump wave.

Constants and pseudo-constants of the Kadomtsev-Petviashvili equation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Case, K.M.

1985-08-01

Elucidating earlier work, it is shown that the Kadomtsev-Petviashvili equation has n + 2 constants for all n greater than or equal to 0. It also has a pseudo-constant from which the constants can be obtained by differentiation with respect to time. The pseudo-constant can be obtained from a basis functional J/sub n/sup (n+2)/ = -1/18 integral y/sup n+2/ q by taking repeated Poisson brackets with the Hamiltonian.

Modeling ultrashort electromagnetic pulses with a generalized Kadomtsev-Petviashvili equation

NASA Astrophysics Data System (ADS)

Hofstrand, A.; Moloney, J. V.

2018-03-01

In this paper we derive a properly scaled model for the nonlinear propagation of intense, ultrashort, mid-infrared electromagnetic pulses (10-100 femtoseconds) through an arbitrary dispersive medium. The derivation results in a generalized Kadomtsev-Petviashvili (gKP) equation. In contrast to envelope-based models such as the Nonlinear Schrödinger (NLS) equation, the gKP equation describes the dynamics of the field's actual carrier wave. It is important to resolve these dynamics when modeling ultrashort pulses. We proceed by giving an original proof of sufficient conditions on the initial pulse for a singularity to form in the field after a finite propagation distance. The model is then numerically simulated in 2D using a spectral-solver with initial data and physical parameters highlighting our theoretical results.

A new multi-symplectic scheme for the generalized Kadomtsev-Petviashvili equation

NASA Astrophysics Data System (ADS)

Li, Haochen; Sun, Jianqiang

2012-09-01

We propose a new scheme for the generalized Kadomtsev-Petviashvili (KP) equation. The multi-symplectic conservation property of the new scheme is proved. Back error analysis shows that the new multi-symplectic scheme has second order accuracy in space and time. Numerical application on studying the KPI equation and the KPII equation are presented in detail.

Travelling-wave solutions of a weakly nonlinear two-dimensional higher-order Kadomtsev-Petviashvili dynamical equation for dispersive shallow-water waves

NASA Astrophysics Data System (ADS)

Seadawy, Aly R.

2017-01-01

The propagation of three-dimensional nonlinear irrotational flow of an inviscid and incompressible fluid of the long waves in dispersive shallow-water approximation is analyzed. The problem formulation of the long waves in dispersive shallow-water approximation lead to fifth-order Kadomtsev-Petviashvili (KP) dynamical equation by applying the reductive perturbation theory. By using an extended auxiliary equation method, the solitary travelling-wave solutions of the two-dimensional nonlinear fifth-order KP dynamical equation are derived. An analytical as well as a numerical solution of the two-dimensional nonlinear KP equation are obtained and analyzed with the effects of external pressure flow.

Quantization of the Kadomtsev-Petviashvili equation

NASA Astrophysics Data System (ADS)

Kozlowski, K.; Sklyanin, E. K.; Torrielli, A.

2017-08-01

We propose a quantization of the Kadomtsev-Petviashvili equation on a cylinder equivalent to an infinite system of nonrelativistic one-dimensional bosons with the masses m = 1, 2,.... The Hamiltonian is Galilei-invariant and includes the split and merge terms Ψ _{{m_1}}^\\dag Ψ _{{m_2}}^\\dag {Ψ _{{m_1} + {m_2}}} and Ψ _{{m_1} + {m_2}}^\\dag {Ψ _{{m_1}}}{Ψ _{{m_2}}} for all combinations of particles with masses m 1, m 2, and m 1 + m 2 for a special choice of coupling constants. We construct the Bethe eigenfunctions for the model and verify the consistency of the coordinate Bethe ansatz and hence the quantum integrability of the model up to the mass M=8 sector.

Transverse instability of solitary waves in the generalized kadomtsev-petviashvili equation

PubMed

Kataoka; Tsutahara; Negoro

2000-04-03

The linear stability of planar solitary waves with respect to long-wavelength transverse perturbations is studied in the framework of the generalized Kadomtsev-Petviashvili equation. It is newly discovered that for some nonlinearities in this family, the solitary waves could be transversely unstable even in a medium with negative dispersion. In the case of positive dispersion, they are found to be always unstable.

On the integrable elliptic cylindrical Kadomtsev-Petviashvili equation.

PubMed

Khusnutdinova, K R; Klein, C; Matveev, V B; Smirnov, A O

2013-03-01

There exist two versions of the Kadomtsev-Petviashvili (KP) equation, related to the Cartesian and cylindrical geometries of the waves. In this paper, we derive and study a new version, related to the elliptic cylindrical geometry. The derivation is given in the context of surface waves, but the derived equation is a universal integrable model applicable to generic weakly nonlinear weakly dispersive waves. We also show that there exist nontrivial transformations between all three versions of the KP equation associated with the physical problem formulation, and use them to obtain new classes of approximate solutions for water waves.

A new bidirectional generalization of (2+1)-dimensional matrix k-constrained Kadomtsev-Petviashvili hierarchy

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chvartatskyi, O. I., E-mail: alex.chvartatskyy@gmail.com; Sydorenko, Yu. M., E-mail: y-sydorenko@franko.lviv.ua

We introduce a new bidirectional generalization of (2+1)-dimensional k-constrained Kadomtsev-Petviashvili (KP) hierarchy ((2+1)-BDk-cKPH). This new hierarchy generalizes (2+1)-dimensional k-cKP hierarchy, (t{sub A}, τ{sub B}) and (γ{sub A}, σ{sub B}) matrix hierarchies. (2+1)-BDk-cKPH contains a new matrix (1+1)-k-constrained KP hierarchy. Some members of (2+1)-BDk-cKPH are also listed. In particular, it contains matrix generalizations of Davey-Stewartson (DS) systems, (2+1)-dimensional modified Korteweg-de Vries equation and the Nizhnik equation. (2+1)-BDk-cKPH also includes new matrix (2+1)-dimensional generalizations of the Yajima-Oikawa and Melnikov systems. Binary Darboux Transformation Dressing Method is also proposed for construction of exact solutions for equations from (2+1)-BDk-cKPH. As an example the exactmore » form of multi-soliton solutions for vector generalization of the DS system is given.« less

Properties of solutions of the Kadomtsev-Petviashvili I equation

NASA Astrophysics Data System (ADS)

Boiti, M.; Pempinelli, F.; Pogrebkov, A.

1994-09-01

The Kadomtsev-Petviashvili I (KPI) equation is considered as a useful laboratory for experimenting with new theoretical tools able to handle the specific features of integrable models in 2+1 dimensions. The linearized version of the KPI equation is first considered by solving the initial value problem for different classes of initial data. Properties of the solutions in different cases are analyzed in details. The obtained results are used as a guideline for studying the properties of the solution u(t,x,y) of the Kadomtsev-Petviashvili I (KPI) equation with given initial data u(0,x,y) belonging to the Schwartz space. The spectral theory associated to KPI is studied in the space of the Fourier transform of the solutions. The variables p={p1,p2} of the Fourier space are shown to be the most convenient spectral variables to use for spectral data. Spectral data are shown to decay rapidly at large p but to be discontinuous at p=0. Direct and inverse problems are solved with special attention to the behavior of all the quantities involved in the neighborhood of t=0 and p=0. It is shown in particular that the solution u(t,x,y) has a time derivative discontinuous at t=0 and that at any t≠0 it does not belong to the Schwartz space no matter how small in norm and rapidly decaying at large distances the initial data are chosen.

Kadomtsev-Petviashvili equation for a flow of highly nonisothermal collisionless plasma

NASA Astrophysics Data System (ADS)

Movsesyants, Yu. B.; Rukhadze, A. A.; Tyuryukanov, P. M.

2016-01-01

It is shown that the equations of two-fluid electrodynamics for a cold ions flow and Boltzmann electrons in the vicinity of the ion-sound point can be reduced to the Kadomtsev-Petviashvili equation. Examples of two-dimensional equilibria with pole singularities obtained by exactly solving the equations are presented. An exact self-similar solution describing a two-dimensional transonic flow and having no pole singularities is found.

On critical behaviour in generalized Kadomtsev-Petviashvili equations

NASA Astrophysics Data System (ADS)

Dubrovin, B.; Grava, T.; Klein, C.

2016-10-01

An asymptotic description of the formation of dispersive shock waves in solutions to the generalized Kadomtsev-Petviashvili (KP) equation is conjectured. The asymptotic description based on a multiscales expansion is given in terms of a special solution to an ordinary differential equation of the Painlevé I hierarchy. Several examples are discussed numerically to provide strong evidence for the validity of the conjecture. The numerical study of the long time behaviour of these examples indicates persistence of dispersive shock waves in solutions to the (subcritical) KP equations, while in the supercritical KP equations a blow-up occurs after the formation of the dispersive shock waves.

New exact periodic solitary-wave solutions for the new (3+1)-dimensional generalized Kadomtsev-Petviashvili equation in multi-temperature electron plasmas

NASA Astrophysics Data System (ADS)

Liu, Jian-Guo; Tian, Yu; Zeng, Zhi-Fang

2017-10-01

In this paper, we aim to introduce a new form of the (3+1)-dimensional generalized Kadomtsev-Petviashvili equation for the long waves of small amplitude with slow dependence on the transverse coordinate. By using the Hirota's bilinear form and the extended homoclinic test approach, new exact periodic solitary-wave solutions for the new (3+1)-dimensional generalized Kadomtsev-Petviashvili equation are presented. Moreover, the properties and characteristics for these new exact periodic solitary-wave solutions are discussed with some figures.

The generation of symmetric and asymmetric lump solitons by a bottom topography

NASA Astrophysics Data System (ADS)

Lu, Zhiming

2016-11-01

A group of Lump solutions to the (2+1)-dimensional Kadomtsev-Petviashvili (KP) equation is obtained analytically by making use of Hirota bilinear transform method. Then the generation of symmetric and asymmetric lump solitons by an obliquely-placed three-dimensional bottom topography is numerically investigated using the forced Kadomtsev-Petviashvili-I (fKP-I) equation. The numerical method is based on the third order Runge-Kutta method and the Crank-Nicolson scheme. The main result is the asymmetric generation of asymmetric lump-type solitons downstream of the obstacle.The lump soliton with a smaller amplitude is generated with a longer period and moves in a larger angle with respect to the positive x-axis than the one with a larger amplitude. The amplitude of the lump solitons strongly depend on the volume of the obstacle rather than the shape. Finally the effects of the detuning parameter on the generation of lump solitons is also studied. Project supported by NSFC with No. 11272196.

Solitary waves, rogue waves and homoclinic breather waves for a (2 + 1)-dimensional generalized Kadomtsev-Petviashvili equation

NASA Astrophysics Data System (ADS)

Dong, Min-Jie; Tian, Shou-Fu; Yan, Xue-Wei; Zou, Li; Li, Jin

2017-10-01

We study a (2 + 1)-dimensional generalized Kadomtsev-Petviashvili (gKP) equation, which characterizes the formation of patterns in liquid drops. By using Bell’s polynomials, an effective way is employed to succinctly construct the bilinear form of the gKP equation. Based on the resulting bilinear equation, we derive its solitary waves, rogue waves and homoclinic breather waves, respectively. Our results can help enrich the dynamical behavior of the KP-type equations.

Virasoro symmetry of the constrained multicomponent Kadomtsev-Petviashvili hierarchy and its integrable discretization

NASA Astrophysics Data System (ADS)

Li, Chuanzhong; He, Jingsong

2016-06-01

We construct Virasoro-type additional symmetries of a kind of constrained multicomponent Kadomtsev-Petviashvili (KP) hierarchy and obtain the Virasoro flow equation for the eigenfunctions and adjoint eigenfunctions. We show that the algebraic structure of the Virasoro symmetry is retained under discretization from the constrained multicomponent KP hierarchy to the discrete constrained multicomponent KP hierarchy.

Bright and dark N-soliton solutions for the (2 + 1)-dimensional Maccari system

NASA Astrophysics Data System (ADS)

Liu, Lei; Tian, Bo; Yuan, Yu-Qiang; Sun, Yan

2018-02-01

Under investigation in this paper is the (2 + 1) -dimensional Maccari system, which is related to the Kadomtsev-Petviashvili (KP) equation. Bright and dark N -soliton solutions in terms of the Gramian are obtained via the KP hierarchy reduction. Oblique and parallel interactions between the bright solitons and between the dark solitons are studied analytically and graphically. We find that there are elastic and inelastic interactions for the bright solitons, but there are only elastic interactions for the dark solitons. Resonance, breather, attraction and repulsion structures are presented. It is expected that these soliton interactions have potential applications in fluid dynamics, nonlinear optics and plasma physics.

Whitham modulation theory for the Kadomtsev- Petviashvili equation.

PubMed

Ablowitz, Mark J; Biondini, Gino; Wang, Qiao

2017-08-01

The genus-1 Kadomtsev-Petviashvili (KP)-Whitham system is derived for both variants of the KP equation; namely the KPI and KPII equations. The basic properties of the KP-Whitham system, including symmetries, exact reductions and its possible complete integrability, together with the appropriate generalization of the one-dimensional Riemann problem for the Korteweg-de Vries equation are discussed. Finally, the KP-Whitham system is used to study the linear stability properties of the genus-1 solutions of the KPI and KPII equations; it is shown that all genus-1 solutions of KPI are linearly unstable, while all genus-1 solutions of KPII are linearly stable within the context of Whitham theory.

Whitham modulation theory for the Kadomtsev- Petviashvili equation

NASA Astrophysics Data System (ADS)

Ablowitz, Mark J.; Biondini, Gino; Wang, Qiao

2017-08-01

The genus-1 Kadomtsev-Petviashvili (KP)-Whitham system is derived for both variants of the KP equation; namely the KPI and KPII equations. The basic properties of the KP-Whitham system, including symmetries, exact reductions and its possible complete integrability, together with the appropriate generalization of the one-dimensional Riemann problem for the Korteweg-de Vries equation are discussed. Finally, the KP-Whitham system is used to study the linear stability properties of the genus-1 solutions of the KPI and KPII equations; it is shown that all genus-1 solutions of KPI are linearly unstable, while all genus-1 solutions of KPII are linearly stable within the context of Whitham theory.

Periodic wave, breather wave and travelling wave solutions of a (2 + 1)-dimensional B-type Kadomtsev-Petviashvili equation in fluids or plasmas

NASA Astrophysics Data System (ADS)

Hu, Wen-Qiang; Gao, Yi-Tian; Jia, Shu-Liang; Huang, Qian-Min; Lan, Zhong-Zhou

2016-11-01

In this paper, a (2 + 1)-dimensional B-type Kadomtsev-Petviashvili equation is investigated, which has been presented as a model for the shallow water wave in fluids or the electrostatic wave potential in plasmas. By virtue of the binary Bell polynomials, the bilinear form of this equation is obtained. With the aid of the bilinear form, N -soliton solutions are obtained by the Hirota method, periodic wave solutions are constructed via the Riemann theta function, and breather wave solutions are obtained according to the extended homoclinic test approach. Travelling waves are constructed by the polynomial expansion method as well. Then, the relations between soliton solutions and periodic wave solutions are strictly established, which implies the asymptotic behaviors of the periodic waves under a limited procedure. Furthermore, we obtain some new solutions of this equation by the standard extended homoclinic test approach. Finally, we give a generalized form of this equation, and find that similar analytical solutions can be obtained from the generalized equation with arbitrary coefficients.

The polarized Debye sheath effect on Kadomtsev-Petviashvili electrostatic structures in strongly coupled dusty plasma

DOE Office of Scientific and Technical Information (OSTI.GOV)

Shahmansouri, M.; Alinejad, H.

2015-04-15

We give a theoretical investigation on the dynamics of nonlinear electrostatic waves in a strongly coupled dusty plasma with strong electrostatic interaction between dust grains in the presence of the polarization force (i.e., the force due to the polarized Debye sheath). Adopting a reductive perturbation method, we derived a three-dimensional Kadomtsev-Petviashvili equation that describes the evolution of weakly nonlinear electrostatic localized waves. The energy integral equation is used to study the existence domains of the localized structures. The analysis provides the localized structure existence region, in terms of the effects of strong interaction between the dust particles and polarization force.

A semi-discrete Kadomtsev-Petviashvili equation and its coupled integrable system

NASA Astrophysics Data System (ADS)

Li, Chun-Xia; Lafortune, Stéphane; Shen, Shou-Feng

2016-05-01

We establish connections between two cascades of integrable systems generated from the continuum limits of the Hirota-Miwa equation and its remarkable nonlinear counterpart under the Miwa transformation, respectively. Among these equations, we are mainly concerned with the semi-discrete bilinear Kadomtsev-Petviashvili (KP) equation which is seldomly studied in literature. We present both of its Casorati and Grammian determinant solutions. Through the Pfaffianization procedure proposed by Hirota and Ohta, we are able to derive the coupled integrable system for the semi-discrete KP equation.

Bilinear identities for an extended B-type Kadomtsev-Petviashvili hierarchy

NASA Astrophysics Data System (ADS)

Lin, Runliang; Cao, Tiancheng; Liu, Xiaojun; Zeng, Yunbo

2016-03-01

We construct bilinear identities for wave functions of an extended B-type Kadomtsev-Petviashvili (BKP) hierarchy containing two types of (2+1)-dimensional Sawada-Kotera equations with a self-consistent source. Introducing an auxiliary variable corresponding to the extended flow for the BKP hierarchy, we find the τ -function and bilinear identities for this extended BKP hierarchy. The bilinear identities generate all the Hirota bilinear equations for the zero-curvature forms of this extended BKP hierarchy. As examples, we obtain the Hirota bilinear equations for the two types of (2+1)-dimensional Sawada-Kotera equations in explicit form.

Parabola solitons for the nonautonomous KP equation in fluids and plasmas

NASA Astrophysics Data System (ADS)

Yu, Xin; Sun, Zhi-Yuan

2016-04-01

Under investigation in this paper is a nonautonomous Kadomtsev-Petviashvili (KP) equation in fluids and plasmas. The integrability of this equation is examined via the Painlevé analysis and its multi-soliton solutions are constructed. A constraint is proposed to ensure the existence of parabola solitons for such KP equation. Based on the constructed solutions, the solitonic propagation and interaction, including the elastic interaction, inelastic interaction and soliton resonance for parabola solitons, are discussed. The results might be useful for shallow water wave and rogue wave.

On the Discrete Spectrum of the Nonstationary Schrödinger Equation and Multipole Lumps of the Kadomtsev-Petviashvili I Equation

NASA Astrophysics Data System (ADS)

Villarroel, Javier; Ablowitz, Mark J.

The discrete spectrum of the nonstationary Schrödinger equation and localized solutions of the Kadomtsev-Petviashvili-I (KPI) equation are studied via the inverse scattering transform. It is shown that there exist infinitely many real and rationally decaying potentials which correspond to a discrete spectrum whose related eigenfunctions have multiple poles in the spectral parameter. An index or winding number is asssociated with each of these solutions. The resulting localized solutions of KPI behave as collection of individual humps with nonuniform dynamics.

Three dimensional clyindrical Kadomtsev Petviashvili equation in two temperature charged dusty plasma

NASA Astrophysics Data System (ADS)

El-Bedwehy, N. A.; El-Attafi, M. A.; El-Labany, S. K.

2016-09-01

The properties of solitary waves in an unmagnetized, collisionless dusty plasma consisting of nonthermal ions, cold and hot dust grains and Maxwellian electrons have been investigated. Under a suitable coordinate transformation, the three-dimensional cylindrical Kadomtsev-Petviashvili (3D-CKP) equation is obtained. The effect of the nonthermal parameter, the negative charge number of hot and cold dust on the solitary properties are investigated. Furthermore, the solitary profile in the radial, axial, and polar angle coordinates with the time is examined. The present investigation may be applicable in space plasma such as F-ring of Saturn.

LETTER TO THE EDITOR: Solving the Kadomtsev - Petviashvili equation with initial data not vanishing at large distances

NASA Astrophysics Data System (ADS)

Boiti, M.; Pempinelli, F.; Pogrebkov, A.

1997-06-01

We consider, in the framework of the inverse scattering method, the solution of the Kadomtsev - Petviashvili equation in its version called KPI. The spectral theory is extended to the case in which the initial data 0266-5611/13/3/001/img1 are not vanishing along a finite number of directions at large distances on the plane.

The Multidimensional Solitons in a Plasma: Structure Stability and Dynamics

DTIC Science & Technology

2003-07-20

ax(8 H’ / 8u), (2) into GKP (Generalized Kadomtsev - Petviashvili ) class where of equations , and in the case when 13 4nnT / B 2 << 1 1 1 for 6) < OB= eB...that the soliton elastic collisions can lead to formation of complex structures including the multisoliton bound states. 1. Basic equations Eq. (1) with...scribed by equation 2. Stability of 2D and 3D solutions atu + A(t,u)u =f, f= K 0X Ajudx, (1) To study stability of the GKP equation solutions, we =a 2

Cosmic dust-ion-acoustic waves, spherical modified Kadomtsev-Petviashvili model, and symbolic computation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gao Yitian; Tian Bo; State Key Laboratory of Software Development Environment, Beijing University of Aeronautics and Astronautics, Beijing 100083

2006-11-15

The spherical modified Kadomtsev-Petviashvili (smKP) model is hereby derived with symbolic computation for the dust-ion-acoustic waves with zenith-angle perturbation in a cosmic dusty plasma. Formation and properties of both dark and bright smKP nebulons are obtained and discussed. The relevance of those smKP nebulons to the supernova shells and Saturn's F-ring is pointed out, and possibly observable nebulonic effects for the future cosmic plasma experiments are proposed. The difference of the smKP nebulons from other types of nebulons is also analyzed.

New type of a generalized variable-coefficient Kadomtsev-Petviashvili equation with self-consistent sources and its Grammian-type solutions

NASA Astrophysics Data System (ADS)

Zhang, Yi; Xu, Yue; Ma, Kun

2016-08-01

In this paper, the variable-coefficient Kadomtsev-Petviashvili (vcKP) equation with self-consistent sources is presented by two different methods, one is the source generation procedure, the other is the Pfaffianization procedure, and the solutions for the two new coupled systems are given through Grammian-type Pfaffian determinants.

Dynamics of a differential-difference integrable (2+1)-dimensional system.

PubMed

Yu, Guo-Fu; Xu, Zong-Wei

2015-06-01

A Kadomtsev-Petviashvili- (KP-) type equation appears in fluid mechanics, plasma physics, and gas dynamics. In this paper, we propose an integrable semidiscrete analog of a coupled (2+1)-dimensional system which is related to the KP equation and the Zakharov equation. N-soliton solutions of the discrete equation are presented. Some interesting examples of soliton resonance related to the two-soliton and three-soliton solutions are investigated. Numerical computations using the integrable semidiscrete equation are performed. It is shown that the integrable semidiscrete equation gives very accurate numerical results in the cases of one-soliton evolution and soliton interactions.

Bending of solitons in weak and slowly varying inhomogeneous plasma

NASA Astrophysics Data System (ADS)

Mukherjee, Abhik; Janaki, M. S.; Kundu, Anjan

2015-12-01

The bending of solitons in two dimensional plane is presented in the presence of weak and slowly varying inhomogeneous ion density for the propagation of ion acoustic soliton in unmagnetized cold plasma with isothermal electrons. Using reductive perturbation technique, a modified Kadomtsev-Petviashvili equation is obtained with a chosen unperturbed ion density profile. The exact solution of the equation shows that the phase of the solitary wave gets modified by a function related to the unperturbed inhomogeneous ion density causing the soliton to bend in the two dimensional plane, while the amplitude of the soliton remains constant.

Bending of solitons in weak and slowly varying inhomogeneous plasma

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mukherjee, Abhik, E-mail: abhik.mukherjee@saha.ac.in; Janaki, M. S., E-mail: ms.janaki@saha.ac.in; Kundu, Anjan, E-mail: anjan.kundu@saha.ac.in

2015-12-15

The bending of solitons in two dimensional plane is presented in the presence of weak and slowly varying inhomogeneous ion density for the propagation of ion acoustic soliton in unmagnetized cold plasma with isothermal electrons. Using reductive perturbation technique, a modified Kadomtsev-Petviashvili equation is obtained with a chosen unperturbed ion density profile. The exact solution of the equation shows that the phase of the solitary wave gets modified by a function related to the unperturbed inhomogeneous ion density causing the soliton to bend in the two dimensional plane, while the amplitude of the soliton remains constant.

Solitary wave solutions of two-dimensional nonlinear Kadomtsev-Petviashvili dynamic equation in dust-acoustic plasmas

NASA Astrophysics Data System (ADS)

Seadawy, Aly R.

2017-09-01

Nonlinear two-dimensional Kadomtsev-Petviashvili (KP) equation governs the behaviour of nonlinear waves in dusty plasmas with variable dust charge and two temperature ions. By using the reductive perturbation method, the two-dimensional dust-acoustic solitary waves (DASWs) in unmagnetized cold plasma consisting of dust fluid, ions and electrons lead to a KP equation. We derived the solitary travelling wave solutions of the two-dimensional nonlinear KP equation by implementing sech-tanh, sinh-cosh, extended direct algebraic and fraction direct algebraic methods. We found the electrostatic field potential and electric field in the form travelling wave solutions for two-dimensional nonlinear KP equation. The solutions for the KP equation obtained by using these methods can be demonstrated precisely and efficiency. As an illustration, we used the readymade package of Mathematica program 10.1 to solve the original problem. These solutions are in good agreement with the analytical one.

Spherical solitons in Earth'S mesosphere plasma

NASA Astrophysics Data System (ADS)

Annou, K.; Annou, R.

2016-01-01

Soliton formation in Earth's mesosphere plasma is described. Nonlinear acoustic waves in plasmas with two-temperature ions and a variable dust charge where transverse perturbation is dealt with are studied in bounded spherical geometry. Using the perturbation method, a spherical Kadomtsev-Petviashvili equation that describes dust acoustic waves is derived. It is found that the parameters taken into account have significant effects on the properties of nonlinear waves in spherical geometry.

Stable two-dimensional solitary pulses in linearly coupled dissipative Kadomtsev-Petviashvili equations.

PubMed

Feng, Bao-Feng; Malomed, Boris A; Kawahara, Takuji

2002-11-01

We present a two-dimensional (2D) generalization of the stabilized Kuramoto-Sivashinsky system, based on the Kadomtsev-Petviashvili (KP) equation including dissipation of the generic [Newell-Whitehead-Segel (NWS)] type and gain. The system directly applies to the description of gravity-capillary waves on the surface of a liquid layer flowing down an inclined plane, with a surfactant diffusing along the layer's surface. Actually, the model is quite general, offering a simple way to stabilize nonlinear media, combining the weakly 2D dispersion of the KP type with gain and NWS dissipation. Other applications are internal waves in multilayer fluids flowing down an inclined plane, double-front flames in gaseous mixtures, etc. Parallel to this weakly 2D model, we also introduce and study a semiphenomenological one, whose dissipative terms are isotropic, rather than of the NWS type, in order to check if qualitative results are sensitive to the exact form of the lossy terms. The models include an additional linear equation of the advection-diffusion type, linearly coupled to the main KP-NWS equation. The extra equation provides for stability of the zero background in the system, thus opening a way for the existence of stable localized pulses. We focus on the most interesting case, when the dispersive part of the system is of the KP-I type, which corresponds, e.g., to capillary waves, and makes the existence of completely localized 2D pulses possible. Treating the losses and gain as small perturbations and making use of the balance equation for the field momentum, we find that the equilibrium between the gain and losses may select two steady-state solitons from their continuous family existing in the absence of the dissipative terms (the latter family is found in an exact analytical form, and is numerically demonstrated to be stable). The selected soliton with the larger amplitude is expected to be stable. Direct simulations completely corroborate the analytical predictions

Ring dark and antidark solitons in nonlocal media.

PubMed

Horikis, Theodoros P; Frantzeskakis, Dimitrios J

2016-02-01

Ring dark and antidark solitons in nonlocal media are found. These structures have, respectively, the form of annular dips or humps on top of a stable CW background, and exist in a weak or strong nonlocality regime, defined by the sign of a characteristic parameter. It is demonstrated analytically that these solitons satisfy an effective cylindrical Kadomtsev-Petviashvili (aka Johnson's) equation and, as such, can be written explicitly in closed form. Numerical simulations show that they propagate undistorted and undergo quasi-elastic collisions, attesting to their stability properties.

Soliton and periodic solutions for time-dependent coefficient non-linear equation

NASA Astrophysics Data System (ADS)

Guner, Ozkan

2016-01-01

In this article, we establish exact solutions for the generalized (3+1)-dimensional variable coefficient Kadomtsev-Petviashvili (GVCKP) equation. Using solitary wave ansatz in terms of ? functions and the modified sine-cosine method, we find exact analytical bright soliton solutions and exact periodic solutions for the considered model. The physical parameters in the soliton solutions are obtained as function of the dependent model coefficients. The effectiveness and reliability of the method are shown by its application to the GVCKP equation.

Classification of the line-soliton solutions of KPII

NASA Astrophysics Data System (ADS)

Chakravarty, Sarbarish; Kodama, Yuji

2008-07-01

In the previous papers (notably, Kodama Y 2004 J. Phys. A: Math. Gen. 37 11169-90, Biondini G and Chakravarty S 2006 J. Math. Phys. 47 033514), a large variety of line-soliton solutions of the Kadomtsev-Petviashvili II (KPII) equation was found. The line-soliton solutions are solitary waves which decay exponentially in the (x, y)-plane except along certain rays. In this paper, it is shown that those solutions are classified by asymptotic information of the solution as |y| → ∞. The present work then unravels some interesting relations between the line-soliton classification scheme and classical results in the theory of permutations.

Existence, regularity, and concentration phenomenon of nontrivial solitary waves for a class of generalized variable coefficient Kadomtsev-Petviashvili equation

NASA Astrophysics Data System (ADS)

Alves, Claudianor O.; Miyagaki, Olímpio H.

2017-08-01

In this paper, we establish some results concerning the existence, regularity, and concentration phenomenon of nontrivial solitary waves for a class of generalized variable coefficient Kadomtsev-Petviashvili equation. Variational methods are used to get an existence result, as well as, to study the concentration phenomenon, while the regularity is more delicate because we are leading with functions in an anisotropic Sobolev space.

Theory of Soliton Waves.

DTIC Science & Technology

1984-11-01

equation of Kadomtsev and Petviashvili (1970): (ut + 6uu x + U )x = 3 a Uyy, 0 - ± 1. (12) This equation turns out to be integrable for a = ± 1. For...1982b: "Comments on Inverse Scattering for the Kadomtsev - Petviashvili equation ", in Math methods in Hydro. & Integrability in Dyn. Systems, A. I. P. Conf...358. . Joseph, R. I., 1977: J. Phys. A., vol 10, p L225-L227. Kadomtsev , B. B. and Petviashvili , V. I., 1970: Soy. Phys. Doklady, vol 15, pp 539-541

Electrostatic shocks and solitons in pair-ion plasmas in a two-dimensional geometry

DOE Office of Scientific and Technical Information (OSTI.GOV)

Masood, W.; Mahmood, S.; Imtiaz, N.

2009-12-15

Nonlinear electrostatic waves are studied in unmagnetized, dissipative pair-ion plasmas in the presence of weak transverse perturbations. The dissipation in the system is taken into account by incorporating the kinematic viscosity of both positive and negative ions in plasmas. The Kadomtsev-Petviashvili-Burger equation is derived using the small amplitude expansion method. The Kadomtsev-Petviashvili equation for pair-ion plasmas is also presented by ignoring the dissipative effects. Both compressive and rarefactive shocks and solitary waves are found to exist in pair-ion plasmas. The dependence of compression and rarefaction on the temperature ratios between the ion species is numerically shown. The present study maymore » have relevance to the understanding of the formation of electrostatic shocks and solitons in laboratory produced pair-ion plasmas.« less

Scattering transform for nonstationary Schroedinger equation with bidimensionally perturbed N-soliton potential

DOE Office of Scientific and Technical Information (OSTI.GOV)

Boiti, M.; Pempinelli, F.; Pogrebkov, A. K.

2006-12-15

In the framework of the extended resolvent approach the direct and inverse scattering problems for the nonstationary Schroedinger equation with a potential being a perturbation of the N-soliton potential by means of a generic bidimensional smooth function decaying at large spaces are introduced and investigated. The initial value problem of the Kadomtsev-Petviashvili I equation for a solution describing N wave solitons on a generic smooth decaying background is then linearized, giving the time evolution of the spectral data.

Oblique collision of dust acoustic solitons in a strongly coupled dusty plasma

DOE Office of Scientific and Technical Information (OSTI.GOV)

Boruah, A.; Sharma, S. K., E-mail: sumita-sharma82@yahoo.com; Bailung, H.

2015-09-15

The oblique collision between two equal amplitude dust acoustic solitons is observed in a strongly coupled dusty plasma. The solitons are subjected to oblique interaction at different colliding angles. We observe a resonance structure during oblique collision at a critical colliding angle which is described by the idea of three wave resonance interaction modeled by Kadomtsev-Petviashvili equation. After collision, the solitons preserve their identity. The amplitude of the resultant wave formed during interaction is measured for different collision angles as well as for different colliding soliton amplitudes. At resonance, the maximum amplitude of the new soliton formed is nearly 3.7more » times the initial soliton amplitude.« less

Multidimensional Solitons in Complex Media with Variable Dispersion: Structure and Evolution

DTIC Science & Technology

2003-07-20

the results of numerical experiments on Kadomtsev - Petviashvili (KP) equation study of structure and evolution of the nonlinear waves Sx described by...the KP equation with 13 = 3 (t,r) are con- at + auaxu + 03’u =K fAjudx, (1) sidered distracting from a concrete type of media. The -o• numerical...0i)(cot 0- mIM). It is well known that cluding the solutions of the mixed "soliton - non-soliton" the ID solutions of the KdV equation with 3 = const

Nonlocal Symmetries and Interaction Solutions for Potential Kadomtsev-Petviashvili Equation

NASA Astrophysics Data System (ADS)

Ren, Bo; Yu, Jun; Liu, Xi-Zhong

2016-03-01

The nonlocal symmetry for the potential Kadomtsev-Petviashvili (pKP) equation is derived by the truncated Painlevé analysis. The nonlocal symmetry is localized to the Lie point symmetry by introducing the auxiliary dependent variable. Thanks to localization process, the finite symmetry transformations related with the nonlocal symmetry are obtained by solving the prolonged systems. The inelastic interactions among the multiple-front waves of the pKP equation are generated from the finite symmetry transformations. Based on the consistent tanh expansion method, a nonauto-Bäcklund transformation (BT) theorem of the pKP equation is constructed. We can get many new types of interaction solutions because of the existence of an arbitrary function in the nonauto-BT theorem. Some special interaction solutions are investigated both in analytical and graphical ways. Supported by the National Natural Science Foundation of China under Grant Nos. 11305106, 11275129 and 11405110, the Natural Science Foundation of Zhejiang Province of China under Grant No. LQ13A050001

Fusion and fission phenomena for the soliton interactions in a plasma

NASA Astrophysics Data System (ADS)

Chai, Jun; Tian, Bo; Wu, Xiao-Yu; Liu, Lei

2017-02-01

Investigation in this paper is given to a generalized (3 + 1) -dimensional variable-coefficient Kadomtsev-Petviashvili equation for a plasma. Via the bilinear form, the singular and double Wronskian soliton solutions are derived, respectively, under the different variable-coefficient constraints. Interactions between the two solitons are depicted, where the soliton fusion and fission phenomena are respectively pictured out, both for the velocity-unvarying and velocity-varying two solitons. Soliton velocity is related to the variable coefficients h( t), l ( t), q( t), m( t) and n( t), while the soliton amplitude is not affected by them, where h( t), l( t) and q( t) are the perturbed effects, m( t) and n( t) stand for the disturbed wave velocities along the transverse spatial coordinates.

Nonlinear Wave Propagation.

DTIC Science & Technology

1981-11-25

dimensional KdV ( Kadomtsev - Petviashvili ) equation [56). Furthermore it has been found that these newly found decaying mode solutions and usual soliton...Ablowitz and R. Haberman, Phys. Rev. Lett. 35, 1185, 1975. 26. S.V. !anakov, "On the Solutions of the Kadomtsev - Petviashvili equation ; Proc. of Symposium...accomplished relates to fluid mechanics, nonlinear optics, multidimensional solitons, Painlev e equations , long time asymptotic solu- tions, new

Higher-order rational solitons and rogue-like wave solutions of the (2 + 1)-dimensional nonlinear fluid mechanics equations

NASA Astrophysics Data System (ADS)

Wen, Xiao-Yong; Yan, Zhenya

2017-02-01

The novel generalized perturbation (n, M)-fold Darboux transformations (DTs) are reported for the (2 + 1)-dimensional Kadomtsev-Petviashvili (KP) equation and its extension by using the Taylor expansion of the Darboux matrix. The generalized perturbation (1 , N - 1) -fold DTs are used to find their higher-order rational solitons and rogue wave solutions in terms of determinants. The dynamics behaviors of these rogue waves are discussed in detail for different parameters and time, which display the interesting RW and soliton structures including the triangle, pentagon, heptagon profiles, etc. Moreover, we find that a new phenomenon that the parameter (a) can control the wave structures of the KP equation from the higher-order rogue waves (a ≠ 0) into higher-order rational solitons (a = 0) in (x, t)-space with y = const . These results may predict the corresponding dynamical phenomena in the models of fluid mechanics and other physically relevant systems.

Analytical Approach to (2+1)-Dimensional Boussinesq Equation and (3+1)-Dimensional Kadomtsev-Petviashvili Equation

NASA Astrophysics Data System (ADS)

Sarıaydın, Selin; Yıldırım, Ahmet

2010-05-01

In this paper, we studied the solitary wave solutions of the (2+1)-dimensional Boussinesq equation utt -uxx-uyy-(u2)xx-uxxxx = 0 and the (3+1)-dimensional Kadomtsev-Petviashvili (KP) equation uxt -6ux 2 +6uuxx -uxxxx -uyy -uzz = 0. By using this method, an explicit numerical solution is calculated in the form of a convergent power series with easily computable components. To illustrate the application of this method numerical results are derived by using the calculated components of the homotopy perturbation series. The numerical solutions are compared with the known analytical solutions. Results derived from our method are shown graphically.

Numerical studies of the KP line-solitons

NASA Astrophysics Data System (ADS)

Chakravarty, S.; McDowell, T.; Osborne, M.

2017-03-01

The Kadomtsev-Petviashvili (KP) equation admits a class of solitary wave solutions localized along distinct rays in the xy-plane, called the line-solitons, which describe the interaction of shallow water waves on a flat surface. These wave interactions have been observed on long, flat beaches, as well as have been recreated in laboratory experiments. In this paper, the line-solitons are investigated via direct numerical simulations of the KP equation, and the interactions of the evolved solitary wave patterns are studied. The objective is to obtain greater insight into solitary wave interactions in shallow water and to determine the extent the KP equation is a good model in describing these nonlinear interactions.

Interaction of solitons for obliquely propagating magnetoacoustic waves in stellar atmosphere

NASA Astrophysics Data System (ADS)

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

2016-12-01

We study here the nonlinear oblique propagation of magnetoacoustic waves in dense plasmas with degenerate electrons by deriving Kadomtsev-Petviashvili (KP) equation for small but finite amplitude perturbations. The two soliton interaction has been studied by finding the solution of the KP equation using the Hirota bilinear formalism. For illustrative purposes, we have used the plasma parameters typically found in white dwarf stars for both the fast and slow modes of magnetoacoustic waves. It has been observed that the soliton interaction in the fast and slow modes is strongly influenced by the predominant and weak dispersive coefficients of the KP equation. The single soliton behavior has also been explained for the fast and slow magnetoacoustic modes.

New solitary wave solutions to the (2+1)-dimensional Calogero-Bogoyavlenskii-Schiff and the Kadomtsev-Petviashvili hierarchy equations

NASA Astrophysics Data System (ADS)

Baskonus, Haci Mehmet; Sulaiman, Tukur Abdulkadir; Bulut, Hasan

2017-10-01

In this paper, with the help of Wolfram Mathematica 9 we employ the powerful sine-Gordon expansion method in investigating the solution structures of the two well known nonlinear evolution equations, namely; Calogero-Bogoyavlenskii-Schiff and Kadomtsev-Petviashvili hierarchy equations. We obtain new solutions with complex, hyperbolic and trigonometric function structures. All the obtained solutions in this paper verified their corresponding equations. We also plot the three- and two-dimensional graphics of all the obtained solutions in this paper by using the same program in Wolfram Mathematica 9. We finally submit a comprehensive conclusion.

Existence and stability of dispersive solutions to the Kadomtsev-Petviashvili equation in the presence of dispersion effect

NASA Astrophysics Data System (ADS)

Das, Amiya; Ganguly, Asish

2017-07-01

The paper deals with Kadomtsev-Petviashvili (KP) equation in presence of a small dispersion effect. The nature of solutions are examined under the dispersion effect by using Lyapunov function and dynamical system theory. We prove that when dispersion is added to the KP equation, in certain regions, yet there exist bounded traveling wave solutions in the form of solitary waves, periodic and elliptic functions. The general solution of the equation with or without the dispersion effect are obtained in terms of Weirstrass ℘ functions and Jacobi elliptic functions. New form of kink-type solutions are established by exploring a new technique based on factorization method, use of functional transformation and the Abel's first order nonlinear equation. Furthermore, the stability analysis of the dispersive solutions are examined which shows that the traveling wave velocity is a bifurcation parameter which governs between different classes of waves. We use the phase plane analysis and show that at a critical velocity, the solution has a transcritical bifurcation.

Three dimensional cylindrical Kadomtsev-Petviashvili equation in a very dense electron-positron-ion plasma

DOE Office of Scientific and Technical Information (OSTI.GOV)

Moslem, W. M.; Sabry, R.; Shukla, P. K.

2010-03-15

By using the hydrodynamic equations of ions, Thomas-Fermi electron/positron density distribution, and Poisson equation, a three-dimensional cylindrical Kadomtsev-Petviashvili (CKP) equation is derived for small but finite amplitude ion-acoustic waves. The generalized expansion method is used to analytically solve the CKP equation. New class of solutions admits a train of well-separated bell-shaped periodic pulses is obtained. At certain condition, the latter degenerates to solitary wave solution. The effects of physical parameters on the solitary pulse structures are examined. Furthermore, the energy integral equation is used to study the existence regions of the localized pulses. The present study might be helpful tomore » understand the excitation of nonlinear ion-acoustic waves in a very dense astrophysical objects such as white dwarfs.« less

Characteristics of solitary waves, quasiperiodic solutions, homoclinic breather solutions and rogue waves in the generalized variable-coefficient forced Kadomtsev-Petviashvili equation

NASA Astrophysics Data System (ADS)

Yan, Xue-Wei; Tian, Shou-Fu; Dong, Min-Jie; Zou, Li

2017-12-01

In this paper, the generalized variable-coefficient forced Kadomtsev-Petviashvili (gvcfKP) equation is investigated, which can be used to characterize the water waves of long wavelength relating to nonlinear restoring forces. Using a dependent variable transformation and combining the Bell’s polynomials, we accurately derive the bilinear expression for the gvcfKP equation. By virtue of bilinear expression, its solitary waves are computed in a very direct method. By using the Riemann theta function, we derive the quasiperiodic solutions for the equation under some limitation factors. Besides, an effective way can be used to calculate its homoclinic breather waves and rogue waves, respectively, by using an extended homoclinic test function. We hope that our results can help enrich the dynamical behavior of the nonlinear wave equations with variable-coefficient.

Asymptotics for Large Time of Global Solutions to the Generalized Kadomtsev-Petviashvili Equation

NASA Astrophysics Data System (ADS)

Hayashi, Nakao; Naumkin, Pavel I.; Saut, Jean-Claude

We study the large time asymptotic behavior of solutions to the generalized Kadomtsev-Petviashvili (KP) equations where σ= 1 or σ=- 1. When ρ= 2 and σ=- 1, (KP) is known as the KPI equation, while ρ= 2, σ=+ 1 corresponds to the KPII equation. The KP equation models the propagation along the x-axis of nonlinear dispersive long waves on the surface of a fluid, when the variation along the y-axis proceeds slowly [10]. The case ρ= 3, σ=- 1 has been found in the modeling of sound waves in antiferromagnetics [15]. We prove that if ρ>= 3 is an integer and the initial data are sufficiently small, then the solution u of (KP) satisfies the following estimates: for all t∈R, where κ= 1 if ρ= 3 and κ= 0 if ρ>= 4. We also find the large time asymptotics for the solution.

Bright-dark and dark-dark solitons for the coupled cubic-quintic nonlinear Schrödinger equations in a twin-core nonlinear optical fiber

NASA Astrophysics Data System (ADS)

Yuan, Yu-Qiang; Tian, Bo; Liu, Lei; Chai, Han-Peng

2017-11-01

In this paper, we investigate the coupled cubic-quintic nonlinear Schrödinger equations, which can describe the effects of quintic nonlinearity on the ultrashort optical soliton pulse propagation in a twin-core nonlinear optical fiber. Through the Kadomtsev-Petviashvili hierarchy reduction, we present the bright-dark and dark-dark soliton solutions in terms of the Grammian for such equations. With the help of analytic and graphic analysis, head-on and overtaking elastic interactions between the two solitons are presented, as well as the bound-state solitons. Particularly, we find the inelastic interaction between the bright-dark two solitons. One of the electromagnetic fields presents the V-shape profile, while the other one presents the Y-shape profile.

Shock formation in the dispersionless Kadomtsev-Petviashvili equation

NASA Astrophysics Data System (ADS)

Grava, T.; Klein, C.; Eggers, J.

2016-04-01

The dispersionless Kadomtsev-Petviashvili (dKP) equation {{≤ft({{u}t}+u{{u}x}\\right)}x}={{u}yy} is one of the simplest nonlinear wave equations describing two-dimensional shocks. To solve the dKP equation numerically we use a coordinate transformation inspired by the method of characteristics for the one-dimensional Hopf equation {{u}t}+u{{u}x}=0 . We show numerically that the solutions to the transformed equation stays regular for longer times than the solution of the dKP equation. This permits us to extend the dKP solution as the graph of a multivalued function beyond the critical time when the gradients blow up. This overturned solution is multivalued in a lip shape region in the (x, y) plane, where the solution of the dKP equation exists in a weak sense only, and a shock front develops. A local expansion reveals the universal scaling structure of the shock, which after a suitable change of coordinates corresponds to a generic cusp catastrophe. We provide a heuristic derivation of the shock front position near the critical point for the solution of the dKP equation, and study the solution of the dKP equation when a small amount of dissipation is added. Using multiple-scale analysis, we show that in the limit of small dissipation and near the critical point of the dKP solution, the solution of the dissipative dKP equation converges to a Pearcey integral. We test and illustrate our results by detailed comparisons with numerical simulations of both the regularized equation, the dKP equation, and the asymptotic description given in terms of the Pearcey integral.

Solitons and the Inverse Scattering Transform

DTIC Science & Technology

1980-01-01

1979). 2. Small amplitude waves in more dimensions. (a) The equation of Kadomtsev and Petviashvili (1970), (ut + uux + au )x + Uyy = 0 , (1.6) is...337, 1978. Hasimoto, H. and I. Ono, J. Phys. Soc. Japan, vol. 33, p. 805, 1972. Kadomtsev , B. B. and V. I. Petviashvili , Sov. Phys. Doklady, vol. 15...Abstract "Under appropriate conditions, ocean waves may b modeled by certain nonlinear evolution equations that admit s iton solutions and can be solved

Modified equations, rational solutions, and the Painleve property for the Kadomtsev--Petviashvili and Hirota--Satsuma equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Weiss, J.

1985-09-01

We propose a method for finding the Lax pairs and rational solutions of integrable partial differential equations. That is, when an equation possesses the Painleve property, a Baecklund transformation is defined in terms of an expansion about the singular manifold. This Baecklund transformation obtains (1) a type of modified equation that is formulated in terms of Schwarzian derivatives and (2) a Miura transformation from the modified to the original equation. By linearizing the (Ricati-type) Miura transformation the Lax pair is found. On the other hand, consideration of the (distinct) Baecklund transformations of the modified equations provides a method for themore » iterative construction of rational solutions. This also obtains the Lax pairs for the modified equations. In this paper we apply this method to the Kadomtsev--Petviashvili equation and the Hirota--Satsuma equations.« less

Interaction Solutions for Lump-line Solitons and Lump-kink Waves of the Dimensionally Reduced Generalised KP Equation

NASA Astrophysics Data System (ADS)

Ahmed, Iftikhar

2017-09-01

In this work, we investigate dimensionally reduced generalised Kadomtsev-Petviashvili equation, which can describe many nonlinear phenomena in fluid dynamics. Based on the bilinear formalism, direct Maple symbolic computations are used with an ansätz function to construct three classes of interaction solutions between lump and line solitons. Furthermore, the dynamics of interaction phenomena is explained with 3D plots and 2D contour plots. For the first class of interaction solutions, lump appeared at t=0, and there was a normal interaction between lump and line solitons at t=1, 2, 5, and 10. For the second class of interaction solutions, lump appeared from one side of line soliton at t=0, but it started moving downward at t=1, 2, and 5. Finally, at t=10, this lump was completely swallowed by other side. By contrast, for the third class of interaction solutions, lump appeared from one side of line soliton at t=0, but it started moving upward at t=1, 2, and 5. Finally, at t=10, this lump was completely swallowed by other side. Furthermore, interaction solutions between lump solutions and kink wave are also investigated. These results might be helpful to understand the propagation processes for nonlinear waves in fluid mechanics.

Numerical study of blow-up and stability of line solitons for the Novikov-Veselov equation

NASA Astrophysics Data System (ADS)

Kazeykina, Anna; Klein, Christian

2017-07-01

We study numerically the evolution of perturbed Korteweg-de Vries solitons and of well localized initial data by the Novikov-Veselov (NV) equation at different levels of the ‘energy’ parameter E. We show that as \\vert E\\vert \\to ∞ , NV behaves, as expected, similarly to its formal limit, the Kadomtsev-Petviashvili equation. However at intermediate regimes, i.e. when \\vert E \\vert is not very large, more varied scenarios are possible, in particular, blow-ups are observed. The mechanism of the blow-up is studied.

Nonlinear structures: Cnoidal, soliton, and periodical waves in quantum semiconductor plasma

NASA Astrophysics Data System (ADS)

Tolba, R. E.; El-Bedwehy, N. A.; Moslem, W. M.; El-Labany, S. K.; Yahia, M. E.

2016-01-01

Properties and emerging conditions of various nonlinear acoustic waves in a three dimensional quantum semiconductor plasma are explored. A plasma fluid model characterized by degenerate pressures, exchange correlation, and quantum recoil forces is established and solved. Our analysis approach is based on the reductive perturbation theory for deriving the Kadomtsev-Petviashvili equation from the fluid model and solving it by using Painlevé analysis to come up with different nonlinear solutions that describe different pulse profiles such as cnoidal, soliton, and periodical pulses. The model is then employed to recognize the possible perturbations in GaN semiconductor.

Nonlinear structures: Cnoidal, soliton, and periodical waves in quantum semiconductor plasma

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tolba, R. E., E-mail: tolba-math@yahoo.com; El-Bedwehy, N. A., E-mail: nab-elbedwehy@yahoo.com; Moslem, W. M., E-mail: wmmoslem@hotmail.com

2016-01-15

Properties and emerging conditions of various nonlinear acoustic waves in a three dimensional quantum semiconductor plasma are explored. A plasma fluid model characterized by degenerate pressures, exchange correlation, and quantum recoil forces is established and solved. Our analysis approach is based on the reductive perturbation theory for deriving the Kadomtsev-Petviashvili equation from the fluid model and solving it by using Painlevé analysis to come up with different nonlinear solutions that describe different pulse profiles such as cnoidal, soliton, and periodical pulses. The model is then employed to recognize the possible perturbations in GaN semiconductor.

Solitons and SeaSat,

DTIC Science & Technology

1984-08-01

the Kadomtsev - • . Petviashvili (1) equations . A derivation of Eq. (1) in the case of . " * internal waves is given in reference (2). An important...second statement is demonstrated to be false. The% Kadomtsev -.1etviashvile equation relevant to Internal Waves is shown not to have SOliL -solutions. This...more than one space dimension. The second statement is demonstrated to be false. The Kadomtsev -Petviashvile equation relevant to Internal Waves Is

Extremely Fast Numerical Integration of Ocean Surface Wave Dynamics: Building Blocks for a Higher Order Method

DTIC Science & Technology

2006-09-30

equation known as the Kadomtsev - Petviashvili (KP) equation ): (ηt + coηx +αηηx + βη )x +γηyy = 0 (4) where γ = co / 2 . The KdV equation ...using the spectral formulation of the Kadomtsev - Petviashvili equation , a standard equation for nonlinear, shallow water wave dynamics that is a... Petviashvili and nonlinear Schroedinger equations and higher order corrections have been developed as prerequisites to coding the Boussinesq and Euler

Soliton and quasi-periodic wave solutions for b-type Kadomtsev-Petviashvili equation

NASA Astrophysics Data System (ADS)

Singh, Manjit; Gupta, R. K.

2017-11-01

In this paper, truncated Laurent expansion is used to obtain the bilinear equation of a nonlinear evolution equation. As an application of Hirota's method, multisoliton solutions are constructed from the bilinear equation. Extending the application of Hirota's method and employing multidimensional Riemann theta function, one and two-periodic wave solutions are also obtained in a straightforward manner. The asymptotic behavior of one and two-periodic wave solutions under small amplitude limits is presented, and their relations with soliton solutions are also demonstrated.

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.

Rogue waves and lump solutions for a (3+1)-dimensional generalized B-type Kadomtsev-Petviashvili equation in fluid mechanics

NASA Astrophysics Data System (ADS)

Wu, Xiao-Yu; Tian, Bo; Chai, Han-Peng; Sun, Yan

2017-08-01

Under investigation in this letter is a (3+1)-dimensional generalized B-type Kadomtsev-Petviashvili equation, which describes the weakly dispersive waves propagating in a fluid. Employing the Hirota method and symbolic computation, we obtain the lump, breather-wave and rogue-wave solutions under certain constraints. We graphically study the lump waves with the influence of the parameters h1, h3 and h5 which are all the real constants: When h1 increases, amplitude of the lump wave increases, and location of the peak moves; when h3 increases, lump wave’s amplitude decreases, but location of the peak keeps unchanged; when h5 changes, lump wave’s peak location moves, but amplitude keeps unchanged. Breather waves and rogue waves are displayed: Rogue waves emerge when the periods of the breather waves go to the infinity.

Extremely Fast Numerical Integration of Ocean Surface Wave Dynamics

DTIC Science & Technology

2007-09-30

sub-processor must be added as shown in the blue box of Fig. 1. We first consider the Kadomtsev - Petviashvili (KP) equation ηt + coηx +αηηx + βη ...analytic integration of the so-called “soliton equations ,” I have discovered how the GFT can be used to solved higher order equations for which study...analytical study and extremely fast numerical integration of the extended nonlinear Schroedinger equation for fully three dimensional wave motion

FAST TRACK COMMUNICATION: Soliton solutions of the KP equation with V-shape initial waves

NASA Astrophysics Data System (ADS)

Kodama, Y.; Oikawa, M.; Tsuji, H.

2009-08-01

We consider the initial value problems of the Kadomtsev-Petviashvili (KP) equation for symmetric V-shape initial waves consisting of two semi-infinite line solitons with the same amplitude. Those are particularly important for studies of large amplitude waves such as tsunami in shallow water. Numerical simulations show that the solutions of the initial value problem approach asymptotically to certain exact solutions of the KP equation found recently in [1]. We then use a chord diagram to explain the asymptotic result. This provides an analytical method to study asymptotic behavior for the initial value problem of the KP equation. We also demonstrate a real experiment of shallow water waves which may represent the solution discussed in this communication.

The Analytic Structures of Dynamical Systems.

DTIC Science & Technology

1986-01-01

equations , rational solutions, and the Painlev6 property for the Kadomtsev - Petviashvili and Hirota-Satsuma equations ", J. Math. Phys. 26 2174 (1985) 5...of rational solutions. This also obtains the Lax pairs for the modified equations . In this paper we apply this method to the Kadomtsev - Petviashvili ...3 . . . . .. .. ," ,",,....". . ".’..’.-.: -.... ., Modified equations , rational solutions, and the Painlev6 property for the Kadomtsev

Bright-dark solitons for a set of the general coupled nonlinear Schrödinger equations in a birefringent fiber

NASA Astrophysics Data System (ADS)

Yuan, Yu-Qiang; Tian, Bo; Liu, Lei; Sun, Yan

2017-11-01

Under investigation in this paper is the coupled nonlinear Schrödinger equations with the four-wave mixing term, which describe the optical solitons in a birefringent fiber. Via the Kadomtsev-Petviashvili hierarchy reduction, we obtain the N-bright-dark soliton solutions in terms of the Gram determinant. Propagation and interaction of the solitons corresponding to the electric fields in the two orthogonal polarizations are discussed and presented graphically. We find that the one bright-dark soliton possesses the periodic oscillation and exhibits the breather-like profile, which is different from that in the previous literature. Besides, for the one soliton, we observe that the larger velocity leads to the fiercer oscillation. Elastic interactions including the head-on and overtaking interactions between the two bright-dark solitons are demonstrated. Particularly, we find the oblique inelastic interaction between the two bright-dark solitons, which possess the V-shape profile in the zero background component and the Y-shape profile in the nonzero background component. Besides, we present two cases of the bound-state solitons. For the one case, the two solitons interact with each other all the time along a direction and for the other case, the resonance phenomenon is raised.

Rational Degenerations of M-Curves, Totally Positive Grassmannians and KP2-Solitons

NASA Astrophysics Data System (ADS)

Abenda, Simonetta; Grinevich, Petr G.

2018-03-01

We establish a new connection between the theory of totally positive Grassmannians and the theory of M-curves using the finite-gap theory for solitons of the KP equation. Here and in the following KP equation denotes the Kadomtsev-Petviashvili 2 equation [see (1)], which is the first flow from the KP hierarchy. We also assume that all KP times are real. We associate to any point of the real totally positive Grassmannian Gr^{tp} (N,M) a reducible curve which is a rational degeneration of an M-curve of minimal genus {g=N(M-N)} , and we reconstruct the real algebraic-geometric data á la Krichever for the underlying real bounded multiline KP soliton solutions. From this construction, it follows that these multiline solitons can be explicitly obtained by degenerating regular real finite-gap solutions corresponding to smooth M-curves. In our approach, we rule the addition of each new rational component to the spectral curve via an elementary Darboux transformation which corresponds to a section of a specific projection Gr^{tp} (r+1,M-N+r+1)\\mapsto Gr^{tp} (r,M-N+r).

Mixed lump-kink and rogue wave-kink solutions for a (3 + 1) -dimensional B-type Kadomtsev-Petviashvili equation in fluid mechanics

NASA Astrophysics Data System (ADS)

Hu, Cong-Cong; Tian, Bo; Wu, Xiao-Yu; Yuan, Yu-Qiang; Du, Zhong

2018-02-01

Under investigation is a (3 + 1) -dimensional B-type Kadomtsev-Petviashvili equation, which describes the weakly dispersive waves in a fluid. Via the Hirota method and symbolic computation, we obtain the mixed lump-kink and mixed rogue wave-kink solutions. Through the mixed lump-kink solutions, we observe three different phenomena between a lump and one kink. For the fusion phenomenon, a lump and a kink are merged with the lump's energy transferring into the kink gradually, until the lump merges into the kink completely. Fission phenomenon displays that a lump separates from a kink. The last phenomenon shows that a lump travels together with a kink with their amplitudes unchanged. In addition, we graphically study the interaction between a rogue wave and a pair of the kinks. It can be observed that the rogue wave arises from one kink and disappears into the other kink. At certain time, the amplitude of the rogue wave reaches the maximum.

The KP hierarchy with self-consistent sources: construction, Wronskian solutions and bilinear identities

NASA Astrophysics Data System (ADS)

Lin, Runliang; Liu, Xiaojun; Zeng, Yunbo

2014-10-01

In this paper, we will present some of our results on the soliton hierarchy with self-consistent sources (SHSCSs). The Kadomtsev-Petviashvili (KP) hierarchy will be used as an illustrative example to show the method to construct the SHSCSs. Some properties of the KP hierarchy with self-consistent sources will also be given, such as the dressing approach, the Wronskian solutions (including soliton solutions), its bilinear identities and the tau function.

Nonlinear excitations in electron-positron-ion plasmas in accretion disks of active galactic nuclei

DOE Office of Scientific and Technical Information (OSTI.GOV)

Moslem, W. M.; Kourakis, I.; Shukla, P. K.

2007-10-15

The propagation of acoustic nonlinear excitations in an electron-positron-ion (e-p-i) plasma composed of warm electrons and positrons, as well as hot ions, has been investigated by adopting a two-dimensional cylindrical geometry. The electrons and positrons are modeled by hydrodynamic fluid equations, while the ions are assumed to follow a temperature-parametrized Boltzmann distribution (the fixed ion model is recovered in the appropriate limit). This situation applies in the accretion disk near a black hole in active galactic nuclei, where the ion temperature may be as high as 3 to 300 times that of the electrons. Using a reductive perturbation technique, amore » cylindrical Kadomtsev-Petviashvili equation is derived and its exact soliton solutions are presented. Furthermore, real situations in which the strength of the nonlinearity may be weak are considered, so that higher-order nonlinearity plays an important role. Accordingly, an extended cylindrical Kadomtsev-Petviashvili equation is derived, which admits both soliton and double-layer solutions. The characteristics of the nonlinear excitations obtained are investigated in detail.« less

DOE Office of Scientific and Technical Information (OSTI.GOV)

Biondini, Gino

We study soliton solutions of the Kadomtsev-Petviashvili II equation (-4u{sub t}+6uu{sub x}+3u{sub xxx}){sub x}+u{sub yy}=0 in terms of the amplitudes and directions of the interacting solitons. In particular, we classify elastic N-soliton solutions, namely, solutions for which the number, directions, and amplitudes of the N asymptotic line solitons as y{yields}{infinity} coincide with those of the N asymptotic line solitons as y{yields}-{infinity}. We also show that the (2N-1){exclamation_point}{exclamation_point} types of solutions are uniquely characterized in terms of the individual soliton parameters, and we calculate the soliton position shifts arising from the interactions.

Optical Kerr Spatiotemporal Dark-Lump Dynamics of Hydrodynamic Origin

NASA Astrophysics Data System (ADS)

Baronio, Fabio; Wabnitz, Stefan; Kodama, Yuji

2016-04-01

There is considerable fundamental and applicative interest in obtaining nondiffractive and nondispersive spatiotemporal localized wave packets propagating in optical cubic nonlinear or Kerr media. Here, we analytically predict the existence of a novel family of spatiotemporal dark lump solitary wave solutions of the (2 +1 )D nonlinear Schrödinger equation. Dark lumps represent multidimensional holes of light on a continuous wave background. We analytically derive the dark lumps from the hydrodynamic exact soliton solutions of the (2 +1 )D shallow water Kadomtsev-Petviashvili model, inheriting their complex interaction properties. This finding opens a novel path for the excitation and control of optical spatiotemporal waveforms of hydrodynamic footprint and multidimensional optical extreme wave phenomena.

Optical Kerr Spatiotemporal Dark-Lump Dynamics of Hydrodynamic Origin.

PubMed

Baronio, Fabio; Wabnitz, Stefan; Kodama, Yuji

2016-04-29

There is considerable fundamental and applicative interest in obtaining nondiffractive and nondispersive spatiotemporal localized wave packets propagating in optical cubic nonlinear or Kerr media. Here, we analytically predict the existence of a novel family of spatiotemporal dark lump solitary wave solutions of the (2+1)D nonlinear Schrödinger equation. Dark lumps represent multidimensional holes of light on a continuous wave background. We analytically derive the dark lumps from the hydrodynamic exact soliton solutions of the (2+1)D shallow water Kadomtsev-Petviashvili model, inheriting their complex interaction properties. This finding opens a novel path for the excitation and control of optical spatiotemporal waveforms of hydrodynamic footprint and multidimensional optical extreme wave phenomena.

Darboux Transformation and N-soliton Solution for Extended Form of Modified Kadomtsev—Petviashvili Equation with Variable-Coefficient

NASA Astrophysics Data System (ADS)

Luo, Xing-Yu; Chen, Yong

2016-08-01

The extended form of modified Kadomtsev—Petviashvili equation with variable-coefficient is investigated in the framework of Painlevé analysis. The Lax pairs are obtained by analysing two Painlevé branches of this equation. Starting with the Lax pair, the N-times Darboux transformation is constructed and the N-soliton solution formula is given, which contains 2n free parameters and two arbitrary functions. Furthermore, with different combinations of the parameters, several types of soliton solutions are calculated from the first order to the third order. The regularity conditions are discussed in order to avoid the singularity of the solutions. Moreover, we construct the generalized Darboux transformation matrix by considering a special limiting process and find a rational-type solution for this equation. Supported by the Global Change Research Program of China under Grant No. 2015CB953904, National Natural Science Foundation of China under Grant Nos. 11275072 and 11435005, Doctoral Program of Higher Education of China under Grant No. 20120076110024, The Network Information Physics Calculation of basic research innovation research group of China under Grant No. 61321064, Shanghai Collaborative Innovation Center of Trustworthy Software for Internet of Things under Grant No. ZF1213, Shanghai Minhang District talents of high level scientific research project

Nonlinear Waves.

DTIC Science & Technology

1988-02-01

in Multi- dimensions II, P.M. Santini and A.S. Fokas, preprint INS#67, 1986. The Recursion Operator of the Kadomtsev - Petviashvili Equation and the...solitons, multidimensional inverse problems, Painleve equations , direct linearizations of certain nonlinear wave equations , DBAR problems, Riemann...the Navy is (a) the recent discovery that many of the equations describing ship hydrodynamics in channels of finite depth obey nonlinear equations

Effect of nonthermal electrons on the propagation characteristics and stability of two-dimensional nonlinear electrostatic coherent structures in relativistic electron positron ion plasmas

DOE Office of Scientific and Technical Information (OSTI.GOV)

Masood, W.; National Centre for Physics; Rizvi, H.

2011-06-15

Two-dimensional propagation of nonlinear ion acoustic shock and solitary waves in an unmagnetized plasma consisting of nonthermal electrons, Boltzmannian positrons, and singly charged hot ions streaming with relativistic velocities are investigated. The system of fluid equations is reduced to Kadomtsev-Petviashvili-Burgers and Kadomtsev-Petviashvili (KP) equations in the limit of small amplitude perturbation. The dependence of the ion acoustic shock and solitary waves on various plasma parameters are explored in detail. Interestingly, it is observed that increasing the nonthermal electron population increases the wave dispersion which enervates the strength of the ion acoustic shock wave; however, the same effect leads to anmore » enhancement of the soliton amplitude due to the absence of dissipation in the KP equation. The present investigation may be useful to understand the two-dimensional propagation characteristics of small but finite amplitude localized shock and solitary structures in planetary magnetospheres and auroral plasmas where nonthermal populations of electrons have been observed by several satellite missions.« less

Nonlinear Wave Propagation

DTIC Science & Technology

1989-05-22

multidimensional systems of physi- cal significance. Prototypes are the Kadomtsev - Petviashvili and Davey-Stewartson equations . The nature of the boundary value...Ono equation bears many similarities to multidimensional problems, specifically the Kadomtsev - Petviashvili equation . In some sense the nonlocality...Inverse scattering and Direct Linearizing Transforms for the Kadomtsev - Petviashvili Equations , A.S. Fokas, and M.J. Ablowitz, Phys. Lett. Vol., 94A, No. 2

Nonlinear Wave Propagation

DTIC Science & Technology

2000-03-17

scattering problem has intrinsic interest in its own right. A new class of lump type solutions of the multidimensional Kadomtsev - Petviashvili (KP) equation ...solutions associated with the Kadomtsev - Petviashvili equation have more com- plicated interaction properties than the previously known lump...B-3. New Solutions of the Nonstationary Schrödinger and Kadomtsev - Petviashvili Equations , M.J. Ablowitz and J. Villarroel, in Symmetries and

Parabola solitons for the nonautonomous KP equation in fluids and plasmas

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yu, Xin, E-mail: yuxin@buaa.edu.cn; Sun, Zhi-Yuan

Under investigation in this paper is a nonautonomous Kadomtsev–Petviashvili (KP) equation in fluids and plasmas. The integrability of this equation is examined via the Painlevé analysis and its multi-soliton solutions are constructed. A constraint is proposed to ensure the existence of parabola solitons for such KP equation. Based on the constructed solutions, the solitonic propagation and interaction, including the elastic interaction, inelastic interaction and soliton resonance for parabola solitons, are discussed. The results might be useful for shallow water wave and rogue wave.

Nonlinear Waves.

DTIC Science & Technology

1986-05-27

purposes will be the Korteweg-deVries (KdV) equation u, 6uu, u. , =0 (1) in one spatial dimension, and the Kadomtsev - Petviashvili (KP) equation (u, - 6uu...one temporal dimen- sion: the Modified Kadomtsev - Petviashvili II (MKPII), and Davey-Stewartson I (OSII) equation . The hyperoolic analogs of (1), (2...by introducing ’Ś an intermediate version of the equations associated with (1), an infinite family of conserva- Kadomtsev - Petviashvili equation

Nonlinear Wave Propagation

DTIC Science & Technology

1983-12-30

Transform for the Kadomtsev - Petviashvili Equation , M.J. Ablowitz , D. Bar Yaacov and A.S. Fokas, to appear in Stud. in Appl. Math. I.N.S. #21 preprint...Benjamin-Ono equation bears many similariti to the multidimensional problem, especially the Kadomtsev - Petviashvili equation . We discuss many of these...appear in Stud. in Appl. Math. I.N.S. #22 preprint, 1982. 67. On the Inverse Scattering Transform for the Kadomtsev - Petviashvili Equation , M.J. Ablowitz

Nonplanar KdV and KP equations for quantum electron-positron-ion plasma

NASA Astrophysics Data System (ADS)

Dutta, Debjit

2015-12-01

Nonlinear quantum ion-acoustic waves with the effects of nonplanar cylindrical geometry, quantum corrections, and transverse perturbations are studied. By using the standard reductive perturbation technique, a cylindrical Kadomtsev-Petviashvili equation for ion-acoustic waves is derived by incorporating quantum-mechanical effects. The quantum-mechanical effects via quantum diffraction and quantum statistics and the role of transverse perturbations in cylindrical geometry on the dynamics of this wave are studied analytically. It is found that the dynamics of ion-acoustic solitary waves (IASWs) is governed by a three-dimensional cylindrical Kadomtsev-Petviashvili equation (CKPE). The results could help in a theoretical analysis of astrophysical and laser produced plasmas.

Nonlinear Ocean Waves

DTIC Science & Technology

1994-09-30

equation due to Kadomtsev & Petviashvili (1970), Dx(atu + 6 ui)u + a8 3U) + 3 ay2u = 0, (KP) is known to describe approximately the evolution of...to be stable to perturbations, and their amplitudes need not be small. The Kadomtsev - Petviashvili (KP) equation is known to describe approximately the...predicted with reasonable accuracy by a family of exact solutions of an equation due to Kadomtsev and Petviashvili (1970): (ft + 6 ffx + f )x + 3fyy

Nonlinear Wave Propagation.

DTIC Science & Technology

1987-11-23

e.g. the Kadomtsev - Petviashvili . Davey-Stewartson, and three-wave interaction equations -see for example the review [11]). little progress has been made... equations for our purposes will be the Korteweg-deVries (KdV) equation u, - 6uu., + u, =0 ( ) in one spatial dimension, and the Kadomtsev - Petviashvili (KP...similarities with KP [4] than with u, =sin u, (2) KdV (the IST for (5) has been recently considered and the Kadomtsev - Petviashvili (KP) equation in ref. [ 5

Aspects of Integrability in One and Several Dimensions,

DTIC Science & Technology

1986-01-01

Kadomtsev - Petviashvili (KP) equation , the modified KdV to the modified KP, the non-linear Schr6d- inger to the Davey-Stewartson, etc. Furthermore...but a function de- noted in 20 by T12. This function also generates recursion operators in analogy with T. i % 61 4. THE KADOMTSEV - PETVIASHVILI EQUATION ...and its Appl., 19 L • 11 (1985). [41] Caudrey, P.J., Discrete and Periodic Spectral Transforms Related to the Kadomtsev - Petviashvili Equation (preprint

KPII: Cauchy-Jost function, Darboux transformations and totally nonnegative matrices

NASA Astrophysics Data System (ADS)

Boiti, M.; Pempinelli, F.; Pogrebkov, A. K.

2017-07-01

Direct definition of the Cauchy-Jost (known also as Cauchy-Baker-Akhiezer) function is given in the case of a pure solitonic solution. Properties of this function are discussed in detail using the Kadomtsev-Petviashvili II equation as an example. This enables formulation of the Darboux transformations in terms of the Cauchy-Jost function and classification of these transformations. Action of Darboux transformations on Grassmanians—i.e. on the space of soliton parameters—is derived and the relation of the Darboux transformations with the property of total nonnegativity of elements of corresponding Grassmanians is discussed. To the memory of our friend and colleague Peter P Kulish

Multicomponent integrable reductions in the Kadomtsev-Petviashvilli hierarchy

NASA Astrophysics Data System (ADS)

Sidorenko, Jurij; Strampp, Walter

1993-04-01

New types of reductions of the Kadomtsev-Petviashvili (KP) hierarchy are considered on the basis of Sato's approach. Within this approach the KP hierarchy is represented by infinite sets of equations for potentials u2,u3,..., of pseudodifferential operators and their eigenfunctions Ψ and adjoint eigenfunctions Ψ*. The KP hierarchy was studied under constraints of the following type (∑ni=1 ΨiΨ*i)x = Sκ,x where Sκ,x are symmetries for the KP equation and Ψi(λi), Ψ*i(λi) are eigenfunctions with eigenvalue λi. It is shown that for the first three cases κ=2,3,4 these constraints give rise to hierarchies of 1+1-dimensional commuting flows for the variables u2, Ψ1,...,Ψn, Ψ*1,...,Ψ*n. Bi-Hamiltonian structures for the new hierarchies are presented.

Nonlinear Problems in Fluid Dynamics and Inverse Scattering

DTIC Science & Technology

1993-05-31

nonlinear Kadomtsev - Petviashvili (KP) equations , have solutions which will become infinite in finite time. This phenomenon is sometimes referred to as...40 (November 1992). 4 7. Wave Collapse and Instability of Solitary Waves of a Generalized Nonlinear Kaoiomtsev- Petviashvili Equation , X.P. Wang, M.J...words) The inverse scattering of a class of differential-difference equations and multidimensional operators has been constructed. Solutions of nonlinear

Nearshore Wave and Circulation Modelling

DTIC Science & Technology

1998-02-01

1995), "The unified Kadomtsev - Petviashvili equation for interfacial waves," J. Fluid Mech., 288, 383-408. Chen, Y. and Liu, P. L.-F. (1996), "On...modified Kadomtsev - Petviashvili equation for interfacial wave propagation near the critical depth level," Wave Motion (to appear). Cox, D. T. and Kobayashi...94-13. Chen, Y. and Liu, P.L.-F. (1995), "Numerical Study of the Unified Kadomtsev - Petviashvili Equation ," CACR-95-04. Chen, Y. and Liu, P.L.-F

Breather soliton dynamics in microresonators

NASA Astrophysics Data System (ADS)

Yu, Mengjie; Jang, Jae K.; Okawachi, Yoshitomo; Griffith, Austin G.; Luke, Kevin; Miller, Steven A.; Ji, Xingchen; Lipson, Michal; Gaeta, Alexander L.

2017-02-01

The generation of temporal cavity solitons in microresonators results in coherent low-noise optical frequency combs that are critical for applications in spectroscopy, astronomy, navigation or telecommunications. Breather solitons also form an important part of many different classes of nonlinear wave systems, manifesting themselves as a localized temporal structure that exhibits oscillatory behaviour. To date, the dynamics of breather solitons in microresonators remains largely unexplored, and its experimental characterization is challenging. Here we demonstrate the excitation of breather solitons in two different microresonator platforms based on silicon nitride and on silicon. We investigate the dependence of the breathing frequency on pump detuning and observe the transition from period-1 to period-2 oscillation. Our study constitutes a significant contribution to understanding the soliton dynamics within the larger context of nonlinear science.

Soliton-type solutions for two models in mathematical physics

NASA Astrophysics Data System (ADS)

Al-Ghafri, K. S.

2018-04-01

In this paper, the generalised Klein-Gordon and Kadomtsov-Petviashvili Benjamin-Bona-Mahony equations with power law nonlinearity are investigated. Our study is based on reducing the form of both equations to a first-order ordinary differential equation having the travelling wave solutions. Subsequently, soliton-type solutions such as compacton and solitary pattern solutions are obtained analytically. Additionally, the peaked soliton has been derived where it exists under a specific restrictions. In addition to the soliton solutions, the mathematical method which is exploited in this work also creates a few amount of travelling wave solutions.

An Analytical Model of Periodic Waves in Shallow Water,

DTIC Science & Technology

1984-07-01

the KP equation , "f’ + 6f +x + 3 f 0 (1.8) "’ S(t o x yy describes their evolution if they are weakly two-dimensional ( Kadomtsev & Petviashvili ...directions. Both short-crested and long-crested waves are available from the model. Every wave pattern is an exact solution of the Kadomtsev - Petviashvili ...vol. 9, pp 65-66 Kadomtsev , B. B. & V. I. Petviashvili , 1970, Soy. Phys. Doklady, vol. 15, pp 539-541 Korteweg, D. J. & G. de~ries, 1895, Phil Mag

Research in Nonlinear Motion.

DTIC Science & Technology

1984-06-30

solved one version of the Kadomtsev - Petviashvili equation , (ut + 6uux + U )x - 3uyy, (KP) on the plane (- * < x, y < -). Nanakov’s results were formal...dimensions. 3. Periodic Waves In Shallow Water The other version of the Kadomtsev - Petviashvili equation is (ut + 6uux U )x 3Uy 0. (KP2) Both equations have...A. I. P. Conf. Proc. #88, ed. by M. Tabor & Y. M. Treve, 1982, with T. Bountis. 14. "Comments on Inverse Scattering for the Kadomtsev - Petviashvili

Atmospheric Fluctuations Which Lead to Trackable Radar Signals in the Marine Boundary Layer.

DTIC Science & Technology

1981-07-01

Eq. (3.14) should be replaced by the Kadomtsev - Petviashvili equation , 36 (uT + 6 uux + UXXX) + Unn 0 , (3.15) where n is measured along the crest of...the wave (e.g., see Kadomtsev and Petviashvili , 1970; or Ablowitz and Segur, 1979). Other balances are possible as well. Equations (3.14) and (3.15) are...R., (197z); "Atmospheric Gravity Waves from Winds and Storms", J. Atmos. Sci. 29, 445-456. Kadomtsev , B. B., and Petviashvili , V. I., (1970); "On the

Light Meets Water in Nonlocal Media: Surface Tension Analogue in Optics

NASA Astrophysics Data System (ADS)

Horikis, Theodoros P.; Frantzeskakis, Dimitrios J.

2017-06-01

Shallow water wave phenomena find their analogue in optics through a nonlocal nonlinear Schrödinger (NLS) model in 2 +1 dimensions. We identify an analogue of surface tension in optics, namely, a single parameter depending on the degree of nonlocality, which changes the sign of dispersion, much like surface tension does in the shallow water wave problem. Using multiscale expansions, we reduce the NLS model to a Kadomtsev-Petviashvili (KP) equation, which is of the KPII (KPI) type, for strong (weak) nonlocality. We demonstrate the emergence of robust optical antidark solitons forming Y -, X -, and H -shaped wave patterns, which are approximated by colliding KPII line solitons, similar to those observed in shallow waters.

Light Meets Water in Nonlocal Media: Surface Tension Analogue in Optics.

PubMed

Horikis, Theodoros P; Frantzeskakis, Dimitrios J

2017-06-16

Shallow water wave phenomena find their analogue in optics through a nonlocal nonlinear Schrödinger (NLS) model in 2+1 dimensions. We identify an analogue of surface tension in optics, namely, a single parameter depending on the degree of nonlocality, which changes the sign of dispersion, much like surface tension does in the shallow water wave problem. Using multiscale expansions, we reduce the NLS model to a Kadomtsev-Petviashvili (KP) equation, which is of the KPII (KPI) type, for strong (weak) nonlocality. We demonstrate the emergence of robust optical antidark solitons forming Y-, X-, and H-shaped wave patterns, which are approximated by colliding KPII line solitons, similar to those observed in shallow waters.

Note on Solutions to a Class of Nonlinear Singular Integro-Differential Equations,

DTIC Science & Technology

1986-08-01

KdV) ut + 2uu x +Uxx x a 0, (1) the sine-Gordon equation Uxt a sin u, (2) and the Kadomtsev - Petviashvili (KP) equation (Ut + 2uu x + UXXx)x -3a 2u yy...SOUIN OA LSFNN ! /" / M.. \\boiz A.S ::-:- and ,M.O.. .- :1/1 / NOTE ON SOLUTIONS TO A CLASS OF NON \\ / LINEAR SINGULAR INTEGRO-DIFFERENTIA[ EQUATIONS by...important nonlinear evolution equations which can be linearized. Many of these equations fall into the category of linearization via soliton theory and

Nonlinear Mechanisms for the Generation of Nearshore Wave Phenomena.

DTIC Science & Technology

1988-04-01

Kadomtsev - Petviashvili equation . Numerical solutions of this equation indicate that steady state is reached only if dispersion is negative; otherwise...leads to a forced Kadomtsev - Petviashvili equation . Numerical solutions of this equation indicate that steady state is reached only if dispersion is

Bäcklund transformation, infinitely-many conservation laws, solitary and periodic waves of an extended (3 + 1)-dimensional Jimbo-Miwa equation with time-dependent coefficients

NASA Astrophysics Data System (ADS)

Deng, Gao-Fu; Gao, Yi-Tian; Gao, Xin-Yi

2018-07-01

In this paper, an extended (3+1)-dimensional Jimbo-Miwa equation with time-dependent coefficients is investigated, which comes from the second member of the Kadomtsev-Petviashvili hierarchy and is shown to be conditionally integrable. Bilinear form, Bäcklund transformation, Lax pair and infinitely-many conservation laws are derived via the binary Bell polynomials and symbolic computation. With the help of the bilinear form, one-, two- and three-soliton solutions are obtained via the Hirota method, one-periodic wave solutions are constructed via the Riemann theta function. Additionally, propagation and interaction of the solitons are investigated analytically and graphically, from which we find that the interaction between the solitons is elastic and the time-dependent coefficients can affect the soliton velocities, but the soliton amplitudes remain unchanged. One-periodic waves approach the one-solitary waves with the amplitudes vanishing and can be viewed as a superposition of the overlapping solitary waves, placed one period apart.

Exact solution of CKP equation and formation and interaction of two solitons in pair-ion-electron plasma

DOE Office of Scientific and Technical Information (OSTI.GOV)

Batool, Nazia; Jahangir, R.; National Center of Physics

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–demore » Vries equation. The importance of the present investigation to understand the formation and interaction of solitons in laboratory produced pair plasmas is also highlighted.« less

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

NASA Astrophysics Data System (ADS)

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

2003-03-01

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

Two dimensional cylindrical fast magnetoacoustic solitary waves in a dust plasma

DOE Office of Scientific and Technical Information (OSTI.GOV)

Liu Haifeng; Wang Shiqing; Engineering and Technical College of Chengdu University of Technology, Leshan 614000

2011-04-15

The nonlinear fast magnetoacoustic solitary waves in a dust plasma with the combined effects of bounded cylindrical geometry and transverse perturbation are investigated in a new equation. In this regard, cylindrical Kadomtsev-Petviashvili (CKP) equation is derived using the small amplitude perturbation expansion method. Under a suitable coordinate transformation, the CKP equation can be solved analytically. It is shown that the dust cylindrical fast magnetoacoustic solitary waves can exist in the CKP equation. The present investigation may have relevance in the study of nonlinear electromagnetic soliton waves both in laboratory and astrophysical plasmas.

Waveguide coupling in the few-cycle regime

NASA Astrophysics Data System (ADS)

Leblond, Hervé; Terniche, Said

2016-04-01

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

Integrable hierarchies of Heisenberg ferromagnet equation

NASA Astrophysics Data System (ADS)

Nugmanova, G.; Azimkhanova, A.

2016-08-01

In this paper we consider the coupled Kadomtsev-Petviashvili system. From compatibility conditions we obtain the form of matrix operators. After using a gauge transformation, obtained a new type of Lax representation for the hierarchy of Heisenberg ferromagnet equation, which is equivalent to the gauge coupled Kadomtsev-Petviashvili system.

Boundary Conditions for Infinite Conservation Laws

NASA Astrophysics Data System (ADS)

Rosenhaus, V.; Bruzón, M. S.; Gandarias, M. L.

2016-12-01

Regular soliton equations (KdV, sine-Gordon, NLS) are known to possess infinite sets of local conservation laws. Some other classes of nonlinear PDE possess infinite-dimensional symmetries parametrized by arbitrary functions of independent or dependent variables; among them are Zabolotskaya-Khokhlov, Kadomtsev-Petviashvili, Davey-Stewartson equations and Born-Infeld equation. Boundary conditions were shown to play an important role for the existence of local conservation laws associated with infinite-dimensional symmetries. In this paper, we analyze boundary conditions for the infinite conserved densities of regular soliton equations: KdV, potential KdV, Sine-Gordon equation, and nonlinear Schrödinger equation, and compare them with boundary conditions for the conserved densities obtained from infinite-dimensional symmetries with arbitrary functions of independent and dependent variables.

Secondary Bifurcation and Change of Type for Three Dimensional Standing Waves in Shallow Water.

DTIC Science & Technology

1986-02-01

field of standing K-P waves. A set of two non-interacting (to first order) solutions of the K-P equation ( Kadomtsev - Petviashvili 1970). The K-P equation ...P equation was first derived by Kadomtsev & Petviashvili (1970) in their study of the stability of solitary waves to transverse perturbations. A...Scientists, Springer-Verlag 6. B.A. Dubrovin (1981), "Theta Functions and Non-linear Equations ", Russian Mat. Surveys, 36, 11-92 7 B.B. Kadomtsev

Dark soliton dynamics and interactions in continuous-wave-induced lattices.

PubMed

Tsopelas, Ilias; Kominis, Yannis; Hizanidis, Kyriakos

2007-10-01

The dynamics of dark spatial soliton beams and their interaction under the presence of a continuous wave (CW), which dynamically induces a photonic lattice, are investigated. It is shown that appropriate selection of the characteristic parameters of the CW result in controllable steering of a single soliton as well as controllable interaction between two solitons. Depending on the CW parameters, the soliton angle of propagation can be changed drastically, while two-soliton interaction can be either enhanced or reduced, suggesting a reconfigurable soliton control mechanism. Our analytical approach, based on the variational perturbation method, provides a dynamical system for the dark soliton evolution parameters. Analytical results are shown in good agreement with direct numerical simulations.

On the dispersionless Kadomtsev-Petviashvili equation with arbitrary nonlinearity and dimensionality: exact solutions, longtime asymptotics of the Cauchy problem, wave breaking and shocks

NASA Astrophysics Data System (ADS)

Santucci, F.; Santini, P. M.

2016-10-01

We study the generalization of the dispersionless Kadomtsev-Petviashvili (dKP) equation in n+1 dimensions and with nonlinearity of degree m+1, a model equation describing the propagation of weakly nonlinear, quasi one-dimensional waves in the absence of dispersion and dissipation, and arising in several physical contexts, like acoustics, plasma physics, hydrodynamics and nonlinear optics. In 2 + 1 dimensions and with quadratic nonlinearity, this equation is integrable through a novel inverse scattering transform, and it has been recently shown to be a prototype model equation in the description of the two-dimensional wave breaking of localized initial data. In higher dimensions and with higher nonlinearity, the generalized dKP equations are not integrable, but their invariance under motions on the paraboloid allows one to construct in this paper a family of exact solutions describing waves constant on their paraboloidal wave front and breaking simultaneously in all points of it, developing after breaking either multivaluedness or single-valued discontinuous profiles (shocks). Then such exact solutions are used to build the longtime behavior of the solutions of the Cauchy problem, for small and localized initial data, showing that wave breaking of small initial data takes place in the longtime regime if and only if m(n-1)≤slant 2. Lastly, the analytic aspects of such wave breaking are investigated in detail in terms of the small initial data, in both cases in which the solution becomes multivalued after breaking or it develops a shock. These results, contained in the 2012 master’s thesis of one of the authors (FS) [1], generalize those obtained in [2] for the dKP equation in n+1 dimensions with quadratic nonlinearity, and are obtained following the same strategy.

Dark-Bright Soliton Dynamics Beyond the Mean-Field Approximation

NASA Astrophysics Data System (ADS)

Katsimiga, Garyfallia; Koutentakis, Georgios; Mistakidis, Simeon; Kevrekidis, Panagiotis; Schmelcher, Peter; Theory Group of Fundamental Processes in Quantum Physics Team

2017-04-01

The dynamics of dark bright solitons beyond the mean-field approximation is investigated. We first examine the case of a single dark-bright soliton and its oscillations within a parabolic trap. Subsequently, we move to the setting of collisions, comparing the mean-field approximation to that involving multiple orbitals in both the dark and the bright component. Fragmentation is present and significantly affects the dynamics, especially in the case of slower solitons and in that of lower atom numbers. It is shown that the presence of fragmentation allows for bipartite entanglement between the distinguishable species. Most importantly the interplay between fragmentation and entanglement leads to the decay of each of the initial mean-field dark-bright solitons into fast and slow fragmented dark-bright structures. A variety of excitations including dark-bright solitons in multiple (concurrently populated) orbitals is observed. Dark-antidark states and domain-wall-bright soliton complexes can also be observed to arise spontaneously in the beyond mean-field dynamics. Deutsche Forschungsgemeinschaft (DFG) in the framework of the SFB 925 ``Light induced dynamics and control of correlated quantum systems''.

Multi-Periodic Waves in Shallow Water

DTIC Science & Technology

1992-09-01

models-the Kadomtsev - Petviashvili (KP) equation . The KP equation describes the evolu- tion of weakly nonlinear, weakly two-dimensional waves on water of...experimentally. The analytical model is a family of periodic solutions of the Kadomtsev -Petviashuili equation . The experiments demonstrate the accuracy... Petviashvili Equation (with Norman Schef- fner & Harvey Segur). Proceedings, Nonlinear Water Waves Workshop, University of Bristol. England, 1991. Resonant

Dark solitons in laser radiation build-up dynamics.

PubMed

Woodward, R I; Kelleher, E J R

2016-03-01

We reveal the existence of slowly decaying dark solitons in the radiation build-up dynamics of bright pulses in all-normal dispersion mode-locked fiber lasers, numerically modeled in the framework of a generalized nonlinear Schrödinger equation. The evolution of noise perturbations to quasistationary dark solitons is examined, and the significance of background shape and soliton-soliton collisions on the eventual soliton decay is established. We demonstrate the role of a restoring force in extending soliton interactions in conservative systems to include the effects of dissipation, as encountered in laser cavities, and generalize our observations to other nonlinear systems.

Nonlocal Symmetry and Interaction Solutions of a Generalized Kadomtsev—Petviashvili Equation

NASA Astrophysics Data System (ADS)

Huang, Li-Li; Chen, Yong; Ma, Zheng-Yi

2016-08-01

A generalized Kadomtsev—Petviashvili equation is studied by nonlocal symmetry method and consistent Riccati expansion (CRE) method in this paper. Applying the truncated Painlevé analysis to the generalized Kadomtsev—Petviashvili equation, some Bäcklund transformations (BTs) including auto-BT and non-auto-BT are obtained. The auto-BT leads to a nonlocal symmetry which corresponds to the residual of the truncated Painlevé expansion. Then the nonlocal symmetry is localized to the corresponding nonlocal group by introducing two new variables. Further, by applying the Lie point symmetry method to the prolonged system, a new type of finite symmetry transformation is derived. In addition, the generalized Kadomtsev—Petviashvili equation is proved consistent Riccati expansion (CRE) solvable. As a result, the soliton-cnoidal wave interaction solutions of the equation are explicitly given, which are difficult to be found by other traditional methods. Moreover, figures are given out to show the properties of the explicit analytic interaction solutions. Supported by the Global Change Research Program of China under Grant No. 2015CB953904, National Natural Science Foundation of under Grant Nos. 11275072 and 11435005, Doctoral Program of Higher Education of China under Grant No. 20120076110024, the Network Information Physics Calculation of Basic Research Innovation Research Group of China under Grant No. 61321064, and Shanghai Collaborative Innovation Center of Trustworthy Software for Internet of Things under Grant No. ZF1213, and Zhejiang Provincial Natural Science Foundation of China under Grant No. LY14A010005

Spherical solitons in Earth’S mesosphere plasma

DOE Office of Scientific and Technical Information (OSTI.GOV)

Annou, K., E-mail: kannou@cdta.dz; Annou, R.

2016-01-15

Soliton formation in Earth’s mesosphere plasma is described. Nonlinear acoustic waves in plasmas with two-temperature ions and a variable dust charge where transverse perturbation is dealt with are studied in bounded spherical geometry. Using the perturbation method, a spherical Kadomtsev–Petviashvili equation that describes dust acoustic waves is derived. It is found that the parameters taken into account have significant effects on the properties of nonlinear waves in spherical geometry.

Recursion Operators and Bi-Hamiltonian Structures in Multidimensions II,

DTIC Science & Technology

1986-07-01

a Symmifetry (1.2). For example the Kadomtsev - Petviashvili (KP) equation and the Davey-Stewartson (DS) equation admit two such hierarchies of...Degasperis, Nuovo Cimento, 398, 1 (1977). [16] P. Caudrey, Discrete and Periodic Spectral Transforms Related to the Kadomtsev - Petviashvili Equation ...these equations possess infinitely many time dependent symmetries and constants of motion. The master symmetries T for these equations are simply derived

Soliton Dynamics of an Atomic Spinor Condensate on a Ring Lattice

DTIC Science & Technology

2013-02-22

REPORT Soliton dynamics of an atomic spinor condensate on a Ring Lattice 14. ABSTRACT 16. SECURITY CLASSIFICATION OF: We study the dynamics of...8/98) Prescribed by ANSI Std. Z39.18 - Soliton dynamics of an atomic spinor condensate on a Ring Lattice Report Title ABSTRACT We study the dynamics...Report Number Soliton dynamics of an atomic spinor condensat Block 13: Supplementary Note © 2013 . Published in Physical Review A (accepted), Vol. Ed

Cauchy-Jost function and hierarchy of integrable equations

NASA Astrophysics Data System (ADS)

Boiti, M.; Pempinelli, F.; Pogrebkov, A. K.

2015-11-01

We describe the properties of the Cauchy-Jost (also known as Cauchy-Baker-Akhiezer) function of the Kadomtsev-Petviashvili-II equation. Using the bar partial -method, we show that for this function, all equations of the Kadomtsev-Petviashvili-II hierarchy are given in a compact and explicit form, including equations for the Cauchy-Jost function itself, time evolutions of the Jost solutions, and evolutions of the potential of the heat equation.

Nonlinear dynamics of 3D beams of fast magnetosonic waves propagating in the ionospheric and magnetospheric plasma

NASA Astrophysics Data System (ADS)

Belashov, V. Yu.; Belashova, E. S.

2016-11-01

On the basis of the model of the three-dimensional (3D) generalized Kadomtsev-Petviashvili equation for magnetic field h = B / B the formation, stability, and dynamics of 3D soliton-like structures, such as the beams of fast magnetosonic (FMS) waves generated in ionospheric and magnetospheric plasma at a low-frequency branch of oscillations when β = 4 πnT/ B 2 ≪ 1 and β > 1, are studied. The study takes into account the highest dispersion correction determined by values of the plasma parameters and the angle θ = ( B, k), which plays a key role in the FMS beam propagation at those angles to the magnetic field that are close to π/2. The stability of multidimensional solutions is studied by an investigation of the Hamiltonian boundness under its deformations on the basis of solving of the corresponding variational problem. The evolution and dynamics of the 3D FMS wave beam are studied by the numerical integration of equations with the use of specially developed methods. The results can be interpreted in terms of the self-focusing phenomenon, as the formation of a stationary beam and the scattering and self-focusing of the solitary beam of FMS waves. These cases were studied with a detailed investigation of all evolutionary stages of the 3D FMS wave beams in the ionospheric and magnetospheric plasma.

Generation of dark solitons and their instability dynamics in two-dimensional condensates

NASA Astrophysics Data System (ADS)

Verma, Gunjan; Rapol, Umakant D.; Nath, Rejish

2017-04-01

We analyze numerically the formation and the subsequent dynamics of two-dimensional matter wave dark solitons in a Thomas-Fermi rubidium condensate using various techniques. An initially imprinted sharp phase gradient leads to the dynamical formation of a stationary soliton as well as very shallow gray solitons, whereas a smooth gradient only creates gray solitons. The depth and hence, the velocity of the soliton is provided by the spatial width of the phase gradient, and it also strongly influences the snake-instability dynamics of the two-dimensional solitons. The vortex dipoles stemming from the unstable soliton exhibit rich dynamics. Notably, the annihilation of a vortex dipole via a transient dark lump or a vortexonium state, the exchange of vortices between either a pair of vortex dipoles or a vortex dipole and a single vortex, and so on. For sufficiently large width of the initial phase gradient, the solitons may decay directly into vortexoniums instead of vortex pairs, and also the decay rate is augmented. Later, we discuss alternative techniques to generate dark solitons, which involve a Gaussian potential barrier and time-dependent interactions, both linear and periodic. The properties of the solitons can be controlled by tuning the amplitude or the width of the potential barrier. In the linear case, the number of solitons and their depths are determined by the quench time of the interactions. For the periodic modulation, a transient soliton lattice emerges with its periodicity depending on the modulation frequency, through a wave number selection governed by the local Bogoliubov spectrum. Interestingly, for sufficiently low barrier potential, both Faraday pattern and soliton lattice coexist. The snake instability dynamics of the soliton lattice is characteristically modified if the Faraday pattern is present.

Adiabatic Invariant Approach to Transverse Instability: Landau Dynamics of Soliton Filaments.

PubMed

Kevrekidis, P G; Wang, Wenlong; Carretero-González, R; Frantzeskakis, D J

2017-06-16

Consider a lower-dimensional solitonic structure embedded in a higher-dimensional space, e.g., a 1D dark soliton embedded in 2D space, a ring dark soliton in 2D space, a spherical shell soliton in 3D space, etc. By extending the Landau dynamics approach [Phys. Rev. Lett. 93, 240403 (2004)PRLTAO0031-900710.1103/PhysRevLett.93.240403], we show that it is possible to capture the transverse dynamical modes (the "Kelvin modes") of the undulation of this "soliton filament" within the higher-dimensional space. These are the transverse stability or instability modes and are the ones potentially responsible for the breakup of the soliton into structures such as vortices, vortex rings, etc. We present the theory and case examples in 2D and 3D, corroborating the results by numerical stability and dynamical computations.

Quantum many-body dynamics of dark solitons in optical lattices

NASA Astrophysics Data System (ADS)

Mishmash, R. V.; Danshita, I.; Clark, Charles W.; Carr, L. D.

2009-11-01

We present a fully quantum many-body treatment of dark solitons formed by ultracold bosonic atoms in one-dimensional optical lattices. Using time-evolving block decimation to simulate the single-band Bose-Hubbard Hamiltonian, we consider the quantum dynamics of density and phase engineered dark solitons as well as the quantum evolution of mean-field dark solitons injected into the quantum model. The former approach directly models how one may create quantum entangled dark solitons in experiment. While we have already presented results regarding the latter approach elsewhere [R. V. Mishmash and L. D. Carr, Phys. Rev. Lett. 103, 140403 (2009)], we expand upon those results in this work. In both cases, quantum fluctuations cause the dark soliton to fill in and may induce an inelasticity in soliton-soliton collisions. Comparisons are made to the Bogoliubov theory which predicts depletion into an anomalous mode that fills in the soliton. Our many-body treatment allows us to go beyond the Bogoliubov approximation and calculate explicitly the dynamics of the system’s natural orbitals.

A Few New 2+1-Dimensional Nonlinear Dynamics and the Representation of Riemann Curvature Tensors

NASA Astrophysics Data System (ADS)

Wang, Yan; Zhang, Yufeng; Zhang, Xiangzhi

2016-09-01

We first introduced a linear stationary equation with a quadratic operator in ∂x and ∂y, then a linear evolution equation is given by N-order polynomials of eigenfunctions. As applications, by taking N=2, we derived a (2+1)-dimensional generalized linear heat equation with two constant parameters associative with a symmetric space. When taking N=3, a pair of generalized Kadomtsev-Petviashvili equations with the same eigenvalues with the case of N=2 are generated. Similarly, a second-order flow associative with a homogeneous space is derived from the integrability condition of the two linear equations, which is a (2+1)-dimensional hyperbolic equation. When N=3, the third second flow associative with the homogeneous space is generated, which is a pair of new generalized Kadomtsev-Petviashvili equations. Finally, as an application of a Hermitian symmetric space, we established a pair of spectral problems to obtain a new (2+1)-dimensional generalized Schrödinger equation, which is expressed by the Riemann curvature tensors.

Integrable Equations in Multi-Dimensions (2+1) are Bi-Hamiltonian Systems,

DTIC Science & Technology

1987-02-01

equation [18]. It should be noted that the 80 equation has more similarities [19] with the Kadomtsev - Petviashvili (KP...Cimento, 39B, 1 (1977). [31] P. Caudrey, Discrete and Periodic Spectral Transforms Related to the Kadomtsev - Petviashvili Equation , preprint U.M.I.S.T. (1985). II ’AI D p-I 4, - -- - -- - - -w 4 ...TOM NONLINEAR STUDIES IDTIC I IELEC )// MAR 2 51988 I / \\ / Integrable Equations in Multi- dimensions (2+1) are Bi-Hamiltonian Systems by A.S.

Different evolution dynamics of vector solitons depending on their polarization states

NASA Astrophysics Data System (ADS)

Chen, Wei-Cheng; Chen, Guo-Jie

2014-03-01

There are three types of temporal evolution dynamics of vector solitons observed in a ring fiber laser with a semiconductor saturable absorption mirror (SESAM) as a mode-locker. It is found that the polarization property of vector solitons is an important factor for achieving different evolution dynamics. The vector soliton with a uniform polarization state across the whole pulse profile and zero polarization extinction ratio operates at a fundamental repetition rate with a single pulse profile. The elliptically polarized vector soliton with a larger polarization extinction ratio exhibits a harmonic pulse train. The soliton bunching with multi-peak structures exists between the above two states and shows elliptical polarization with a small polarization extinction ratio.

Dynamic trapping of a polarization rotation vector soliton in a fiber laser.

PubMed

Liu, Meng; Luo, Ai-Ping; Luo, Zhi-Chao; Xu, Wen-Cheng

2017-01-15

Ultrafast fiber laser, as a dissipative nonlinear optical system, plays an important role in investigating various nonlinear phenomena and soliton dynamics. Vector features of solitons, including polarization locked and polarization rotation vector solitons (PRVSs), are interesting nonlinear dynamics in ultrafast fiber lasers. Herein, we experimentally reveal the trapping characteristics of PRVSs for the first time, to the best of our best knowledge. We show that, for the conventional soliton trapping in the ultrafast fiber laser, the soliton central wavelengths of the two polarization components are constant at the laser output port. However, it is found that the dynamic trapping can be observed for the PRVS. That is, the peak frequencies along the two orthogonal polarization directions are dynamically alternating, depending on the relative intensities of the two polarization components. The obtained results would further unveil the physical mechanism of PRVSs.

Real-time spectral interferometry probes the internal dynamics of femtosecond soliton molecules

NASA Astrophysics Data System (ADS)

Herink, G.; Kurtz, F.; Jalali, B.; Solli, D. R.; Ropers, C.

2017-04-01

Solitons, particle-like excitations ubiquitous in many fields of physics, have been shown to exhibit bound states akin to molecules. The formation of such temporal soliton bound states and their internal dynamics have escaped direct experimental observation. By means of an emerging time-stretch technique, we resolve the evolution of femtosecond soliton molecules in the cavity of a few-cycle mode-locked laser. We track two- and three-soliton bound states over hundreds of thousands of consecutive cavity roundtrips, identifying fixed points and periodic and aperiodic molecular orbits. A class of trajectories acquires a path-dependent geometrical phase, implying that its dynamics may be topologically protected. These findings highlight the importance of real-time detection in resolving interactions in complex nonlinear systems, including the dynamics of soliton bound states, breathers, and rogue waves.

Sasa-Satsuma higher-order nonlinear Schrödinger equation and its bilinearization and multisoliton solutions.

PubMed

Gilson, C; Hietarinta, J; Nimmo, J; Ohta, Y

2003-07-01

Higher-order and multicomponent generalizations of the nonlinear Schrödinger equation are important in various applications, e.g., in optics. One of these equations, the integrable Sasa-Satsuma equation, has particularly interesting soliton solutions. Unfortunately, the construction of multisoliton solutions to this equation presents difficulties due to its complicated bilinearization. We discuss briefly some previous attempts and then give the correct bilinearization based on the interpretation of the Sasa-Satsuma equation as a reduction of the three-component Kadomtsev-Petviashvili hierarchy. In the process, we also get bilinearizations and multisoliton formulas for a two-component generalization of the Sasa-Satsuma equation (the Yajima-Oikawa-Tasgal-Potasek model), and for a (2+1)-dimensional generalization.

Propagation of cylindrical ion acoustic waves in a plasma with q-nonextensive electrons with nonthermal distribution

NASA Astrophysics Data System (ADS)

El-Depsy, A.; Selim, M. M.

2016-12-01

The propagation of ion acoustic waves (IAWs) in a cylindrical collisionless unmagnetized plasma, containing ions and electrons is investigated. The electrons are considered to be nonextensive and follow nonthermal distribution. The reductive perturbation technique (RPT) is used to obtain a nonlinear cylindrical Kadomtsev-Petviashvili (CKP) evolution equation. This equation is solved analytically. The effects of plasma parameters on the IAWs characteristics are discussed in details. Both compressive and rarefactive solitons are found to be created in the proposed plasma system. The profile of IAWs is found to depend on the nonextensive and nonthermal parameters. The present study is useful for understanding IAWs in the regions where mixed electron distribution in space, or laboratory plasmas, exist.

Nonlinear Ocean Waves

DTIC Science & Technology

1993-01-12

work is the fact that the equation due to Kadomtsev & Petviashvili (1970), ax(atU + UaxU + a, 3 U) + ay2 U = 0, (KP) describes approximately the...B.B. Kadomtsev & V.1 Petviashvili , Soy. Phys. Doklady, 15, pp. 539- 541, 1970 NTI QRIA@lo310 For, STis GRAU ], DTIC TAB 0 jJUSo catzio DiSt AV ...numerical discretizations of the nonlinear Schr6dinger equation , i atV + axEV + 21VI2V = 0, (NLS) with periodic boundary conditions. This equation is a well

Dynamics of defect-induced dark solitons in an exciton-polariton condensate

NASA Astrophysics Data System (ADS)

Opala, Andrzej; Pieczarka, Maciej; Bobrovska, Nataliya; Matuszewski, Michał

2018-04-01

We study theoretically the emission of dark solitons induced by a moving defect in a nonresonantly pumped exciton-polariton condensate. The number of created dark solitons per unit of time is found to be strongly dependent on the pump power. We relate the observed dynamics of this process to the oscillations of the drag force experienced by the condensate. We investigate the stability of the polariton quantum fluid and present various types of dynamics depending on the condensate and moving obstacle parameters. Furthermore, we provide analytical expressions for dark soliton dynamics using the variational method adapted to the nonequilibrium polariton system. The determined dynamical equations are found to be in excellent agreement with the results of numerical simulations.

Paraxial Stage of the Spatiotemporal Dynamics of Loop Solitons

NASA Astrophysics Data System (ADS)

Sazonov, Sergey V.

2018-03-01

Using the averaged Lagrangian method, an analytic study of the spatiotemporal dynamics of extremely short loop solitons of the generalized Vakhnenko-Schäfer-Wayne equation is carried out. The conditions under which soliton propagation occurs in the modes of defocusing and self-focusing are determined. It is shown that transverse defocusing is accompanied by a temporal compression of the soliton and a decrease in its amplitude. At the same time, with transverse self-focusing, its temporal broadening and peak amplification occur.

Universal dynamics and deterministic switching of dissipative Kerr solitons in optical microresonators

NASA Astrophysics Data System (ADS)

Guo, H.; Karpov, M.; Lucas, E.; Kordts, A.; Pfeiffer, M. H. P.; Brasch, V.; Lihachev, G.; Lobanov, V. E.; Gorodetsky, M. L.; Kippenberg, T. J.

2017-01-01

Temporal dissipative Kerr solitons in optical microresonators enable the generation of ultrashort pulses and low-noise frequency combs at microwave repetition rates. They have been demonstrated in a growing number of microresonator platforms, enabling chip-scale frequency combs, optical synthesis of low-noise microwaves and multichannel coherent communications. In all these applications, accessing and maintaining a single-soliton state is a key requirement--one that remains an outstanding challenge. Here, we study the dynamics of multiple-soliton states and report the discovery of a simple mechanism that deterministically switches the soliton state by reducing the number of solitons one by one. We demonstrate this control in Si3N4 and MgF2 resonators and, moreover, we observe a secondary peak to emerge in the response of the system to a pump modulation, an effect uniquely associated with the soliton regime. Exploiting this feature, we map the multi-stability diagram of a microresonator experimentally. Our measurements show the physical mechanism of the soliton switching and provide insight into soliton dynamics in microresonators. The technique provides a method to sequentially reduce, monitor and stabilize an arbitrary state with solitons, in particular allowing for feedback stabilization of single-soliton states, which is necessary for practical applications.

Ultrafast spectral dynamics of dual-color-soliton intracavity collision in a mode-locked fiber laser

NASA Astrophysics Data System (ADS)

Wei, Yuan; Li, Bowen; Wei, Xiaoming; Yu, Ying; Wong, Kenneth K. Y.

2018-02-01

The single-shot spectral dynamics of dual-color-soliton collisions inside a mode-locked laser is experimentally and numerically investigated. By using the all-optically dispersive Fourier transform, we spectrally unveil the collision-induced soliton self-reshaping process, which features dynamic spectral fringes over the soliton main lobe, and the rebuilding of Kelly sidebands with wavelength drifting. Meanwhile, the numerical simulations validate the experimental observation and provide additional insights into the physical mechanism of the collision-induced spectral dynamics from the temporal domain perspective. It is verified that the dynamic interference between the soliton and the dispersive waves is responsible for the observed collision-induced spectral evolution. These dynamic phenomena not only demonstrate the role of dispersive waves in the sophisticated soliton interaction inside the laser cavity, but also facilitate a deeper understanding of the soliton's inherent stability.

Nonplanar dust-ion acoustic shock waves with transverse perturbation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Xue Jukui

2005-01-01

The nonlinear dust-ion acoustic shock waves in dusty plasmas with the combined effects of bounded cylindrical/spherical geometry, the transverse perturbation, the dust charge fluctuation, and the nonthermal electrons are studied. Using the perturbation method, a cylindrical/spherical Kadomtsev-Petviashvili Burgers equation that describes the dust-ion acoustic shock waves is deduced. A particular solution of the cylindrical/spherical Kadomtsev-Petviashvili Burgers equation is also obtained. It is shown that the dust-ion acoustic shock wave propagating in cylindrical/spherical geometry with transverse perturbation will be slightly deformed as time goes on.

Upstream-advancing waves generated by three-dimensional moving disturbances

NASA Astrophysics Data System (ADS)

Lee, Seung-Joon; Grimshaw, Roger H. J.

1990-02-01

The wave field resulting from a surface pressure or a bottom topography in a horizontally unbounded domain is studied. Upstream-advancing waves successively generated by various forcing disturbances moving with near-resonant speeds are found by numerically solving a forced Kadomtsev-Petviashvili (fKP) equation, which shows in its simplest form the interplay of a basic linear wave operator, longitudinal and transverse dispersion, nonlinearity, and forcing. Curved solitary waves are found as a slowly varying similarity solution of the Kadomtsev-Petviashvili (KP) equation, and are favorably compared with the upstream-advancing waves numerically obtained.

Bent dark soliton dynamics in two spatial dimensions beyond the mean field approximation

NASA Astrophysics Data System (ADS)

Mistakidis, Simeon; Katsimiga, Garyfallia; Koutentakis, Georgios; Kevrekidis, Panagiotis; Schmelcher, Peter; Theory Group of Fundamental Processes in Quantum Physics Team

2017-04-01

The dynamics of a bented dark soliton embedded in two spatial dimensions beyond the mean-field approximation is explored. We examine the case of a single bented dark soliton comparing the mean-field approximation to a correlated approach that involves multiple orbitals. Fragmentation is generally present and significantly affects the dynamics, especially in the case of stronger interparticle interactions and in that of lower atom numbers. It is shown that the presence of fragmentation allows for the appearance of solitonic and vortex structures in the higher-orbital dynamics. In particular, a variety of excitations including dark solitons in multiple orbitals and vortex-antidark complexes is observed to arise spontaneously within the beyond mean-field dynamics. Deutsche Forschungsgemeinschaft (DFG) in the framework of the SFB 925 ``Light induced dynamics and control of correlated quantum systems''.

Kuznetsov-Ma Soliton Dynamics Based on the Mechanical Effect of Light

NASA Astrophysics Data System (ADS)

Xiong, Hao; Gan, Jinghui; Wu, Ying

2017-10-01

A Kuznetsov-Ma soliton that exhibits an unusual pulsating dynamics has attracted particular attention in hydrodynamics and plasma physics in the context of understanding nonlinear coherent phenomena. Here, we demonstrate theoretically the formation of a novel form of Kuznetsov-Ma soliton in a microfabricated optomechanical array, where both photonic and phononic evolutionary dynamics exhibit periodic structure and coherent localized behavior enabled by radiation-pressure coupling of optical fields and mechanical oscillations, which is a manifestation of the unique property of optomechanical systems. Numerical calculations of the optomechanical dynamics show an excellent agreement with this theory. In addition to providing insight into optomechanical nonlinearity, optomechanical Kuznetsov-Ma soliton dynamics fundamentally broadens the regime of cavity optomechanics and may find applications in on-chip manipulation of light propagation.

Dark-soliton dynamics in Bose-Einstein condensates at finite temperature

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jackson, B.; Proukakis, N. P.; Barenghi, C. F.

2007-05-15

The dynamics of a dark soliton in an elongated Bose-Einstein condensate is studied at finite temperatures. In addition to accurately reproducing all stages of the decay of the soliton observed in the experiment of Burger et al. [Phys. Rev. Lett. 83, 5198 (1999)], our numerical simulations reveal the existence of an experimentally accessible parameter regime for which phase-imprinted dark solitons can execute at least one full axial oscillation prior to their decay. The dependence of the decay time scale on temperature and initial soliton depth is analyzed and the role of interatomic collisions quantified.

Dynamics of generalized sine-Gordon soliton in inhomogeneous media

NASA Astrophysics Data System (ADS)

Gharaati, A.; Khordad, R.

2011-03-01

In this paper we introduce a few novel generalized sine-Gordon equations and study the dynamics of its solitons in inhomogeneous media. We consider length, mass, gravitational acceleration and spring stiffness of a coupled pendulums chain as a function of position x. Then in the continuum limit we derive semi-analytical and numerical soliton solutions of the modified sine-Gordon equation in the inhomogeneous media. The obtained results confirm that the behavior of solitons in these media is similar to that of a classical point particle moved in an external potential.

The KP Approximation Under a Weak Coriolis Forcing

NASA Astrophysics Data System (ADS)

Melinand, Benjamin

2018-02-01

In this paper, we study the asymptotic behavior of weakly transverse water-waves under a weak Coriolis forcing in the long wave regime. We derive the Boussinesq-Coriolis equations in this setting and we provide a rigorous justification of this model. Then, from these equations, we derive two other asymptotic models. When the Coriolis forcing is weak, we fully justify the rotation-modified Kadomtsev-Petviashvili equation (also called Grimshaw-Melville equation). When the Coriolis forcing is very weak, we rigorously justify the Kadomtsev-Petviashvili equation. This work provides the first mathematical justification of the KP approximation under a Coriolis forcing.

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

PubMed

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

2001-08-01

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

Dynamic behavior of ion acoustic waves in electron-positron-ion magnetoplasmas with superthermal electrons and positrons

DOE Office of Scientific and Technical Information (OSTI.GOV)

Saha, Asit, E-mail: asit-saha123@rediffmail.com, E-mail: prasantachatterjee1@rediffmail.com; Department of Mathematics, Siksha Bhavana, Visva Bharati University, Santiniketan-731235; Pal, Nikhil

The dynamic behavior of ion acoustic waves in electron-positron-ion magnetoplasmas with superthermal electrons and positrons has been investigated in the framework of perturbed and non-perturbed Kadomtsev-Petviashili (KP) equations. Applying the reductive perturbation technique, we have derived the KP equation in electron-positron-ion magnetoplasma with kappa distributed electrons and positrons. Bifurcations of ion acoustic traveling waves of the KP equation are presented. Using the bifurcation theory of planar dynamical systems, the existence of the solitary wave solutions and the periodic traveling wave solutions has been established. Two exact solutions of these waves have been derived depending on the system parameters. Then, usingmore » the Hirota's direct method, we have obtained two-soliton and three-soliton solutions of the KP equation. The effect of the spectral index κ on propagations of the two-soliton and the three-soliton has been shown. Considering an external periodic perturbation, we have presented the quasi periodic behavior of ion acoustic waves in electron-positron-ion magnetoplasmas.« less

Novel tunable dynamic tweezers using dark-bright soliton collision control in an optical add/drop filter.

PubMed

Teeka, Chat; Jalil, Muhammad Arif; Yupapin, Preecha P; Ali, Jalil

2010-12-01

We propose a novel system of the dynamic optical tweezers generated by a dark soliton in the fiber optic loop. A dark soliton known as an optical tweezer is amplified and tuned within the microring resonator system. The required tunable tweezers with different widths and powers can be controlled. The analysis of dark-bright soliton conversion using a dark soliton pulse propagating within a microring resonator system is analyzed. The dynamic behaviors of soliton conversion in add/drop filter is also analyzed. The control dark soliton is input into the system via the add port of the add/drop filter. The dynamic behavior of the dark-bright soliton conversion is observed. The required stable signal is obtained via a drop and throughput ports of the add/drop filter with some suitable parameters. In application, the trapped light/atom and transportation can be realized by using the proposed system.

The effects of five-order nonlinear on the dynamics of dark solitons in optical fiber.

PubMed

He, Feng-Tao; Wang, Xiao-Lin; Duan, Zuo-Liang

2013-01-01

We study the influence of five-order nonlinear on the dynamic of dark soliton. Starting from the cubic-quintic nonlinear Schrodinger equation with the quadratic phase chirp term, by using a similarity transformation technique, we give the exact solution of dark soliton and calculate the precise expressions of dark soliton's width, amplitude, wave central position, and wave velocity which can describe the dynamic behavior of soliton's evolution. From two different kinds of quadratic phase chirps, we mainly analyze the effect on dark soliton's dynamics which different fiver-order nonlinear term generates. The results show the following two points with quintic nonlinearities coefficient increasing: (1) if the coefficients of the quadratic phase chirp term relate to the propagation distance, the solitary wave displays a periodic change and the soliton's width increases, while its amplitude and wave velocity reduce. (2) If the coefficients of the quadratic phase chirp term do not depend on propagation distance, the wave function only emerges in a fixed area. The soliton's width increases, while its amplitude and the wave velocity reduce.

The Effects of Five-Order Nonlinear on the Dynamics of Dark Solitons in Optical Fiber

PubMed Central

Wang, Xiao-Lin; Duan, Zuo-Liang

2013-01-01

We study the influence of five-order nonlinear on the dynamic of dark soliton. Starting from the cubic-quintic nonlinear Schrodinger equation with the quadratic phase chirp term, by using a similarity transformation technique, we give the exact solution of dark soliton and calculate the precise expressions of dark soliton's width, amplitude, wave central position, and wave velocity which can describe the dynamic behavior of soliton's evolution. From two different kinds of quadratic phase chirps, we mainly analyze the effect on dark soliton's dynamics which different fiver-order nonlinear term generates. The results show the following two points with quintic nonlinearities coefficient increasing: (1) if the coefficients of the quadratic phase chirp term relate to the propagation distance, the solitary wave displays a periodic change and the soliton's width increases, while its amplitude and wave velocity reduce. (2) If the coefficients of the quadratic phase chirp term do not depend on propagation distance, the wave function only emerges in a fixed area. The soliton's width increases, while its amplitude and the wave velocity reduce. PMID:23818814

Solitons riding on solitons and the quantum Newton's cradle.

PubMed

Ma, Manjun; Navarro, R; Carretero-González, R

2016-02-01

The reduced dynamics for dark and bright soliton chains in the one-dimensional nonlinear Schrödinger equation is used to study the behavior of collective compression waves corresponding to Toda lattice solitons. We coin the term hypersoliton to describe such solitary waves riding on a chain of solitons. It is observed that in the case of dark soliton chains, the formulated reduction dynamics provides an accurate an robust evolution of traveling hypersolitons. As an application to Bose-Einstein condensates trapped in a standard harmonic potential, we study the case of a finite dark soliton chain confined at the center of the trap. When the central chain is hit by a dark soliton, the energy is transferred through the chain as a hypersoliton that, in turn, ejects a dark soliton on the other end of the chain that, as it returns from its excursion up the trap, hits the central chain repeating the process. This periodic evolution is an analog of the classical Newton's cradle.

Real-time full-field characterization of transient dissipative soliton dynamics in a mode-locked laser

NASA Astrophysics Data System (ADS)

Ryczkowski, P.; Närhi, M.; Billet, C.; Merolla, J.-M.; Genty, G.; Dudley, J. M.

2018-04-01

Dissipative solitons are remarkably localized states of a physical system that arise from the dynamical balance between nonlinearity, dispersion and environmental energy exchange. They are the most universal form of soliton that can exist, and are seen in far-from-equilibrium systems in many fields, including chemistry, biology and physics. There has been particular interest in studying their properties in mode-locked lasers, but experiments have been limited by the inability to track the dynamical soliton evolution in real time. Here, we use simultaneous dispersive Fourier transform and time-lens measurements to completely characterize the spectral and temporal evolution of ultrashort dissipative solitons as their dynamics pass through a transient unstable regime with complex break-up and collisions before stabilization. Further insight is obtained from reconstruction of the soliton amplitude and phase and calculation of the corresponding complex-valued eigenvalue spectrum. These findings show how real-time measurements provide new insights into ultrafast transient dynamics in optics.

Dark-dark-soliton dynamics in two density-coupled Bose-Einstein condensates

NASA Astrophysics Data System (ADS)

Morera, I.; Mateo, A. Muñoz; Polls, A.; Juliá-Díaz, B.

2018-04-01

We study the one-dimensional dynamics of dark-dark solitons in the miscible regime of two density-coupled Bose-Einstein condensates having repulsive interparticle interactions within each condensate (g >0 ). By using an adiabatic perturbation theory in the parameter g12/g , we show that, contrary to the case of two solitons in scalar condensates, the interactions between solitons are attractive when the interparticle interactions between condensates are repulsive g12>0 . As a result, the relative motion of dark solitons with equal chemical potential μ is well approximated by harmonic oscillations of angular frequency wr=(μ /ℏ ) √{(8 /15 ) g12/g } . We also show that, in finite systems, the resonance of this anomalous excitation mode with the spin-density mode of lowest energy gives rise to alternating dynamical instability and stability fringes as a function of the perturbative parameter. In the presence of harmonic trapping (with angular frequency Ω ) the solitons are driven by the superposition of two harmonic motions at a frequency given by w2=(Ω/√{2 }) 2+wr2 . When g12<0 , these two oscillators compete to give rise to an overall effective potential that can be either single well or double well through a pitchfork bifurcation. All our theoretical results are compared with numerical solutions of the Gross-Pitaevskii equation for the dynamics and the Bogoliubov equations for the linear stability. A good agreement is found between them.

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

PubMed

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

2012-05-01

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

Solitary waves with weak transverse perturbations in quantum dusty plasmas

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ur-Rehman, H.; Masood, W.; Siddiq, M.

2008-12-15

Using the quantum hydrodynamic model, quantum dust ion-acoustic solitary waves are investigated in the presence of weak transverse perturbations. The linear dispersion relation is obtained using the Fourier analysis. The two-dimensional (2D) propagation of small amplitude nonlinear waves is studied by deriving the Kadomtsev-Petviashvili (KP) equation. The traveling wave solution of the KP equation is obtained by employing the tanh method. By dint of this solution, the effects of quantum Bohm pressure and the dust concentration on the 2D solitary structure are studied. The effect of quantum Bohm potential on the stability of the KP soliton is also investigated. Themore » results are supported by the numerical analysis and the relevance of the present investigation in dense astrophysical environments is also pointed out.« less

An Analytical Model of Periodic Waves in Shallow Water--Summary.

DTIC Science & Technology

1984-01-01

Petviashvili equation , and is based on a Riemann theta function of genus 2. These bi-periodic waves are direct generalizations of the well-known (simply... Petviashvili (KP; 1970) equation , (ut 6uux + U ) 3uyy -0, (1) is a scaled, dimensionless equation that describes the evolution of long water waves of...Fluid Mech., vol. 92, pp 691-715 Dubrovin, B. A., 1981, Russ. Math. Surveys, vol. 36, pp 11-92 Kadomtsev , B. B. & V. I. Petviashvili , 1970,) Soy. Phys

Non-integrable dynamics of matter-wave solitons in a density-dependent gauge theory

NASA Astrophysics Data System (ADS)

Dingwall, R. J.; Edmonds, M. J.; Helm, J. L.; Malomed, B. A.; Öhberg, P.

2018-04-01

We study interactions between bright matter-wave solitons which acquire chiral transport dynamics due to an optically-induced density-dependent gauge potential. Through numerical simulations, we find that the collision dynamics feature several non-integrable phenomena, from inelastic collisions including population transfer and radiation losses to the formation of short-lived bound states and soliton fission. An effective quasi-particle model for the interaction between the solitons is derived by means of a variational approximation, which demonstrates that the inelastic nature of the collision arises from a coupling of the gauge field to velocities of the solitons. In addition, we derive a set of interaction potentials which show that the influence of the gauge field appears as a short-range potential, that can give rise to both attractive and repulsive interactions.

Cylindrical fast magnetosonic solitary waves in quantum degenerate electron-positron-ion plasma

NASA Astrophysics Data System (ADS)

Abdikian, A.

2018-02-01

The nonlinear properties of fast magnetosonic solitary waves in a quantum degenerate electron-positron (e-p) plasma in the presence of stationary ions for neutralizing the plasma background of bounded cylindrical geometry were studied. By employing the standard reductive perturbation technique and the quantum hydrodynamic model for the e-p fluid, the cylindrical Kadomtsev-Petviashvili (CKP) equation was derived for small, but finite, amplitude waves and was given the solitary wave solution for the parameters relevant to dense astrophysical objects such as white dwarf stars. By a suitable coordinate transformation, the CKP equation can be solved analytically. An analytical solution for magnetosonic solitons and periodic waves is presented. The numerical results reveal that the Bohm potential has a main effect on the periodic and solitary wave structures. By increasing the values of the plasma parameters, the amplitude of the solitary wave will be increased. The present study may be helpful in the understanding of nonlinear electromagnetic soliton waves propagating in both laboratory and astrophysical plasmas, and can help in providing good agreement between theoretical results and laboratory plasma experiments.

Statics and dynamics of atomic dark-bright solitons in the presence of impurities

DOE Office of Scientific and Technical Information (OSTI.GOV)

Achilleos, V.; Frantzeskakis, D. J.; Kevrekidis, P. G.

2011-11-15

Adopting a mean-field description for a two-component atomic Bose-Einstein condensate, we study the statics and dynamics of dark-bright solitons in the presence of localized impurities. We use adiabatic perturbation theory to derive an equation of motion for the dark-bright soliton center. We show that, counterintuitively, an attractive (repulsive) delta-like impurity, acting solely on the bright-soliton component, induces an effective localized barrier (well) in the effective potential felt by the soliton; this way, dark-bright solitons are reflected from (transmitted through) attractive (repulsive) impurities. Our analytical results for the small-amplitude oscillations of solitons are found to be in good agreement with resultsmore » obtained via a Bogoliubov-de Gennes analysis and direct numerical simulations.« less

Cylindrical dust acoustic solitary waves with transverse perturbations in quantum dusty plasmas

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mushtaq, A.

2007-11-15

The nonlinear quantum dust acoustic waves with effects of nonplanar cylindrical geometry, quantum corrections, and transverse perturbations are studied. By using the perturbation method, a cylindrical Kadomtsev-Petviashvili equation for dust acoustic waves is derived by incorporating quantum-mechanical effects. The quantum-mechanical effects via quantum diffraction and quantum statistics, and the role of transverse perturbations in cylindrical geometry on the dynamics of this wave, are studied both analytically and numerically.

Dynamics of vector dark solitons propagation and tunneling effect in the variable coefficient coupled nonlinear Schrödinger equation.

PubMed

Musammil, N M; Porsezian, K; Subha, P A; Nithyanandan, K

2017-02-01

We investigate the dynamics of vector dark solitons propagation using variable coefficient coupled nonlinear Schrödinger (Vc-CNLS) equation. The dark soliton propagation and evolution dynamics in the inhomogeneous system are studied analytically by employing the Hirota bilinear method. It is apparent from our asymptotic analysis that the collision between the dark solitons is elastic in nature. The various inhomogeneous effects on the evolution and interaction between dark solitons are explored, with a particular emphasis on nonlinear tunneling. It is found that the tunneling of the soliton depends on a condition related to the height of the barrier and the amplitude of the soliton. The intensity of the tunneling soliton either forms a peak or a valley, thus retaining its shape after tunneling. For the case of exponential background, the soliton tends to compress after tunneling through the barrier/well. Thus, a comprehensive study of dark soliton pulse evolution and propagation dynamics in Vc-CNLS equation is presented in the paper.

Two dimensional nonplanar evolution of electrostatic shock waves in pair-ion plasmas

DOE Office of Scientific and Technical Information (OSTI.GOV)

Masood, W.; Rizvi, H.

2012-01-15

Electrostatic waves in a two dimensional nonplanar geometry are studied in an unmagnetized, dissipative pair-ion plasma in the presence of weak transverse perturbations. The dissipation in the system is taken into account by incorporating the kinematic viscosity of both positive and negative ions in plasmas. The nonplanar Kadomtsev-Petviashvili-Burgers (KPB) as well as the Burgers Kadomtsev-Petviashvili (Burgers KP) equations are derived using the small amplitude expansion method and the range of applicability of both the equations are discussed. The system under consideration is observed to admit compressive rarefactive shocks. The present study may have relevance to understand the formation of twomore » dimensional nonplanar electrostatic shocks in laboratory plasmas.« less

Quasi-ideal dynamics of vortex solitons embedded in flattop nonlinear Bessel beams.

PubMed

Porras, Miguel A; Ramos, Francisco

2017-09-01

The applications of vortex solitons are severely limited by the diffraction and self-defocusing spreading of the background beam where they are nested. Nonlinear Bessel beams in self-defocusing media are nondiffracting, flattop beams where the nested vortex solitons can survive for propagation distances that are one order of magnitude larger than in the Gaussian or super-Gaussian beams. The dynamics of the vortex solitons is studied numerically and found to approach that in the ideal, uniform background, preventing vortex spiraling and decay, which eases vortex steering for applications.

On the evolution of perturbations to solutions of the Kadomtsev-Petviashvilli equation using the Benney-Luke equation

NASA Astrophysics Data System (ADS)

Ablowitz, Mark J.; Curtis, Christopher W.

2011-05-01

The Benney-Luke equation, which arises as a long wave asymptotic approximation of water waves, contains the Kadomtsev-Petviashvilli (KP) equation as a leading-order maximal balanced approximation. The question analyzed is how the Benney-Luke equation modifies the so-called web solutions of the KP equation. It is found that the Benney-Luke equation introduces dispersive radiation which breaks each of the symmetric soliton-like humps well away from the interaction region of the KP web solution into a tail of multi-peaked oscillating profiles behind the main solitary hump. Computation indicates that the wave structure is modified near the center of the interaction region. Both analytical and numerical techniques are employed for working with non-periodic, non-decaying solutions on unbounded domains.

A Fluid Dynamic Approach to the Dust-Acoustic Soliton

NASA Astrophysics Data System (ADS)

McKenzie, J. F.; Doyle, T. B.

2002-12-01

The properties of dust-acoustic solitons are derived from a fluid dynamic viewpoint in which conservation of total momentum, combined with the Bernoulli-like energy equations for each species, yields the structure equation for the heavy (or dust) speed in the stationary wave. This fully nonlinear approach reveals the crucial role played by the heavy sonic point in limiting the collective dust-acoustic Mach number, above which solitons cannot exist. An exact solution illustrates that the cold heavy species is compressed and this implies concomitant contraints on the potential and on the flow speed of the electrons and protons in the wave.

Spatiotemporal optical dark X solitary waves.

PubMed

Baronio, Fabio; Chen, Shihua; Onorato, Miguel; Trillo, Stefano; Wabnitz, Stefan; Kodama, Yuji

2016-12-01

We introduce spatiotemporal optical dark X solitary waves of the (2+1)D hyperbolic nonlinear Schrödinger equation (NLSE), which rules wave propagation in a self-focusing and normally dispersive medium. These analytical solutions are derived by exploiting the connection between the NLSE and a well-known equation of hydrodynamics, namely the type II Kadomtsev-Petviashvili (KP-II) equation. As a result, families of shallow water X soliton solutions of the KP-II equation are mapped into optical dark X solitary wave solutions of the NLSE. Numerical simulations show that optical dark X solitary waves may propagate for long distances (tens of nonlinear lengths) before they eventually break up, owing to the modulation instability of the continuous wave background. This finding opens a novel path for the excitation and control of X solitary waves in nonlinear optics.

Nonlinear Waves and Inverse Scattering

DTIC Science & Technology

1992-01-29

equations include the Kadomtsev - Petviashvili (K-P), Davey-Stewartson (D-S), 2+1 Toda, and Self-Dual Yang-Mills (SDYM) equations . We have uncovered a... Petviashvili Equation and Associated Constraints, M.J. Ablowitz and Javier Villaroel, Studies in Appl. Math. 85, (1991), 195-213. 12. On the Hamiltonian...nonlinear wave equations of physical significance, multidimensional inverse scattering, numer- ically induced instabilities and chaos, and forced

Propagation of Electron Acoustic Soliton, Periodic and Shock Waves in Dissipative Plasma with a q-Nonextensive Electron Velocity Distribution

NASA Astrophysics Data System (ADS)

El-Hanbaly, A. M.; El-Shewy, E. K.; Elgarayhi, A.; Kassem, A. I.

2015-11-01

The nonlinear properties of small amplitude electron-acoustic (EA) solitary and shock waves in a homogeneous system of unmagnetized collisionless plasma with nonextensive distribution for hot electrons have been investigated. A reductive perturbation method used to obtain the Kadomstev-Petviashvili-Burgers equation. Bifurcation analysis has been discussed for non-dissipative system in the absence of Burgers term and reveals different classes of the traveling wave solutions. The obtained solutions are related to periodic and soliton waves and their behavior are shown graphically. In the presence of the Burgers term, the EXP-function method is used to solve the Kadomstev-Petviashvili-Burgers equation and the obtained solution is related to shock wave. The obtained results may be helpful in better conception of waves propagation in various space plasma environments as well as in inertial confinement fusion laboratory plasmas.

The Analysis and Simulation of Compressible Turbulence

DTIC Science & Technology

1990-02-01

University. Kadomtsev , B.B.; and Petviashvili , V.I. 1973 - Acoustic Turbulence. Sov. Phys. Dokl. 18, 115. Kovasznay, L.S.G. 1957 - Turbulence in Supersonic...incompressible turbulence such as the Kolmogorov spectrum (Zakharov and Sagdeev 1970, Kadomtsev and Petvishvili 1973, Moiseev,Sagdeev, Tur and...The first attempt to solve numerically the equations of motion for compressible homogeneous turbulence is due to Feiereisen, Reynolds and Ferziger

The fluid-dynamic paradigm of the dust-acoustic soliton

NASA Astrophysics Data System (ADS)

McKenzie, J. F.

2002-06-01

In most studies, the properties of dust-acoustic solitons are derived from the first integral of the Poisson equation, in which the shape of the pseudopotential determines both the conditions in which a soliton may exist and its amplitude. Here this first integral is interpreted as conservation of total momentum, which, along with the Bernoulli-like energy equations for each species, may be cast as the structure equation for the dust (or heavy-ion) speed in the wave. In this fluid-dynamic picture, the significance of the sonic points of each species becomes apparent. In the wave, the heavy-ion (or dust) flow speed is supersonic (relative to its sound speed), whereas the protons and electrons are subsonic (relative to their sound speeds), and the dust flow is driven towards its sonic point. It is this last feature that limits the strength (amplitude) of the wave, since the equilibrium point (the centre of the wave) must be reached before the dust speed becomes sonic. The wave is characterized by a compression in the heavies and a compression (rarefaction) in the electrons and a rarefaction (compression) in the protons if the heavies have positive (negative) charge, and the corresponding potential is a hump (dip). These features are elucidated by an exact analytical soliton, in a special case, which provides the fully nonlinear counterpoint to the weakly nonlinear sech2-type solitons associated with the Korteweg de Vries equation, and indicates the parameter regimes in which solitons may exist.

The ion-acoustic soliton: A gas-dynamic viewpoint

NASA Astrophysics Data System (ADS)

McKenzie, J. F.

2002-03-01

The properties of fully nonlinear ion-acoustic solitons are investigated by interpreting conservation of total momentum as the structure equation for the proton flow in the wave. In most studies momentum conservation is regarded as the first integral of the Poisson equation for the electric potential and is interpreted as being analogous to a particle moving in a pseudo-potential well. By adopting an essentially gas-dynamic viewpoint, which emphasizes momentum conservation and the properties of the Bernoulli-type energy equations, the crucial role played by the proton sonic point becomes apparent. The relationship (implied by energy conservation) between the electron and proton speeds in the transition yields a locus—the hodograph of the system-which shows that, in the first half of the soliton, the electrons initially lag behind the protons until the charge neutral point is reached, after which they run ahead of the protons. The system reaches an equilibrium point (the center of the soliton) before the proton flow goes sonic. It follows that the critical ion-acoustic Mach number, Mc, above which smooth, continuous solitons cannot be constructed, stems from the requirement that the two equilibrium points of the structure equation coalesce at the proton sonic point of the flow. In general the range of the ion-acoustic Mach numbers, Mep, in which solitons exist, is extended beyond the classical range 1solitons exist only if 1

Internal polarization dynamics of vector dissipative-soliton-resonance pulses in normal dispersion fiber lasers.

PubMed

Li, Daojing; Shen, Deyuan; Li, Lei; Tang, Dingyuan; Su, Lei; Zhao, Luming

2018-03-15

Internal polarization dynamics of vector dissipative-soliton-resonance (DSR) pulses in a mode-locked fiber laser are investigated. By utilizing a wave plate analyzer configuration to analyze the special structure of a DSR pulse, we find that polarization state is not uniform across a resonant dissipative soliton. Specifically, although the central plane wave of the resonant dissipative soliton acquires nearly a single fixed polarization, the dissipative fronts feature polarization states that are different and spatially varying. This distinct polarization distribution is maintained while the whole soliton extends with increasing gain. Numerical simulation further confirms the experimental observations.

Electron-acoustic solitary waves in dense quantum electron-ion plasmas

DOE Office of Scientific and Technical Information (OSTI.GOV)

Misra, A. P.; Shukla, P. K.; Bhowmik, C.

2007-08-15

A quantum hydrodynamic (QHD) model is used to investigate the propagation characteristics of nonlinear electron-acoustic solitary waves (EASWs) in a dense quantum plasma whose constituents are two groups of electrons: one inertial cold electrons and other inertialess hot electrons, and the stationary ions which form the neutralizing background. By using the standard reductive perturbation technique, a Kadomtsev-Petviashvili (KP) equation, which governs the dynamics of EASWs, is derived in both spherical and cylindrical geometry. The effects of cold electrons and the density correlations due to quantum fluctuations on the profiles of the amplitudes and widths of the solitary structures are examinedmore » numerically. The nondimensional parameter {delta}=n{sub c0}/n{sub h0}, which is the equilibrium density ratio of the cold to hot electron component, is shown to play a vital role in the formation of both bright and dark solitons. It is also found that the angular dependence of the physical quantities and the presence of cold electrons in a quantum plasma lead to the coexistence of some new interesting novel solitary structures quite distinctive from the classical ones.« less

Dynamics of bright-bright solitons in Bose-Einstein condensate with Raman-induced one-dimensional spin-orbit coupling

NASA Astrophysics Data System (ADS)

Wen, Lin; Zhang, Xiao-Fei; Hu, Ai-Yuan; Zhou, Jing; Yu, Peng; Xia, Lei; Sun, Qing; Ji, An-Chun

2018-03-01

We investigate the dynamics of bright-bright solitons in one-dimensional two-component Bose-Einstein condensates with Raman-induced spin-orbit coupling, via the variational approximation and the numerical simulation of Gross-Pitaevskii equations. For the uniform system without trapping potential, we obtain two population balanced stationary solitons. By performing the linear stability analysis, we find a Goldstone eigenmode and an oscillation eigenmode around these stationary solitons. Moreover, we derive a general dynamical solution to describe the center-of-mass motion and spin evolution of the solitons under the action of spin-orbit coupling. The effects of a harmonic trap have also been discussed.

Adiabatic Soliton Laser

NASA Astrophysics Data System (ADS)

Bednyakova, Anastasia; Turitsyn, Sergei K.

2015-03-01

The key to generating stable optical pulses is mastery of nonlinear light dynamics in laser resonators. Modern techniques to control the buildup of laser pulses are based on nonlinear science and include classical solitons, dissipative solitons, parabolic pulses (similaritons) and various modifications and blending of these methods. Fiber lasers offer remarkable opportunities to apply one-dimensional nonlinear science models for the design and optimization of very practical laser systems. Here, we propose a new concept of a laser based on the adiabatic amplification of a soliton pulse in the cavity—the adiabatic soliton laser. The adiabatic change of the soliton parameters during evolution in the resonator relaxes the restriction on the pulse energy inherent in traditional soliton lasers. Theoretical analysis is confirmed by extensive numerical modeling.

Nonlinear Waves

DTIC Science & Technology

1989-06-15

Hamiltonian Formulation of the Kadomtsev - Petviashvili and Benjamin-Ono Equations , A.S. Fokas and P.M. Santini, J. Math. Phys. 29 (3) 604-617 (1988...Prototypes are the so-called Kadomtsev -Petviashvilli and Davey-Stewartson equations . These equations arise in a variety of physical instances such as water...plasma physics. Moreover the study of solutions to some of the underlying nonlinear evolution equations has led naturally to the investigation and new

Multicomponent long-wave-short-wave resonance interaction system: Bright solitons, energy-sharing collisions, and resonant solitons.

PubMed

Sakkaravarthi, K; Kanna, T; Vijayajayanthi, M; Lakshmanan, M

2014-11-01

We consider a general multicomponent (2+1)-dimensional long-wave-short-wave resonance interaction (LSRI) system with arbitrary nonlinearity coefficients, which describes the nonlinear resonance interaction of multiple short waves with a long wave in two spatial dimensions. The general multicomponent LSRI system is shown to be integrable by performing the Painlevé analysis. Then we construct the exact bright multisoliton solutions by applying the Hirota's bilinearization method and study the propagation and collision dynamics of bright solitons in detail. Particularly, we investigate the head-on and overtaking collisions of bright solitons and explore two types of energy-sharing collisions as well as standard elastic collision. We have also corroborated the obtained analytical one-soliton solution by direct numerical simulation. Also, we discuss the formation and dynamics of resonant solitons. Interestingly, we demonstrate the formation of resonant solitons admitting breather-like (localized periodic pulse train) structure and also large amplitude localized structures akin to rogue waves coexisting with solitons. For completeness, we have also obtained dark one- and two-soliton solutions and studied their dynamics briefly.

Dark soliton fiber lasers.

PubMed

Tang, Dingyuan; Guo, Jun; Song, Yufeng; Zhang, Han; Zhao, Luming; Shen, Deyuan

2014-08-11

Dark soliton formation and soliton dynamics in all-normal dispersion cavity fiber ring lasers without an anti-saturable absorber in cavity is studied both theoretically and numerically. It is shown that under suitable conditions the dark solitons formed could be described by the nonlinear Schrödinger equation. The dark soliton formation in an all-normal-dispersion cavity erbium-doped fiber ring laser without an anti-saturable absorber in cavity is first experimentally demonstrated. Individual dark solitons are experimentally identified. Excellent agreement between theory and experiment is observed.

Quantum Dynamics of Solitons in Strongly Interacting Systems on Optical Lattices

NASA Astrophysics Data System (ADS)

Rubbo, Chester; Balakrishnan, Radha; Reinhardt, William; Satija, Indubala; Rey, Ana; Manmana, Salvatore

2012-06-01

We present results of the quantum dynamics of solitons in XXZ spin-1/2 systems which in general can be derived from a system of spinless fermions or hard-core bosons (HCB) with nearest neighbor interaction on a lattice. A mean-field treatment using spin-coherent states revealed analytic solutions of both bright and dark solitons [1]. We take these solutions and apply a full quantum evolution using the adaptive time-dependent density matrix renormalization group method (adaptive t-DMRG), which takes into account the effect of strong correlations. We use local spin observables, correlations functions, and entanglement entropies as measures for the stability of these soliton solutions over the simulation times. [4pt] [1] R. Balakrishnan, I.I. Satija, and C.W. Clark, Phys. Rev. Lett. 103, 230403 (2009).

A new (2+1) dimensional integrable evolution equation for an ion acoustic wave in a magnetized plasma

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mukherjee, Abhik, E-mail: abhik.mukherjee@saha.ac.in; Janaki, M. S., E-mail: ms.janaki@saha.ac.in; Kundu, Anjan, E-mail: anjan.kundu@saha.ac.in

2015-07-15

A new, completely integrable, two dimensional evolution equation is derived for an ion acoustic wave propagating in a magnetized, collisionless plasma. The equation is a multidimensional generalization of a modulated wavepacket with weak transverse propagation, which has resemblance to nonlinear Schrödinger (NLS) equation and has a connection to Kadomtsev-Petviashvili equation through a constraint relation. Higher soliton solutions of the equation are derived through Hirota bilinearization procedure, and an exact lump solution is calculated exhibiting 2D structure. Some mathematical properties demonstrating the completely integrable nature of this equation are described. Modulational instability using nonlinear frequency correction is derived, and the correspondingmore » growth rate is calculated, which shows the directional asymmetry of the system. The discovery of this novel (2+1) dimensional integrable NLS type equation for a magnetized plasma should pave a new direction of research in the field.« less

Optical solitons, complexitons, Gaussian soliton and power series solutions of a generalized Hirota equation

NASA Astrophysics Data System (ADS)

Mao, Jin-Jin; Tian, Shou-Fu; Zou, Li; Zhang, Tian-Tian

2018-05-01

In this paper, we consider a generalized Hirota equation with a bounded potential, which can be used to describe the propagation properties of optical soliton solutions. By employing the hypothetical method and the sub-equation method, we construct the bright soliton, dark soliton, complexitons and Gaussian soliton solutions of the Hirota equation. Moreover, we explicitly derive the power series solutions with their convergence analysis. Finally, we provide the graphical analysis of such soliton solutions in order to better understand their dynamical behavior.

Symmetries and BI-Hamiltonian Structures of 2+1 Dimensional Systems,

DTIC Science & Technology

1986-01-01

and 0 aisociated with the Kadomtsev - 12 12 Petviashvili (KP) equation 2 -1qtq + 6qqx+ 3aD-q, (1.2) we have developed the theory associated with...generalized to equations in muLtidimensions. Applications to physically relevant equations like the Kadomcsev- Petviashvili equation are illustrated...integro-differenrial evo- lucion equations like the Benjamin-Ono equation are shown to be also described by this generalized V theory. IDSTEBO STP8 3

Modelling Bathymetric Control of Near Coastal Wave Climate: Report 3

DTIC Science & Technology

1992-02-01

complexity would occur if we were to make the full set of restrictions appropriate to the parabolic approximation of the KP equation ( Kadomtsev ... Kadomtsev , B.B. and Petviashvili , V.I., 1970, "On the stability of solitary waves in weakly dispersing media", Soy. Phys. Dokl., 15, 539-541. 24 Kirby...bar theory. Theory for Small Amplitude Bars The theory which provides the framework for analysis here is given by an extended mild-slope equation

Polarisation Dynamics of Vector Soliton Molecules in Mode Locked Fibre Laser

NASA Astrophysics Data System (ADS)

Tsatourian, Veronika; Sergeyev, Sergey V.; Mou, Chengbo; Rozhin, Alex; Mikhailov, Vitaly; Rabin, Bryan; Westbrook, Paul S.; Turitsyn, Sergei K.

2013-11-01

Two fundamental laser physics phenomena - dissipative soliton and polarisation of light are recently merged to the concept of vector dissipative soliton (VDS), viz. train of short pulses with specific state of polarisation (SOP) and shape defined by an interplay between anisotropy, gain/loss, dispersion, and nonlinearity. Emergence of VDSs is both of the fundamental scientific interest and is also a promising technique for control of dynamic SOPs important for numerous applications from nano-optics to high capacity fibre optic communications. Using specially designed and developed fast polarimeter, we present here the first experimental results on SOP evolution of vector soliton molecules with periodic polarisation switching between two and three SOPs and superposition of polarisation switching with SOP precessing. The underlying physics presents an interplay between linear and circular birefringence of a laser cavity along with light induced anisotropy caused by polarisation hole burning.

Single-mode dispersive waves and soliton microcomb dynamics

PubMed Central

Yi, Xu; Yang, Qi-Fan; Zhang, Xueyue; Yang, Ki Youl; Li, Xinbai; Vahala, Kerry

2017-01-01

Dissipative Kerr solitons are self-sustaining optical wavepackets in resonators. They use the Kerr nonlinearity to both compensate dispersion and offset optical loss. Besides providing insights into nonlinear resonator physics, they can be applied in frequency metrology, precision clocks, and spectroscopy. Like other optical solitons, the dissipative Kerr soliton can radiate power as a dispersive wave through a process that is the optical analogue of Cherenkov radiation. Dispersive waves typically consist of an ensemble of optical modes. Here, a limiting case is studied in which the dispersive wave is concentrated into a single cavity mode. In this limit, its interaction with the soliton induces hysteresis behaviour in the soliton's spectral and temporal properties. Also, an operating point of enhanced repetition-rate stability occurs through balance of dispersive-wave recoil and Raman-induced soliton-self-frequency shift. The single-mode dispersive wave can therefore provide quiet states of soliton comb operation useful in many applications. PMID:28332495

Two-soliton interaction as an elementary act of soliton turbulence in integrable systems

NASA Astrophysics Data System (ADS)

Pelinovsky, E. N.; Shurgalina, E. G.; Sergeeva, A. V.; Talipova, T. G.; El, G. A.; Grimshaw, R. H. J.

2013-01-01

Two-soliton interactions play a definitive role in the formation of the structure of soliton turbulence in integrable systems. To quantify the contribution of these interactions to the dynamical and statistical characteristics of the nonlinear wave field of soliton turbulence we study properties of the spatial moments of the two-soliton solution of the Korteweg-de Vries (KdV) equation. While the first two moments are integrals of the KdV evolution, the 3rd and 4th moments undergo significant variations in the dominant interaction region, which could have strong effect on the values of the skewness and kurtosis in soliton turbulence.

Integrable model for density-modulated quantum condensates: Solitons passing through a soliton lattice.

PubMed

Takahashi, Daisuke A

2016-06-01

An integrable model possessing inhomogeneous ground states is proposed as an effective model of nonuniform quantum condensates such as supersolids and Fulde-Ferrell-Larkin-Ovchinnikov superfluids. The model is a higher-order analog of the nonlinear Schrödinger equation. We derive an n-soliton solution via the inverse scattering theory with elliptic-functional background and reveal various kinds of soliton dynamics such as dark soliton billiards, dislocations, gray solitons, and envelope solitons. We also provide the exact bosonic and fermionic quasiparticle eigenstates and show their tunneling phenomena. The solutions are expressed by a determinant of theta functions.

Dynamics of lumps and dark-dark solitons in the multi-component long-wave-short-wave resonance interaction system.

PubMed

Rao, Jiguang; Porsezian, Kuppuswamy; He, Jingsong; Kanna, Thambithurai

2018-01-01

General semi-rational solutions of an integrable multi-component (2+1)-dimensional long-wave-short-wave resonance interaction system comprising multiple short waves and a single long wave are obtained by employing the bilinear method. These solutions describe the interactions between various types of solutions, including line rogue waves, lumps, breathers and dark solitons. We only focus on the dynamical behaviours of the interactions between lumps and dark solitons in this paper. Our detailed study reveals two different types of excitation phenomena: fusion and fission. It is shown that the fundamental (simplest) semi-rational solutions can exhibit fission of a dark soliton into a lump and a dark soliton or fusion of one lump and one dark soliton into a dark soliton. The non-fundamental semi-rational solutions are further classified into three subclasses: higher-order, multi- and mixed-type semi-rational solutions. The higher-order semi-rational solutions show the process of annihilation (production) of two or more lumps into (from) one dark soliton. The multi-semi-rational solutions describe N ( N ≥2) lumps annihilating into or producing from N -dark solitons. The mixed-type semi-rational solutions are a hybrid of higher-order semi-rational solutions and multi-semi-rational solutions. For the mixed-type semi-rational solutions, we demonstrate an interesting dynamical behaviour that is characterized by partial suppression or creation of lumps from the dark solitons.

Dynamics of lumps and dark-dark solitons in the multi-component long-wave-short-wave resonance interaction system

NASA Astrophysics Data System (ADS)

Rao, Jiguang; Porsezian, Kuppuswamy; He, Jingsong; Kanna, Thambithurai

2018-01-01

General semi-rational solutions of an integrable multi-component (2+1)-dimensional long-wave-short-wave resonance interaction system comprising multiple short waves and a single long wave are obtained by employing the bilinear method. These solutions describe the interactions between various types of solutions, including line rogue waves, lumps, breathers and dark solitons. We only focus on the dynamical behaviours of the interactions between lumps and dark solitons in this paper. Our detailed study reveals two different types of excitation phenomena: fusion and fission. It is shown that the fundamental (simplest) semi-rational solutions can exhibit fission of a dark soliton into a lump and a dark soliton or fusion of one lump and one dark soliton into a dark soliton. The non-fundamental semi-rational solutions are further classified into three subclasses: higher-order, multi- and mixed-type semi-rational solutions. The higher-order semi-rational solutions show the process of annihilation (production) of two or more lumps into (from) one dark soliton. The multi-semi-rational solutions describe N(N≥2) lumps annihilating into or producing from N-dark solitons. The mixed-type semi-rational solutions are a hybrid of higher-order semi-rational solutions and multi-semi-rational solutions. For the mixed-type semi-rational solutions, we demonstrate an interesting dynamical behaviour that is characterized by partial suppression or creation of lumps from the dark solitons.

Many-body quantum dynamics in the decay of bent dark solitons of Bose-Einstein condensates

NASA Astrophysics Data System (ADS)

Katsimiga, G. C.; Mistakidis, S. I.; Koutentakis, G. M.; Kevrekidis, P. G.; Schmelcher, P.

2017-12-01

The beyond mean-field (MF) dynamics of a bent dark soliton (BDS) embedded in a two-dimensional repulsively interacting Bose-Einstein condensate is explored. We examine the case of a single BDS comparing the MF dynamics to a correlated approach, the multi-configuration time-dependent Hartree method for bosons. Dynamical snaking of this bent structure is observed, signaling the onset of fragmentation which becomes significant during the vortex nucleation. In contrast to the MF approximation ‘filling’ of the vortex core is observed, leading in turn to the formation of filled-core vortices, instead of the MF vortex-antivortex pairs. The resulting smearing effect in the density is a rather generic feature, occurring when solitonic structures are exposed to quantum fluctuations. Here, we show that this filling owes its existence to the dynamical building of an antidark structure developed in the next-to-leading order orbital. We further demonstrate that the aforementioned beyond MF dynamics can be experimentally detected using the variance of single shot measurements. Additionally, a variety of excitations including vortices, oblique dark solitons, and open ring dark soliton-like structures building upon higher-lying orbitals is observed. We demonstrate that signatures of the higher-lying orbital excitations emerge in the total density, and can be clearly captured by inspecting the one-body coherence. In the latter context, the localization of one-body correlations exposes the existence of the multi-orbital vortex-antidark structure.

Polarisation Dynamics of Vector Soliton Molecules in Mode Locked Fibre Laser

PubMed Central

Tsatourian, Veronika; Sergeyev, Sergey V.; Mou, Chengbo; Rozhin, Alex; Mikhailov, Vitaly; Rabin, Bryan; Westbrook, Paul S.; Turitsyn, Sergei K.

2013-01-01

Two fundamental laser physics phenomena - dissipative soliton and polarisation of light are recently merged to the concept of vector dissipative soliton (VDS), viz. train of short pulses with specific state of polarisation (SOP) and shape defined by an interplay between anisotropy, gain/loss, dispersion, and nonlinearity. Emergence of VDSs is both of the fundamental scientific interest and is also a promising technique for control of dynamic SOPs important for numerous applications from nano-optics to high capacity fibre optic communications. Using specially designed and developed fast polarimeter, we present here the first experimental results on SOP evolution of vector soliton molecules with periodic polarisation switching between two and three SOPs and superposition of polarisation switching with SOP precessing. The underlying physics presents an interplay between linear and circular birefringence of a laser cavity along with light induced anisotropy caused by polarisation hole burning. PMID:24193374

CALL FOR PAPERS: Optical solitons

NASA Astrophysics Data System (ADS)

Drummond, P. D.; Haelterman, Marc; Vilaseca, R.

2003-06-01

A topical issue of Journal of Optics B: Quantum and Semiclassical Optics will be devoted to recent advances in optical solitons. The topics to be covered will include, but are not limited to: bulletProperties, control and dynamics of temporal solitons bulletProperties, control and dynamics of spatial solitons bulletCavity solitons in passive and active resonators bulletThree-dimensional spatial solitons bulletDark, bright, grey solitons; interface dynamics bulletCompound or vector solitons; incoherent solitons bulletLight and matter solitons in BEC bulletNonlinear localized structures in microstructured and nanostructured materials (photonic crystals, etc) bulletAngular momentum effects associated with localized light structures; vortex solitons bulletQuantum effects associated with localized light structures bulletInteraction of solitons with atoms and other media bulletApplications of optical solitons The DEADLINE for submission of contributions is 31 July 2003 to allow the topical issue to appear in about February 2004. All papers will be peer-reviewed in accordance with the normal refereeing procedures and standards of Journal of Optics B: Quantum and Semiclassical Optics. Advice on publishing your work in the journal may be found at www.iop.org/journals/authors/jopb. Submissions should ideally be in either standard LaTeX form or Microsoft Word. There are no page charges for publication. In addition to the usual 50 free reprints, the corresponding author of each paper published will receive a complimentary copy of the topical issue. Contributions to the topical issue should if possible be submitted electronically at www.iop.org/journals/jopb. or by e-mail to jopb@iop.org. Authors unable to submit online or by e-mail may send hard copy contributions (enclosing the electronic code) to: Dr Claire Bedrock (Publisher), Journal of Optics B: Quantum and Semiclassical Optics, Institute of Physics Publishing, Dirac House, Temple Back, Bristol BS1 6BE, UK. All

A new equation in two dimensional fast magnetoacoustic shock waves in electron-positron-ion plasmas

DOE Office of Scientific and Technical Information (OSTI.GOV)

Masood, W.; Jehan, Nusrat; Mirza, Arshad M.

2010-03-15

Nonlinear properties of the two dimensional fast magnetoacoustic waves are studied in a three-component plasma comprising of electrons, positrons, and ions. In this regard, Kadomtsev-Petviashvili-Burger (KPB) equation is derived using the small amplitude perturbation expansion method. Under the condition that the electron and positron inertia are ignored, Burger-Kadomtsev-Petviashvili (Burger-KP) for a fast magnetoacoustic wave is derived for the first time, to the best of author's knowledge. The solutions of both KPB and Burger-KP equations are obtained using the tangent hyperbolic method. The effects of positron concentration, kinematic viscosity, and plasma beta are explored both for the KPB and the Burger-KPmore » shock waves and the differences between the two are highlighted. The present investigation may have relevance in the study of nonlinear electromagnetic shock waves both in laboratory and astrophysical plasmas.« less

Cascade of Solitonic Excitations in a Superfluid Fermi Gas: From Solitons and Vortex Rings to Solitonic Vortices

NASA Astrophysics Data System (ADS)

Ku, Mark; Mukherjee, Biswaroop; Yefsah, Tarik; Zwierlein, Martin

2015-05-01

We follow the evolution of a superfluid Fermi gas of 6Li atoms following a one-sided π phase imprint. Via tomographic imaging, we observe the formation of a planar dark soliton, and its subsequent snaking and decay into a vortex ring. The latter eventually breaks at the boundary of the superfluid, finally leaving behind a single, remnant solitonic vortex. The nodal surface is directly imaged and reveals its decay into a vortex ring via a puncture of the initial soliton plane. At intermediate stages we find evidence for more exotic structures resembling Φ-solitons. The observed evolution of the nodal surface represents dynamics that occurs at the length scale of the interparticle spacing, thus providing new experimental input for microscopic theories of strongly correlated fermions.

Specific sine-Gordon soliton dynamics in the presence of external driving forces

NASA Astrophysics Data System (ADS)

Reinisch, Gilbert; Fernandez, Jean Claude

1981-07-01

We consider the acceleration of a single sine-Gordon (SG) soliton kink wave by an external time-dependent force χ(t), first without any dissipation, and then in the presence of a weak damping effect. We use the method of Fogel, Trullinger, Bishop, and Krumhansl [FTBK,

Dynamical behavior of the random field on the pulsating and snaking solitons in cubic-quintic complex Ginzburg-Landau equation

NASA Astrophysics Data System (ADS)

Bakhtiar, Nurizatul Syarfinas Ahmad; Abdullah, Farah Aini; Hasan, Yahya Abu

2017-08-01

In this paper, we consider the dynamical behaviour of the random field on the pulsating and snaking solitons in a dissipative systems described by the one-dimensional cubic-quintic complex Ginzburg-Landau equation (cqCGLE). The dynamical behaviour of the random filed was simulated by adding a random field to the initial pulse. Then, we solve it numerically by fixing the initial amplitude profile for the pulsating and snaking solitons without losing any generality. In order to create the random field, we choose 0 ≤ ɛ ≤ 1.0. As a result, multiple soliton trains are formed when the random field is applied to a pulse like initial profile for the parameters of the pulsating and snaking solitons. The results also show the effects of varying the random field of the transient energy peaks in pulsating and snaking solitons.

Dynamics of topological solitons, knotted streamlines, and transport of cargo in liquid crystals

NASA Astrophysics Data System (ADS)

Sohn, Hayley R. O.; Ackerman, Paul J.; Boyle, Timothy J.; Sheetah, Ghadah H.; Fornberg, Bengt; Smalyukh, Ivan I.

2018-05-01

Active colloids and liquid crystals are capable of locally converting the macroscopically supplied energy into directional motion and promise a host of new applications, ranging from drug delivery to cargo transport at the mesoscale. Here we uncover how topological solitons in liquid crystals can locally transform electric energy to translational motion and allow for the transport of cargo along directions dependent on frequency of the applied electric field. By combining polarized optical video microscopy and numerical modeling that reproduces both the equilibrium structures of solitons and their temporal evolution in applied fields, we uncover the physical underpinnings behind this reconfigurable motion and study how it depends on the structure and topology of solitons. We show that, unexpectedly, the directional motion of solitons with and without the cargo arises mainly from the asymmetry in rotational dynamics of molecular ordering in liquid crystal rather than from the asymmetry of fluid flows, as in conventional active soft matter systems.

A theorem about Hamiltonian systems.

PubMed

Case, K M

1984-09-01

A simple theorem in Hamiltonian mechanics is pointed out. One consequence is a generalization of the classical result that symmetries are generated by Poisson brackets of conserved functionals. General applications are discussed. Special emphasis is given to the Kadomtsev-Petviashvili equation.

Solitonic Josephson Thermal Transport

NASA Astrophysics Data System (ADS)

Guarcello, Claudio; Solinas, Paolo; Braggio, Alessandro; Giazotto, Francesco

2018-03-01

We explore the coherent thermal transport sustained by solitons through a long Josephson junction as a thermal gradient across the system is established. We observe that a soliton causes the heat current through the system to increase. Correspondingly, the junction warms up in conjunction with the soliton, with temperature peaks up to, e.g., approximately 56 mK for a realistic Nb-based proposed setup at a bath temperature Tbath=4.2 K . The thermal effects on the dynamics of the soliton are also discussed. Markedly, this system inherits the topological robustness of the solitons. In view of these results, the proposed device can effectively find an application as a superconducting thermal router in which the thermal transport can be locally mastered through solitonic excitations, whose positions can be externally controlled through a magnetic field and a bias current.

Intermode Breather Solitons in Optical Microresonators

NASA Astrophysics Data System (ADS)

Guo, Hairun; Lucas, Erwan; Pfeiffer, Martin H. P.; Karpov, Maxim; Anderson, Miles; Liu, Junqiu; Geiselmann, Michael; Jost, John D.; Kippenberg, Tobias J.

2017-10-01

Dissipative solitons can be found in a variety of systems resulting from the double balance between dispersion and nonlinearity, as well as gain and loss. Recently, they have been observed to spontaneously form in Kerr nonlinear microresonators driven by a continuous wave laser, providing a compact source of coherent optical frequency combs. As optical microresonators are commonly multimode, intermode interactions, which give rise to avoided mode crossings, frequently occur and can alter the soliton properties. Recent works have shown that avoided mode crossings cause the soliton to acquire a single-mode dispersive wave, a recoil in the spectrum, or lead to soliton decay. Here, we show that avoided mode crossings can also trigger the formation of breather solitons, solitons that undergo a periodic evolution in their amplitude and duration. This new breather soliton, referred to as an intermode breather soliton, occurs within a laser detuning range where conventionally stationary (i.e., stable) dissipative Kerr solitons are expected. We experimentally demonstrate the phenomenon in two microresonator platforms (crystalline magnesium fluoride and photonic chip-based silicon nitride microresonators) and theoretically describe the dynamics based on a pair of coupled Lugiato-Lefever equations. We show that the breathing is associated with a periodic energy exchange between the soliton and a second optical mode family, a behavior that can be modeled by a response function acting on dissipative solitons described by the Lugiato-Lefever model. The observation of breathing dynamics in the conventionally stable soliton regime is relevant to applications in metrology such as low-noise microwave generation, frequency synthesis, or spectroscopy.

Bose polaronic soliton-molecule and vector solitons in PT -symmetric potential

NASA Astrophysics Data System (ADS)

Boudjemâa, Abdelâali

2017-07-01

We study analytically and numerically the properties of polaronic soliton molecules and vector solitons of a trapped Bose-Einstein condensate (BEC)-impurity mixture subjected to a PT -symmetric potential in a quasi one-dimensional geometry employing our time-dependent Hartree-Fock-Bogoliubov equations. Analytical results, based on a variational approach and checked with direct numerical simulations reveal that the width, chirp, the vibration frequency and the profile of impurity solitons are enhanced by varying the strengths of real and imaginary parts of PT -symmetric potential as well as the boson-boson and boson-impurity interaction. We address the impact of the imaginary part of the potential, which represents a gain-loss mechanism, on the dynamics and on the stability of the impurity soliton-molecule. We show that for sufficiently strong complex part of the potential, the single soliton exhibits a snake instability and the molecule destroys analogous to the dissociation of a diatomic molecule. We discuss, on the other hand, the formation of several unusual families of three-component vector solitons in the BEC-impurity mixture. An unconventional dark (D)-bright (B) soliton conversion is found.

A theorem about Hamiltonian systems

PubMed Central

Case, K. M.

1984-01-01

A simple theorem in Hamiltonian mechanics is pointed out. One consequence is a generalization of the classical result that symmetries are generated by Poisson brackets of conserved functionals. General applications are discussed. Special emphasis is given to the Kadomtsev-Petviashvili equation. PMID:16593515

Modelling of the nonlinear soliton dynamics in the ring fibre cavity

NASA Astrophysics Data System (ADS)

Razukov, Vadim A.; Melnikov, Leonid A.

2018-04-01

Using the cabaret method numerical realization, long-time spatio-temporal dynamics of the electromagnetic field in a nonlinear ring fibre cavity with dispersion is investigated during the hundreds of round trips. Formation of both the temporal cavity solitons and irregular pulse trains is demonstrated and discussed.

Matter-wave dark solitons: stochastic versus analytical results.

PubMed

Cockburn, S P; Nistazakis, H E; Horikis, T P; Kevrekidis, P G; Proukakis, N P; Frantzeskakis, D J

2010-04-30

The dynamics of dark matter-wave solitons in elongated atomic condensates are discussed at finite temperatures. Simulations with the stochastic Gross-Pitaevskii equation reveal a noticeable, experimentally observable spread in individual soliton trajectories, attributed to inherent fluctuations in both phase and density of the underlying medium. Averaging over a number of such trajectories (as done in experiments) washes out such background fluctuations, revealing a well-defined temperature-dependent temporal growth in the oscillation amplitude. The average soliton dynamics is well captured by the simpler dissipative Gross-Pitaevskii equation, both numerically and via an analytically derived equation for the soliton center based on perturbation theory for dark solitons.

Nonlinear low-frequency electrostatic wave dynamics in a two-dimensional quantum plasma

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ghosh, Samiran, E-mail: sran_g@yahoo.com; Chakrabarti, Nikhil, E-mail: nikhil.chakrabarti@saha.ac.in

2016-08-15

The problem of two-dimensional arbitrary amplitude low-frequency electrostatic oscillation in a quasi-neutral quantum plasma is solved exactly by elementary means. In such quantum plasmas we have treated electrons quantum mechanically and ions classically. The exact analytical solution of the nonlinear system exhibits the formation of dark and black solitons. Numerical simulation also predicts the possible periodic solution of the nonlinear system. Nonlinear analysis reveals that the system does have a bifurcation at a critical Mach number that depends on the angle of propagation of the wave. The small-amplitude limit leads to the formation of weakly nonlinear Kadomstev–Petviashvili solitons.

Critical density of a soliton gas

DOE Office of Scientific and Technical Information (OSTI.GOV)

El, G. A., E-mail: g.el@lboro.ac.uk

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.

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.

Rogue waves generation via nonlinear soliton collision in multiple-soliton state of a mode-locked fiber laser.

PubMed

Peng, Junsong; Tarasov, Nikita; Sugavanam, Srikanth; Churkin, Dmitry

2016-09-19

We report for the first time, rogue waves generation in a mode-locked fiber laser that worked in multiple-soliton state in which hundreds of solitons occupied the whole laser cavity. Using real-time spatio-temporal intensity dynamics measurements, it is unveiled that nonlinear soliton collision accounts for the formation of rogue waves in this laser state. The nature of interactions between solitons are also discussed. Our observation may suggest similar formation mechanisms of rogue waves in other systems.

Bound vector solitons and soliton complexes for the coupled nonlinear Schrödinger equations.

PubMed

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

2009-12-01

Dynamic features describing the collisions of the bound vector solitons and soliton complexes are investigated for the coupled nonlinear Schrödinger (CNLS) equations, which model the propagation of the multimode soliton pulses under some physical situations in nonlinear fiber optics. Equations of such type have also been seen in water waves and plasmas. By the appropriate choices of the arbitrary parameters for the multisoliton solutions derived through the Hirota bilinear method, the periodic structures along the propagation are classified according to the relative relations of the real wave numbers. Furthermore, parameters are shown to control the intensity distributions and interaction patterns for the bound vector solitons and soliton complexes. Transformations of the soliton types (shape changing with intensity redistribution) during the collisions of those stationary structures with the regular one soliton are discussed, in which a class of inelastic properties is involved. Discussions could be expected to be helpful in interpreting such structures in the multimode nonlinear fiber optics and equally applied to other systems governed by the CNLS equations, e.g., the plasma physics and Bose-Einstein condensates.

Interesting features of nonlinear shock equations in dissipative pair-ion-electron plasmas

DOE Office of Scientific and Technical Information (OSTI.GOV)

Masood, W.; National Centre for Physics; Rizvi, H.

2011-09-15

Two dimensional nonlinear electrostatic waves are studied in unmagnetized, dissipative pair-ion-electron plasmas in the presence of weak transverse perturbation. The dissipation in the system is taken into account by incorporating the kinematic viscosity of both positive and negative ions. In the linear case, a biquadratic dispersion relation is obtained, which yields the fast and slow modes in a pair-ion-electron plasma. It is shown that the limiting cases of electron-ion and pair-ion can be retrieved from the general biquadratic dispersion relation, and the differences in the characters of the waves propagating in both the cases are also highlighted. Using the smallmore » amplitude approximation method, the nonlinear Kadomtsev Petviashvili Burgers as well as Burgers-Kadomtsev Petviashvili equations are derived and their applicability for pair-ion-electron plasma is explained in detail. The present study may have relevance to understand the formation of two dimensional electrostatic shocks in laboratory produced pair-ion-electron plasmas.« less

N-Soliton Solution and Soliton Resonances for the (2+1)-Dimensional Inhomogeneous Gardner Equation

NASA Astrophysics Data System (ADS)

Wang, Xin; Geng, Xian-Guo

2017-08-01

We derive the Lax pair and Darboux transformation for the (2+1)-dimensional inhomogeneous Gardner equation via the two-singular manifold method from Painlevé analysis. N-soliton solution in a compact determinant representation of Grammian type is presented. As an application, dynamic properties of the bright and dark soliton solutions under periodic and parabolic oscillations up to second order are shown. Resonant behaviors of two bright and two dark solitons are studied, and asymptotic analysis of the corresponding resonant bright and dark two-soliton solutions are performed, respectively. Supported by National Natural Science Foundation of China under Grant No. 11331008 and China Postdoctoral Science Foundation Funded Sixtieth Batches (2016M602252)

Mathematical Tools for Image Reconstruction

DTIC Science & Technology

1991-07-01

l.Diffuse tomography 2.Concentrating a signal in the physical and spectral domains. 3.New explicit solutions for the Kadomtsev - Petviashvili equation 4...the case of the Schroedinger equation it was possible to "beat Heisenberg" with piecewise linear potentials. Finally let me say that the paper Some

Dynamics and elastic interactions of the discrete multi-dark soliton solutions for the Kaup-Newell lattice equation

NASA Astrophysics Data System (ADS)

Liu, Nan; Wen, Xiao-Yong

2018-03-01

Under consideration in this paper is the Kaup-Newell (KN) lattice equation which is an integrable discretization of the KN equation. Infinitely, many conservation laws and discrete N-fold Darboux transformation (DT) for this system are constructed and established based on its Lax representation. Via the resulting N-fold DT, the discrete multi-dark soliton solutions in terms of determinants are derived from non-vanishing background. Propagation and elastic interaction structures of such solitons are shown graphically. Overtaking interaction phenomena between/among the two, three and four solitons are discussed. Numerical simulations are used to explore their dynamical behaviors of such multi-dark solitons. Numerical results show that their evolutions are stable against a small noise. Results in this paper might be helpful for understanding the propagation of nonlinear Alfvén waves in plasmas.

Generation and stability of dynamical skyrmions and droplet solitons.

PubMed

Statuto, Nahuel; Hernàndez, Joan Manel; Kent, Andrew D; Macià, Ferran

2018-08-10

A spin-polarized current in a nanocontact to a magnetic film can create collective magnetic oscillations by compensating the magnetic damping. In particular, in materials with uniaxial magnetic anisotropy, droplet solitons have been observed-a self-localized excitation consisting of partially reversed magnetization that precesses coherently in the nanocontact region. It is also possible to generate topological droplet solitons, known as dynamical skyrmions (DSs). Here, we show that spin-polarized current thresholds for DS creation depend not only on the material's parameters but also on the initial magnetization state and the rise time of the spin-polarized current. We study the conditions that promote either droplet or DS formation and describe their stability in magnetic films without Dzyaloshinskii-Moriya interactions. The Oersted fields from the applied current, the initial magnetization state, and the rise time of the injected current can determine whether a droplet or a DS forms. DSs are found to be more stable than droplets. We also discuss electrical characteristics that can be used to distinguish these magnetic objects.

Protonic transport through solitons in hydrogen-bonded systems

NASA Astrophysics Data System (ADS)

Kavitha, L.; Jayanthi, S.; Muniyappan, A.; Gopi, D.

2011-09-01

We offer an alternative route for investigating soliton solutions in hydrogen-bonded (HB) chains. We invoke the modified extended tangent hyperbolic function method coupled with symbolic computation to solve the governing equation of motion for proton dynamics. We investigate the dynamics of proton transfer in HB chains through bell-shaped soliton excitations, which trigger the bio-energy transport in most biological systems. This solitonic mechanism of proton transfer could play functional roles in muscular contraction, enzymatic activity and oxidative phosphorylation.

Motion of discrete solitons assisted by nonlinearity management.

PubMed

Cuevas, Jesús; Malomed, Boris A; Kevrekidis, P G

2005-06-01

We demonstrate that time-periodic modulation of the nonlinearity coefficient in the discrete nonlinear Schrödinger equation strongly facilitates creation of traveling solitons in the lattice. We predict this possibility in a semi-qualitative form analytically, and test it in direct numerical simulations. Systematic computations reveal several generic dynamical regimes, depending on the amplitude and frequency of the time modulation, and on the initial thrust which sets the soliton in motion. These regimes include irregular motion of the soliton, regular motion of a decaying one, and regular motion of a stable soliton. The motion may occur in both the straight and reverse directions, relative to the initial thrust. In the case of stable motion, extremely long simulations in a lattice with periodic boundary conditions demonstrate that the soliton keeps moving indefinitely long without any visible loss. Velocities of moving stable solitons are in good agreement with the analytical prediction, which is based on requiring a resonance between the ac drive and motion of the soliton through the periodic lattice. The generic dynamical regimes are mapped in the model's parameter space. Collisions between moving stable solitons are briefly investigated too, with a conclusion that two different outcomes are possible: elastic bounce, or bounce with mass transfer from one soliton to the other. The model can be realized experimentally in a Bose-Einstein condensate trapped in a deep optical lattice.

Structure, dynamics and bifurcations of discrete solitons in trapped ion crystals

NASA Astrophysics Data System (ADS)

Landa, H.; Reznik, B.; Brox, J.; Mielenz, M.; Schaetz, T.

2013-09-01

We study discrete solitons (kinks) accessible in the state-of-the-art trapped ion experiments, considering zigzag crystals and quasi-three-dimensional configurations, both theoretically and experimentally. We first extend the theoretical understanding of different phenomena predicted and recently experimentally observed in the structure and dynamics of these topological excitations. Employing tools from topological degree theory, we analyze bifurcations of crystal configurations in dependence on the trapping parameters, and investigate the formation of kink configurations and the transformations of kinks between different structures. This allows us to accurately define and calculate the effective potential experienced by solitons within the Wigner crystal, and study how this (so-called Peierls-Nabarro) potential gets modified to a non-periodic globally trapping potential in certain parameter regimes. The kinks' rest mass (energy) and spectrum of modes are computed and the dynamics of linear and nonlinear kink oscillations are analyzed. We also present novel, experimentally observed, configurations of kinks incorporating a large-mass defect realized by an embedded molecular ion, and of pairs of interacting kinks stable for long times, offering the perspective for exploring and exploiting complex collective nonlinear excitations, controllable on the quantum level.

Soliton interactions and the formation of solitonic patterns

NASA Astrophysics Data System (ADS)

Sears, Suzanne M.

From the stripes of a zebra, to the spirals of cream in a hot cup of coffee, we are surrounded by patterns in the natural world. But why are there patterns? Why drives their formation? In this thesis we study some of the diverse ways patterns can arise due to the interactions between solitary waves in nonlinear systems, sometimes starting from nothing more than random noise. What follows is a set of three studies. In the first, we show how a nonlinear system that supports solitons can be driven to generate exact (regular) Cantor set fractals. As an example, we use numerical simulations to demonstrate the formation of Cantor set fractals by temporal optical solitons. This fractal formation occurs in a cascade of nonlinear optical fibers through the dynamical evolution of a single input soliton. In the second study, we investigate pattern formation initiated by modulation instability in nonlinear partially coherent wave fronts and show that anisotropic noise and/or anisotropic correlation statistics can lead to ordered patterns such as grids and stripes. For the final study, we demonstrate the spontaneous clustering of solitons in partially coherent wavefronts during the final stages of pattern formation initiated by modulation instability and noise. Experimental observations are in agreement with theoretical predictions and are confirmed using numerical simulations.

Interaction of spatially separated oscillating solitons in biased two-photon photorefractive materials

NASA Astrophysics Data System (ADS)

Asif, Noushin; Biswas, Anjan; Jovanoski, Z.; Konar, S.

2015-01-01

This paper presents the dynamics of two spatially separated optical solitons in two-photon photorefractive materials. The variational formalism has been employed to derive evolution equations of different parameters which characterize the dynamics of two interacting solitons. This approach yields a system of coupled ordinary differential equations for evolution of different parameters characterizing solitons such as amplitude, spatial width, chirp, center of gravity, etc., which have been subsequently solved adopting numerical method to extract information on their dynamics. Depending on their initial separation and power, solitons are shown to either disperse or compresses individually and attract each other. Dragging and trapping of a probe soliton by another pump have been discussed.

Three-wave resonant interactions: Multi-dark-dark-dark solitons, breathers, rogue waves, and their interactions and dynamics

NASA Astrophysics Data System (ADS)

Zhang, Guoqiang; Yan, Zhenya; Wen, Xiao-Yong

2018-03-01

We investigate three-wave resonant interactions through both the generalized Darboux transformation method and numerical simulations. Firstly, we derive a simple multi-dark-dark-dark-soliton formula through the generalized Darboux transformation. Secondly, we use the matrix analysis method to avoid the singularity of transformed potential functions and to find the general nonsingular breather solutions. Moreover, through a limit process, we deduce the general rogue wave solutions and give a classification by their dynamics including bright, dark, four-petals, and two-peaks rogue waves. Ever since the coexistence of dark soliton and rogue wave in non-zero background, their interactions naturally become a quite appealing topic. Based on the N-fold Darboux transformation, we can derive the explicit solutions to depict their interactions. Finally, by performing extensive numerical simulations we can predict whether these dark solitons and rogue waves are stable enough to propagate. These results can be available for several physical subjects such as fluid dynamics, nonlinear optics, solid state physics, and plasma physics.

The laboratory investigation of surface envelope solitons: reflection from a vertical wall and collisions of solitons

NASA Astrophysics Data System (ADS)

Slunyaev, Alexey; Klein, Marco; Clauss, Günther F.

2016-04-01

Envelope soliton solutions are key elements governing the nonlinear wave dynamics within a simplified theory for unidirectional weakly modulated weakly nonlinear wave groups on the water surface. Within integrable models the solitons preserve their structure in collisions with other waves; they do not disperse and can carry energy infinitively long. Steep and short soliton-like wave groups have been shown to exist in laboratory tests [1] and, even earlier, in numerical simulations [2, 3]. Thus, long-living wave groups may play important role in the dynamics of intense sea waves and wave-structure interactions. The solitary wave groups may change the wave statistics and can be taken into account when developing approaches for the deterministic forecasting of dangerous waves, including so-called rogue waves. An experimental campaign has been conducted in the wave basin of the Technical University of Berlin on simulations of intense solitary wave groups. The first successful experimental observation of intense envelope solitons took place in this facility [1]. The new experiments aimed at following main goals: 1) to reproduce intense envelope solitons with different carrier wave lengths; 2) to estimate the rate of envelope soliton dissipation; 3) to consider the reflection of envelope solitons on a vertical wall; 4) to consider head-on collisions of envelope solitons, and 5) to consider overtaking interactions of envelope solitons. Up to 9 wave gauges were used in each experimental run, which enabled registration of the surface movement at different distances from the wavemaker, at different locations across the wave flume and near the wall. Besides surface displacements, the group envelope shapes were directly recorded, with use of phase shifts applied to the modulated waves generated by the wavemaker. [1] A. Slunyaev, G.F. Clauss, M. Klein, M. Onorato, Simulations and experiments of short intense envelope solitons of surface water waves. Phys. Fluids 25, 067105

Energy-exchange collisions of dark-bright-bright vector solitons.

PubMed

Radhakrishnan, R; Manikandan, N; Aravinthan, K

2015-12-01

We find a dark component guiding the practically interesting bright-bright vector one-soliton to two different parametric domains giving rise to different physical situations by constructing a more general form of three-component dark-bright-bright mixed vector one-soliton solution of the generalized Manakov model with nine free real parameters. Moreover our main investigation of the collision dynamics of such mixed vector solitons by constructing the multisoliton solution of the generalized Manakov model with the help of Hirota technique reveals that the dark-bright-bright vector two-soliton supports energy-exchange collision dynamics. In particular the dark component preserves its initial form and the energy-exchange collision property of the bright-bright vector two-soliton solution of the Manakov model during collision. In addition the interactions between bound state dark-bright-bright vector solitons reveal oscillations in their amplitudes. A similar kind of breathing effect was also experimentally observed in the Bose-Einstein condensates. Some possible ways are theoretically suggested not only to control this breathing effect but also to manage the beating, bouncing, jumping, and attraction effects in the collision dynamics of dark-bright-bright vector solitons. The role of multiple free parameters in our solution is examined to define polarization vector, envelope speed, envelope width, envelope amplitude, grayness, and complex modulation of our solution. It is interesting to note that the polarization vector of our mixed vector one-soliton evolves in sphere or hyperboloid depending upon the initial parametric choices.

Soliton structure in crystalline acetanilide

DOE Office of Scientific and Technical Information (OSTI.GOV)

Eilbeck, J.C.; Lomdahl, P.S.; Scott, A.C.

1984-10-15

The theory of self-trapping of amide I vibrational energy in crystalline acetanilide is studied in detail. A spectrum of stationary, self-trapped (soliton) solutions is determined and tested for dynamic stability. Only those solutions for which the amide I energy is concentrated near a single molecule were found to be stable. Exciton modes were found to be unstable to decay into solitons.

Soliton structure in crystalline acetanilide

NASA Astrophysics Data System (ADS)

Eilbeck, J. C.; Lomdahl, P. S.; Scott, A. C.

1984-10-01

The theory of self-trapping of amide I vibrational energy in crystalline acetanilide is studied in detail. A spectrum of stationary, self-trapped (soliton) solutions is determined and tested for dynamic stability. Only those solutions for which the amide I energy is concentrated near a single molecule were found to be stable. Exciton modes were found to be unstable to decay into solitons.

Kinetic theory of dark solitons with tunable friction.

PubMed

Hurst, Hilary M; Efimkin, Dmitry K; Spielman, I B; Galitski, Victor

2017-05-01

We study controllable friction in a system consisting of a dark soliton in a one-dimensional Bose-Einstein condensate coupled to a noninteracting Fermi gas. The fermions act as impurity atoms, not part of the original condensate, that scatter off of the soliton. We study semiclassical dynamics of the dark soliton, a particlelike object with negative mass, and calculate its friction coefficient. Surprisingly, it depends periodically on the ratio of interspecies (impurity-condensate) to intraspecies (condensate-condensate) interaction strengths. By tuning this ratio, one can access a regime where the friction coefficient vanishes. We develop a general theory of stochastic dynamics for negative-mass objects and find that their dynamics are drastically different from their positive-mass counterparts: they do not undergo Brownian motion. From the exact phase-space probability distribution function (i.e., in position and velocity), we find that both the trajectory and lifetime of the soliton are altered by friction, and the soliton can undergo Brownian motion only in the presence of friction and a confining potential. These results agree qualitatively with experimental observations by Aycock et al. [Proc. Natl. Acad. Sci. USA 114 , 2503 (2017)] in a similar system with bosonic impurity scatterers.

Kinetic theory of dark solitons with tunable friction

PubMed Central

Hurst, Hilary M.; Efimkin, Dmitry K.; Spielman, I. B.; Galitski, Victor

2018-01-01

We study controllable friction in a system consisting of a dark soliton in a one-dimensional Bose-Einstein condensate coupled to a noninteracting Fermi gas. The fermions act as impurity atoms, not part of the original condensate, that scatter off of the soliton. We study semiclassical dynamics of the dark soliton, a particlelike object with negative mass, and calculate its friction coefficient. Surprisingly, it depends periodically on the ratio of interspecies (impurity-condensate) to intraspecies (condensate-condensate) interaction strengths. By tuning this ratio, one can access a regime where the friction coefficient vanishes. We develop a general theory of stochastic dynamics for negative-mass objects and find that their dynamics are drastically different from their positive-mass counterparts: they do not undergo Brownian motion. From the exact phase-space probability distribution function (i.e., in position and velocity), we find that both the trajectory and lifetime of the soliton are altered by friction, and the soliton can undergo Brownian motion only in the presence of friction and a confining potential. These results agree qualitatively with experimental observations by Aycock et al. [Proc. Natl. Acad. Sci. USA 114, 2503 (2017)] in a similar system with bosonic impurity scatterers. PMID:29744482

Influence of electromagnetic field on soliton-mediated charge transport in biological systems.

PubMed

Brizhik, Larissa

2015-01-01

It is shown that electromagnetic fields affect dynamics of Davydov's solitons which provide charge transport processes in macromolecules during metabolism of the system. There is a resonant frequency of the field at which it can cause the transition of electrons from bound soliton states into delocalised states. Such decay of solitons reduces the effectiveness of charge transport, and, therefore, inhibits redox processes. Solitons radiate their own electromagnetic field of characteristic frequency determined by their average velocity. This self-radiated field leads to synchronization of soliton dynamics and charge transport processes, and is the source of the coherence in the system. Exposition of the system to the oscillating electromagnetic field of the frequency, which coincides with the eigen-frequency of solitons can enhance eigen-radiation of solitons, and, therefore, will enhance synchronization of charge transpor, stimulate the redox processes and increase coherence in the system. Electromagnetic oscillating field causes also ratchet phenomenon of solitons, i.e., drift of solitons in macromolecules in the presence of unbiased periodic field. Such additional drift enhances the charge transport processes. It is shown that temperature facilitates the ratchet drift. In particular, temperature fluctuations lead to the lowering of the critical value of the intensity and period of the field, above which the drift of solitons takes place. Moreover, there is a stochastic resonance in the soliton dynamics in external electromagnetic fields. This means, that there is some optimal temperature at which the drift of solitons is maximal.

Peregrine soliton generation and breakup in standard telecommunications fiber.

PubMed

Hammani, Kamal; Kibler, Bertrand; Finot, Christophe; Morin, Philippe; Fatome, Julien; Dudley, John M; Millot, Guy

2011-01-15

We present experimental and numerical results showing the generation and breakup of the Peregrine soliton in standard telecommunications fiber. The impact of nonideal initial conditions is studied through direct cutback measurements of the longitudinal evolution of the emerging soliton dynamics and is shown to be associated with the splitting of the Peregrine soliton into two subpulses, with each subpulse itself exhibiting Peregrine soliton characteristics. Experimental results are in good agreement with simulations.

Optical Solitons

NASA Astrophysics Data System (ADS)

Taylor, J. R.

2005-08-01

1. Optical solitons in fibres: theoretical review A. Hasegawa; 2. Solitons in optical fibres: an experimental account L. F. Mollenauer; 3. All-optical long-distance soliton-based transmission systems K. Smith and L. F. Mollenauer; 4. Nonlinear propagation effects in optical fibres: numerical studies K. J. Blow and N. J. Doran; 5. Soliton-soliton interactions C. Desem and P. L. Chu; 6. Soliton amplification in erbium-doped fibre amplifiers and its application to soliton communication M. Nakazawa; 7. Nonlinear transformation of laser radiation and generation of Raman solitons in optical fibres E. M. Dianov, A. B. Grudinin, A. M. Prokhorov and V. N. Serkin; 8. Generation and compression of femtosecond solitons in optical fibers P. V. Mamyshev; 9. Optical fibre solitons in the presence of higher order dispersion and birefringence C. R. Menyuk and Ping-Kong A. Wai; 10. Dark optical solitons A. M. Weiner; 11. Soliton Raman effects J. R. Taylor; Bibliography; Index.

Optical Solitons

NASA Astrophysics Data System (ADS)

Taylor, J. R.

1992-04-01

1. Optical solitons in fibres: theoretical review A. Hasegawa; 2. Solitons in optical fibres: an experimental account L. F. Mollenauer; 3. All-optical long-distance soliton-based transmission systems K. Smith and L. F. Mollenauer; 4. Nonlinear propagation effects in optical fibres: numerical studies K. J. Blow and N. J. Doran; 5. Soliton-soliton interactions C. Desem and P. L. Chu; 6. Soliton amplification in erbium-doped fibre amplifiers and its application to soliton communication M. Nakazawa; 7. Nonlinear transformation of laser radiation and generation of Raman solitons in optical fibres E. M. Dianov, A. B. Grudinin, A. M. Prokhorov and V. N. Serkin; 8. Generation and compression of femtosecond solitons in optical fibers P. V. Mamyshev; 9. Optical fibre solitons in the presence of higher order dispersion and birefringence C. R. Menyuk and Ping-Kong A. Wai; 10. Dark optical solitons A. M. Weiner; 11. Soliton Raman effects J. R. Taylor; Bibliography; Index.

Dark-bright soliton pairs: Bifurcations and collisions

NASA Astrophysics Data System (ADS)

Katsimiga, G. C.; Kevrekidis, P. G.; Prinari, B.; Biondini, G.; Schmelcher, P.

2018-04-01

The statics, stability, and dynamical properties of dark-bright soliton pairs are investigated here, motivated by applications in a homogeneous two-component repulsively interacting Bose-Einstein condensate. One of the intraspecies interaction coefficients is used as the relevant parameter controlling the deviation from the integrable Manakov limit. Two different families of stationary states are identified consisting of dark-bright solitons that are either antisymmetric (out-of-phase) or asymmetric (mass imbalanced) with respect to their bright soliton. Both of the above dark-bright configurations coexist at the integrable limit of equal intra and interspecies repulsions and are degenerate in that limit. However, they are found to bifurcate from it in a transcritical bifurcation. This bifurcation interchanges the stability properties of the bound dark-bright pairs rendering the antisymmetric states unstable and the asymmetric ones stable past the associated critical point (and vice versa before it). Finally, on the dynamical side, it is found that large kinetic energies and thus rapid soliton collisions are essentially unaffected by the intraspecies variation, while cases involving near equilibrium states or breathing dynamics are significantly modified under such a variation.

Matter-wave dark solitons in boxlike traps

NASA Astrophysics Data System (ADS)

Sciacca, M.; Barenghi, C. F.; Parker, N. G.

2017-01-01

Motivated by the experimental development of quasihomogeneous Bose-Einstein condensates confined in boxlike traps, we study numerically the dynamics of dark solitons in such traps at zero temperature. We consider the cases where the side walls of the box potential rise either as a power law or a Gaussian. While the soliton propagates through the homogeneous interior of the box without dissipation, it typically dissipates energy during a reflection from a wall through the emission of sound waves, causing a slight increase in the soliton's speed. We characterize this energy loss as a function of the wall parameters. Moreover, over multiple oscillations and reflections in the boxlike trap, the energy loss and speed increase of the soliton can be significant, although the decay eventually becomes stabilized when the soliton equilibrates with the ambient sound field.

Observation of Two-Dimensional Localized Jones-Roberts Solitons in Bose-Einstein Condensates

NASA Astrophysics Data System (ADS)

Meyer, Nadine; Proud, Harry; Perea-Ortiz, Marisa; O'Neale, Charlotte; Baumert, Mathis; Holynski, Michael; Kronjäger, Jochen; Barontini, Giovanni; Bongs, Kai

2017-10-01

Jones-Roberts solitons are the only known class of stable dark solitonic solutions of the nonlinear Schrödinger equation in two and three dimensions. They feature a distinctive elongated elliptical shape that allows them to travel without change of form. By imprinting a triangular phase pattern, we experimentally generate two-dimensional Jones-Roberts solitons in a three-dimensional atomic Bose-Einstein condensate. We monitor their dynamics, observing that this kind of soliton is indeed not affected by dynamic (snaking) or thermodynamic instabilities, that instead make other classes of dark solitons unstable in dimensions higher than one. Our results confirm the prediction that Jones-Roberts solitons are stable solutions of the nonlinear Schrödinger equation and promote them for applications beyond matter wave physics, like energy and information transport in noisy and inhomogeneous environments.

Soliton-sound interactions in quasi-one-dimensional Bose-Einstein condensates.

PubMed

Parker, N G; Proukakis, N P; Leadbeater, M; Adams, C S

2003-06-06

Longitudinal confinement of dark solitons in quasi-one-dimensional Bose-Einstein condensates leads to sound emission and reabsorption. We perform quantitative studies of the dynamics of a soliton oscillating in a tight dimple trap, embedded in a weaker harmonic trap. The dimple depth provides a sensitive handle to control the soliton-sound interaction. In the limit of no reabsorption, the power radiated is found to be proportional to the soliton acceleration squared. An experiment is proposed to detect sound emission as a change in amplitude and frequency of soliton oscillations.

Solitons shedding from Airy beams and bound states of breathing Airy solitons in nonlocal nonlinear media

PubMed Central

Shen, Ming; Gao, Jinsong; Ge, Lijuan

2015-01-01

We investigate the spatially optical solitons shedding from Airy beams and anomalous interactions of Airy beams in nonlocal nonlinear media by means of direct numerical simulations. Numerical results show that nonlocality has profound effects on the propagation dynamics of the solitons shedding from the Airy beam. It is also shown that the strong nonlocality can support periodic intensity distribution of Airy beams with opposite bending directions. Nonlocality also provides a long-range attractive force between Airy beams, leading to the formation of stable bound states of both in-phase and out-of-phase breathing Airy solitons which always repel in local media. PMID:25900878

Real-time visualization of soliton molecules with evolving behavior in an ultrafast fiber laser

NASA Astrophysics Data System (ADS)

Liu, Meng; Li, Heng; Luo, Ai-Ping; Cui, Hu; Xu, Wen-Cheng; Luo, Zhi-Chao

2018-03-01

Ultrafast fiber lasers have been demonstrated to be great platforms for the investigation of soliton dynamics. The soliton molecules, as one of the most fascinating nonlinear phenomena, have been a hot topic in the field of nonlinear optics in recent years. Herein, we experimentally observed the real-time evolving behavior of soliton molecule in an ultrafast fiber laser by using the dispersive Fourier transformation technology. Several types of evolving soliton molecules were obtained in our experiments, such as soliton molecules with monotonically or chaotically evolving phase, flipping and hopping phase. These results would be helpful to the communities interested in soliton nonlinear dynamics as well as ultrafast laser technologies.

A Korteweg-de Vries description of dark solitons in polariton superfluids

NASA Astrophysics Data System (ADS)

Carretero-González, R.; Cuevas-Maraver, J.; Frantzeskakis, D. J.; Horikis, T. P.; Kevrekidis, P. G.; Rodrigues, A. S.

2017-12-01

We study the dynamics of dark solitons in an incoherently pumped exciton-polariton condensate by means of a system composed of a generalized open-dissipative Gross-Pitaevskii equation for the polaritons' wavefunction and a rate equation for the exciton reservoir density. Considering a perturbative regime of sufficiently small reservoir excitations, we use the reductive perturbation method, to reduce the system to a Korteweg-de Vries (KdV) equation with linear loss. This model is used to describe the analytical form and the dynamics of dark solitons. We show that the polariton field supports decaying dark soliton solutions with a decay rate determined analytically in the weak pumping regime. We also find that the dark soliton evolution is accompanied by a shelf, whose dynamics follows qualitatively the effective KdV picture.

A System of ODEs for a Perturbation of a Minimal Mass Soliton

NASA Astrophysics Data System (ADS)

Marzuola, Jeremy L.; Raynor, Sarah; Simpson, Gideon

2010-08-01

We study soliton solutions to the nonlinear Schrödinger equation (NLS) with a saturated nonlinearity. NLS with such a nonlinearity is known to possess a minimal mass soliton. We consider a small perturbation of a minimal mass soliton and identify a system of ODEs extending the work of Comech and Pelinovsky (Commun. Pure Appl. Math. 56:1565-1607, 2003), which models the behavior of the perturbation for short times. We then provide numerical evidence that under this system of ODEs there are two possible dynamical outcomes, in accord with the conclusions of Pelinovsky et al. (Phys. Rev. E 53(2):1940-1953, 1996). Generically, initial data which supports a soliton structure appears to oscillate, with oscillations centered on a stable soliton. For initial data which is expected to disperse, the finite dimensional dynamics initially follow the unstable portion of the soliton curve.

Acoustic solitons in waveguides with Helmholtz resonators: transmission line approach.

PubMed

Achilleos, V; Richoux, O; Theocharis, G; Frantzeskakis, D J

2015-02-01

We report experimental results and study theoretically soliton formation and propagation in an air-filled acoustic waveguide side loaded with Helmholtz resonators. We propose a theoretical modeling of the system, which relies on a transmission-line approach, leading to a nonlinear dynamical lattice model. The latter allows for an analytical description of the various soliton solutions for the pressure, which are found by means of dynamical systems and multiscale expansion techniques. These solutions include Boussinesq-like and Korteweg-de Vries pulse-shaped solitons that are observed in the experiment, as well as nonlinear Schrödinger envelope solitons, that are predicted theoretically. The analytical predictions are in excellent agreement with direct numerical simulations and in qualitative agreement with the experimental observations.

Two-layer-atmospheric blocking in a medium with high nonlinearity and lateral dispersion

NASA Astrophysics Data System (ADS)

Osman, M. S.; Abdel-Gawad, H. I.; El Mahdy, M. A.

2018-03-01

Herein, the extended coupled Kadomtsev-Petviashvili equation (CKPE) with lateral dispersion is investigated for studying the atmospheric blocking in two layers. A variety of new types of polynomial solutions for the CKPE is obtained using the unified method. Furthermore, we use the Hamiltonian systems with two degrees of freedom to discuss the stability of the obtained solutions through the bifurcation diagrams.

Matter-wave solitons in nonlinear optical lattices

NASA Astrophysics Data System (ADS)

Sakaguchi, Hidetsugu; Malomed, Boris A.

2005-10-01

We introduce a dynamical model of a Bose-Einstein condensate based on the one-dimensional (1D) Gross-Pitaevskii equation (GPE) with a nonlinear optical lattice (NOL), which is represented by the cubic term whose coefficient is periodically modulated in the coordinate. The model describes a situation when the atomic scattering length is spatially modulated, via the optically controlled Feshbach resonance, in an optical lattice created by interference of two laser beams. Relatively narrow solitons supported by the NOL are predicted by means of the variational approximation (VA), and an averaging method is applied to broad solitons. A different feature is a minimum norm (number of atoms), N=Nmin , necessary for the existence of solitons. The VA predicts Nmin very accurately. Numerical results are chiefly presented for the NOL with the zero spatial average value of the nonlinearity coefficient. Solitons with values of the amplitude A larger than at N=Nmin are stable. Unstable solitons with smaller, but not too small, A rearrange themselves into persistent breathers. For still smaller A , the soliton slowly decays into radiation without forming a breather. Broad solitons with very small A are practically stable, as their decay is extremely slow. These broad solitons may freely move across the lattice, featuring quasielastic collisions. Narrow solitons, which are strongly pinned to the NOL, can easily form stable complexes. Finally, the weakly unstable low-amplitude solitons are stabilized if a cubic term with a constant coefficient, corresponding to weak attraction, is included in the GPE.

Solitonic dynamics and excitations of the nonlinear Schrödinger equation with third-order dispersion in non-Hermitian PT-symmetric potentials.

PubMed

Chen, Yong; Yan, Zhenya

2016-03-22

Solitons are of the important significant in many fields of nonlinear science such as nonlinear optics, Bose-Einstein condensates, plamas physics, biology, fluid mechanics, and etc. The stable solitons have been captured not only theoretically and experimentally in both linear and nonlinear Schrödinger (NLS) equations in the presence of non-Hermitian potentials since the concept of the parity-time -symmetry was introduced in 1998. In this paper, we present novel bright solitons of the NLS equation with third-order dispersion in some complex -symmetric potentials (e.g., physically relevant -symmetric Scarff-II-like and harmonic-Gaussian potentials). We find stable nonlinear modes even if the respective linear -symmetric phases are broken. Moreover, we also use the adiabatic changes of the control parameters to excite the initial modes related to exact solitons to reach stable nonlinear modes. The elastic interactions of two solitons are exhibited in the third-order NLS equation with -symmetric potentials. Our results predict the dynamical phenomena of soliton equations in the presence of third-order dispersion and -symmetric potentials arising in nonlinear fiber optics and other physically relevant fields.

Solitonic dynamics and excitations of the nonlinear Schrödinger equation with third-order dispersion in non-Hermitian PT-symmetric potentials

PubMed Central

Chen, Yong; Yan, Zhenya

2016-01-01

Solitons are of the important significant in many fields of nonlinear science such as nonlinear optics, Bose-Einstein condensates, plamas physics, biology, fluid mechanics, and etc. The stable solitons have been captured not only theoretically and experimentally in both linear and nonlinear Schrödinger (NLS) equations in the presence of non-Hermitian potentials since the concept of the parity-time -symmetry was introduced in 1998. In this paper, we present novel bright solitons of the NLS equation with third-order dispersion in some complex -symmetric potentials (e.g., physically relevant -symmetric Scarff-II-like and harmonic-Gaussian potentials). We find stable nonlinear modes even if the respective linear -symmetric phases are broken. Moreover, we also use the adiabatic changes of the control parameters to excite the initial modes related to exact solitons to reach stable nonlinear modes. The elastic interactions of two solitons are exhibited in the third-order NLS equation with -symmetric potentials. Our results predict the dynamical phenomena of soliton equations in the presence of third-order dispersion and -symmetric potentials arising in nonlinear fiber optics and other physically relevant fields. PMID:27002543

Bright solitons in non-equilibrium coherent quantum matter

PubMed Central

Pinsker, F.; Flayac, H.

2016-01-01

We theoretically demonstrate a mechanism for bright soliton generation in spinor non-equilibrium Bose–Einstein condensates made of atoms or quasi-particles such as polaritons in semiconductor microcavities. We give analytical expressions for bright (half) solitons as minimizing functions of a generalized non-conservative Lagrangian elucidating the unique features of inter and intra-competition in non-equilibrium systems. The analytical results are supported by a detailed numerical analysis that further shows the rich soliton dynamics inferred by their instability and mutual cross-interactions. PMID:26997892

Soliton switching in a site-dependent ferromagnet

NASA Astrophysics Data System (ADS)

Senjudarvannan, R.; Sathishkumar, P.; Vijayalakshmi, S.

2017-02-01

Switching of soliton in a ferromagnetic medium offers the possibility of developing a new innovative approach for information storage technologies. The nonlinear spin dynamics of a site-dependent Heisenberg ferromagnetic spin chain with Gilbert damping under the influence of external magnetic field is expressed in the form of the Landau-Lifshitz-Gilbert equation in the classical continuum limit. The corresponding evolution equation is developed through stereographic projection technique by projecting the unit sphere of spin onto a complex plane. The exact soliton solutions are constructed by solving the associated evolution equation through the modified extended tanh-function method. The impact of damping and external magnetic field on the magnetic soliton under the invariant inhomogeneity is investigated and finally, the magnetization switching in the form of shape changing solitons are demonstrated.

Elliptic-type soliton combs in optical ring microresonators

NASA Astrophysics Data System (ADS)

Dikandé Bitha, Rodrigues D.; Dikandé, Alain M.

2018-03-01

Soliton crystals are periodic patterns of multispot optical fields formed from either time or space entanglements of equally separated identical high-intensity pulses. These specific nonlinear optical structures have gained interest in recent years with the advent and progress in nonlinear optical fibers and fiber lasers, photonic crystals, wave-guided wave systems, and most recently optical ring microresonator devices. In this work an extensive analysis of characteristic features of soliton crystals is carried out, with an emphasis on their one-to-one correspondence with elliptic solitons. With this purpose in mind, we examine their formation, their stability, and their dynamics in ring-shaped nonlinear optical media within the framework of the Lugiato-Lefever equation. The stability analysis deals with internal modes of the system via a 2 ×2 -matrix Lamé-type eigenvalue problem, the spectrum of which is shown to possess a rich set of bound states consisting of stable zero-fequency modes and unstable decaying as well as growing modes. Turning towards the dynamics of elliptic solitons in ring-shaped fiber resonators with Kerr nonlinearity, we first propose a collective-coordinate approach, based on a Lagrangian formalism suitable for elliptic-soliton solutions to the nonlinear Schrödinger equation with an arbitrary perturbation. Next we derive time evolutions of elliptic-soliton parameters in the specific context of ring-shaped optical fiber resonators, where the optical field evolution is thought to be governed by the Lugiato-Lefever equation. By solving numerically the collective-coordinate equations an analysis of the amplitude, the position, the phase of internal oscillations, the phase velocity, the energy, and phase portraits of the amplitude is carried out and reveals a complex dynamics of the elliptic soliton in ring-shaped optical microresonators. Direct numerical simulations of the Lugiato-Lefever equation are also carried out seeking for stationary

From Nothing to Something II: Nonlinear Systems via Consistent Correlated Bang

NASA Astrophysics Data System (ADS)

Lou, Sen-Yue

2017-06-01

Chinese ancient sage Laozi said everything comes from \\emph{\\bf \\em "nothing"}. \\rm In the first letter (Chin. Phys. Lett. 30 (2013) 080202), infinitely many discrete integrable systems have been obtained from "nothing" via simple principles (Dao). In this second letter, a new idea, the consistent correlated bang, is introduced to obtain nonlinear dynamic systems including some integrable ones such as the continuous nonlinear Schr\\"odinger equation (NLS), the (potential) Korteweg de Vries (KdV) equation, the (potential) Kadomtsev-Petviashvili (KP) equation and the sine-Gordon (sG) equation. These nonlinear systems are derived from nothing via suitable "Dao", the shifted parity, the charge conjugate, the delayed time reversal, the shifted exchange, the shifted-parity-rotation and so on.

Quasi-periodicity of vector solitons in a graphene mode-locked fiber laser

NASA Astrophysics Data System (ADS)

Song, Yu Feng; Li, Lei; Tang, Ding Yuan; Shen, De Yuan

2013-12-01

We report on the experimental observation of quasi-periodic dynamics of vector solitons in an erbium-doped fiber laser passively mode-locked with atomic layer graphene. Apart from the stable polarization-locked vector soliton emission, it was found that under certain conditions the fiber laser could also emit vector solitons with quasi-periodic pulse energy variation and polarization rotation during the cavity roundtrips. We show that the physical mechanism for the quasi-periodic vector soliton evolution is cavity-induced soliton modulation instability. Quasi-periodic evolution of multiple vector solitons was also observed in the same laser.

Nonlinear Waves and Inverse Scattering

DTIC Science & Technology

1990-09-18

to be published Proceedings: conference Chaos in Australia (February 1990). 5. On the Kadomtsev Petviashvili Equation and Associated Constraints by...Scattering Transfoni (IST). IST is a method which alows one to’solve nonlinear wave equations by solving certain related direct and inverse scattering...problems. We use these results to find solutions to nonlinear wave equations much like one uses Fourier analysis for linear problems. Moreover the

Nonlinear Waves and Inverse Scattering

DTIC Science & Technology

1989-01-01

transform provides a linearization.’ Well known systems include the Kadomtsev - Petviashvili , Davey-Stewartson and Self-Dual Yang-Mills equations . The d...which employs inverse scattering theory in order to linearize the given nonlinear equation . I.S.T. has led to new developments in both fields: inverse...scattering and nonlinear wave equations . Listed below are some of the problems studied and a short description of results. - Multidimensional

Emergence and space-time structure of lump solution to the (2+1)-dimensional generalized KP equation

NASA Astrophysics Data System (ADS)

Tan, Wei; Dai, Houping; Dai, Zhengde; Zhong, Wenyong

2017-11-01

A periodic breather-wave solution is obtained using homoclinic test approach and Hirota's bilinear method with a small perturbation parameter u0 for the (2+1)-dimensional generalized Kadomtsev-Petviashvili equation. Based on the periodic breather-wave, a lump solution is emerged by limit behaviour. Finally, three different forms of the space-time structure of the lump solution are investigated and discussed using the extreme value theory.

Soliton-plasma nonlinear dynamics in mid-IR gas-filled hollow-core fibers.

PubMed

Selim Habib, Md; Markos, Christos; Bang, Ole; Bache, Morten

2017-06-01

We investigate numerically soliton-plasma interaction in a noble-gas-filled silica hollow-core anti-resonant fiber pumped in the mid-IR at 3.0 μm. We observe multiple soliton self-compression stages due to distinct stages where either the self-focusing or the self-defocusing nonlinearity dominates. Specifically, the parameters may be tuned so the competing plasma self-defocusing nonlinearity only dominates over the Kerr self-focusing nonlinearity around the soliton self-compression stage, where the increasing peak intensity on the leading pulse edge initiates a competing self-defocusing plasma nonlinearity acting nonlocally on the trailing edge, effectively preventing soliton formation there. As the plasma switches off after the self-compression stage, self-focusing dominates again, initiating another soliton self-compression stage in the trailing edge. This process is accompanied by supercontinuum generation spanning 1-4 μm. We find that the spectral coherence drops as the secondary compression stage is initiated.

Modelling rogue waves through exact dynamical lump soliton controlled by ocean currents.

PubMed

Kundu, Anjan; Mukherjee, Abhik; Naskar, Tapan

2014-04-08

Rogue waves are extraordinarily high and steep isolated waves, which appear suddenly in a calm sea and disappear equally fast. However, though the rogue waves are localized surface waves, their theoretical models and experimental observations are available mostly in one dimension, with the majority of them admitting only limited and fixed amplitude and modular inclination of the wave. We propose two dimensions, exactly solvable nonlinear Schrödinger (NLS) equation derivable from the basic hydrodynamic equations and endowed with integrable structures. The proposed two-dimensional equation exhibits modulation instability and frequency correction induced by the nonlinear effect, with a directional preference, all of which can be determined through precise analytic result. The two-dimensional NLS equation allows also an exact lump soliton which can model a full-grown surface rogue wave with adjustable height and modular inclination. The lump soliton under the influence of an ocean current appears and disappears preceded by a hole state, with its dynamics controlled by the current term. These desirable properties make our exact model promising for describing ocean rogue waves.

Modelling rogue waves through exact dynamical lump soliton controlled by ocean currents

PubMed Central

Kundu, Anjan; Mukherjee, Abhik; Naskar, Tapan

2014-01-01

Rogue waves are extraordinarily high and steep isolated waves, which appear suddenly in a calm sea and disappear equally fast. However, though the rogue waves are localized surface waves, their theoretical models and experimental observations are available mostly in one dimension, with the majority of them admitting only limited and fixed amplitude and modular inclination of the wave. We propose two dimensions, exactly solvable nonlinear Schrödinger (NLS) equation derivable from the basic hydrodynamic equations and endowed with integrable structures. The proposed two-dimensional equation exhibits modulation instability and frequency correction induced by the nonlinear effect, with a directional preference, all of which can be determined through precise analytic result. The two-dimensional NLS equation allows also an exact lump soliton which can model a full-grown surface rogue wave with adjustable height and modular inclination. The lump soliton under the influence of an ocean current appears and disappears preceded by a hole state, with its dynamics controlled by the current term. These desirable properties make our exact model promising for describing ocean rogue waves. PMID:24711719

Dark solitons in the presence of higher-order effects.

PubMed

Horikis, Theodoros P; Frantzeskakis, Dimitrios J

2013-12-01

Dark soliton propagation is studied in the presence of higher-order effects, including third-order dispersion, self-steepening, linear/nonlinear gain/loss, and Raman scattering. It is found that for certain values of the parameters a stable evolution can exist for both the soliton and the relative continuous-wave background. Using a newly developed perturbation theory we show that the perturbing effects give rise to a shelf that accompanies the soliton in its propagation. Although, the stable solitons are not affected by the shelf it remains an integral part of the dynamics otherwise not considered so far in studies of higher-order nonlinear Schrödinger models.

Dark soliton interaction of spinor Bose-Einstein condensates in an optical lattice

DOE Office of Scientific and Technical Information (OSTI.GOV)

Li Zaidong; Li Qiuyan

2007-08-15

We study the magnetic soliton dynamics of spinor Bose-Einstein condensates in an optical lattice which results in an effective Hamiltonian of anisotropic pseudospin chain. An equation of nonlinear Schroedinger type is derived and exact magnetic soliton solutions are obtained analytically by means of Hirota method. Our results show that the critical external field is needed for creating the magnetic soliton in spinor Bose-Einstein condensates. The soliton size, velocity and shape frequency can be controlled in practical experiment by adjusting the magnetic field. Moreover, the elastic collision of two solitons is investigated in detail.

Thermal diffusion of Boussinesq solitons.

PubMed

Arévalo, Edward; Mertens, Franz G

2007-10-01

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

Interactions of bright and dark solitons with localized PT-symmetric potentials.

PubMed

Karjanto, N; Hanif, W; Malomed, B A; Susanto, H

2015-02-01

We study collisions of moving nonlinear-Schrödinger solitons with a PT-symmetric dipole embedded into the one-dimensional self-focusing or defocusing medium. Accurate analytical results are produced for bright solitons, and, in a more qualitative form, for dark ones. In the former case, an essential aspect of the approximation is that it must take into regard the intrinsic chirp of the soliton, thus going beyond the framework of the simplest quasi-particle description of the soliton's dynamics. Critical velocities separating reflection and transmission of the incident bright solitons are found by means of numerical simulations, and in the approximate semi-analytical form. An exact solution for the dark soliton pinned by the complex PT-symmetric dipole is produced too.

Detection of Moving Targets Using Soliton Resonance Effect

NASA Technical Reports Server (NTRS)

Kulikov, Igor K.; Zak, Michail

2013-01-01

The objective of this research was to develop a fundamentally new method for detecting hidden moving targets within noisy and cluttered data-streams using a novel "soliton resonance" effect in nonlinear dynamical systems. The technique uses an inhomogeneous Korteweg de Vries (KdV) equation containing moving-target information. Solution of the KdV equation will describe a soliton propagating with the same kinematic characteristics as the target. The approach uses the time-dependent data stream obtained with a sensor in form of the "forcing function," which is incorporated in an inhomogeneous KdV equation. When a hidden moving target (which in many ways resembles a soliton) encounters the natural "probe" soliton solution of the KdV equation, a strong resonance phenomenon results that makes the location and motion of the target apparent. Soliton resonance method will amplify the moving target signal, suppressing the noise. The method will be a very effective tool for locating and identifying diverse, highly dynamic targets with ill-defined characteristics in a noisy environment. The soliton resonance method for the detection of moving targets was developed in one and two dimensions. Computer simulations proved that the method could be used for detection of singe point-like targets moving with constant velocities and accelerations in 1D and along straight lines or curved trajectories in 2D. The method also allows estimation of the kinematic characteristics of moving targets, and reconstruction of target trajectories in 2D. The method could be very effective for target detection in the presence of clutter and for the case of target obscurations.

Nonlinear instability of half-solitons on star graphs

NASA Astrophysics Data System (ADS)

Kairzhan, Adilbek; Pelinovsky, Dmitry E.

2018-06-01

We consider a half-soliton stationary state of the nonlinear Schrödinger equation with the power nonlinearity on a star graph consisting of N edges and a single vertex. For the subcritical power nonlinearity, the half-soliton state is a degenerate critical point of the action functional under the mass constraint such that the second variation is nonnegative. By using normal forms, we prove that the degenerate critical point is a saddle point, for which the small perturbations to the half-soliton state grow slowly in time resulting in the nonlinear instability of the half-soliton state. The result holds for any N ≥ 3 and arbitrary subcritical power nonlinearity. It gives a precise dynamical characterization of the previous result of Adami et al. (2012) [2], where the half-soliton state was shown to be a saddle point of the action functional under the mass constraint for N = 3 and for cubic nonlinearity.

Coupled matter-wave solitons in optical lattices

NASA Astrophysics Data System (ADS)

Golam Ali, Sk; Talukdar, B.

2009-06-01

We make use of a potential model to study the dynamics of two coupled matter-wave or Bose-Einstein condensate (BEC) solitons loaded in optical lattices. With separate attention to linear and nonlinear lattices we find some remarkable differences for response of the system to effects of these lattices. As opposed to the case of linear optical lattice (LOL), the nonlinear lattice (NOL) can be used to control the mutual interaction between the two solitons. For a given lattice wave number k, the effective potentials in which the two solitons move are such that the well (Veff(NOL)), resulting from the juxtaposition of soliton interaction and nonlinear lattice potential, is deeper than the corresponding well Veff(LOL). But these effective potentials have opposite k dependence in the sense that the depth of Veff(LOL) increases as k increases and that of Veff(NOL) decreases for higher k values. We verify that the effectiveness of optical lattices to regulate the motion of the coupled solitons depends sensitively on the initial locations of the motionless solitons as well as values of the lattice wave number. For both LOL and NOL the two solitons meet each other due to mutual interaction if their initial locations are taken within the potential wells with the difference that the solitons in the NOL approach each other rather rapidly and take roughly half the time to meet as compared with the time needed for such coalescence in the LOL. In the NOL, the soliton profiles can move freely and respond to the lattice periodicity when the separation between their initial locations are as twice as that needed for a similar free movement in the LOL. We observe that, in both cases, slow tuning of the optical lattices by varying k with respect to a time parameter τ drags the oscillatory solitons apart to take them to different locations. In our potential model the oscillatory solitons appear to propagate undistorted. But a fully numerical calculation indicates that during evolution

Massive soliton stars

NASA Technical Reports Server (NTRS)

Chiu, Hong-Yee

1990-01-01

The structure of nontopological solutions of Einstein field equations as proposed by Friedberg, Lee, and Pang (1987) is examined. This analysis incorporates finite temperature effects and pair creation. Quarks are assumed to be the only species that exist in interior of soliton stars. The possibility of primordial creation of soliton stars in the incomplete decay of the degenerate vacuum in early universe is explored. Because of dominance of pair creation inside soliton stars, the luminosity of soliton stars is not determined by its radiative transfer characteristics, and the surface temperature of soliton stars can be the same as its interior temperature. It is possible that soliton stars are intense X-ray radiators at large distances. Soliton stars are nearly 100 percent efficient energy converters, converting the rest energy of baryons entering the interior into radiation. It is possible that a sizable number of baryons may also be trapped inside soliton stars during early epochs of the universe. In addition, if soliton stars exist they could assume the role played by massive black holes in galactic centers.

Ponderable soliton stars

NASA Technical Reports Server (NTRS)

Chiu, Hong-Yee

1990-01-01

The theory of Lee and Pang (1987), who obtained solutions for soliton stars composed of zero-temperature fermions and bosons, is applied here to quark soliton stars. Model soliton stars based on a simple physical model of the proton are computed, and the properties of the solitons are discussed, including the important problem of the existence of a limiting mass and thus the possible formation of black holes of primordial origin. It is shown that there is a definite mass limit for ponderable soliton stars, so that during cooling a soliton star might reach a stage beyond which no equilibrium configuration exists and the soliton star probably will collapse to become a black hole. The radiation of ponderable soliton stars may alter the short-wavelength character of the cosmic background radiation, and may be observed as highly redshifted objects at z of about 100,000.

Dark soliton beats in the time-varying background of Bose-Einstein condensates

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wu Lei; Li Lu; Zhang Jiefang

2009-07-15

We investigate the dynamics of dark solitons in one-dimensional Bose-Einstein condensates. In the large particle limit, by introducing the lens-type transformation, we find that the macroscopic wave function evolves self-similarly when its initial profile strays from that of the equilibrium state, which provides a time-varying background for the propagation of dark solitons. The interaction of dark solitons with this kind of background is studied both analytically and numerically. We find that the center-of-mass motion of the dark soliton is deeply affected by the time-varying background, and the beating phenomena of dark soliton emerge when the intrinsic frequency of the darkmore » soliton approaches that of the background. Lastly, we investigate the propagation of dark solitons in the freely expanding background.« less

Local Discontinuous Galerkin Methods for the Cahn-Hilliard Type Equations

DTIC Science & Technology

2007-01-01

Kuramoto-Sivashinsky equations , the Ito-type coupled KdV equa- tions, the Kadomtsev - Petviashvili equation , and the Zakharov-Kuznetsov equation . A common...Local discontinuous Galerkin methods for the Cahn-Hilliard type equations Yinhua Xia∗, Yan Xu† and Chi-Wang Shu ‡ Abstract In this paper we develop...local discontinuous Galerkin (LDG) methods for the fourth-order nonlinear Cahn-Hilliard equation and system. The energy stability of the LDG methods is

On the generation of cnoidal waves in ion beam-dusty plasma containing superthermal electrons and ions

NASA Astrophysics Data System (ADS)

El-Bedwehy, N. A.

2016-07-01

The reductive perturbation technique is used for investigating an ion beam-dusty plasma system consisting of two opposite polarity dusty grains, and superthermal electrons and ions in addition to ion beam. A two-dimensional Kadomtsev-Petviashvili equation is derived. The solution of this equation, employing Painlevé analysis, leads to cnoidal waves. The dependence of the structural features of these waves on the physical plasma parameters is investigated.

Two-dimensional evolution equation of finite-amplitude internal gravity waves in a uniformly stratified fluid

PubMed

Kataoka; Tsutahara; Akuzawa

2000-02-14

We derive a fully nonlinear evolution equation that can describe the two-dimensional motion of finite-amplitude long internal waves in a uniformly stratified three-dimensional fluid of finite depth. The derived equation is the two-dimensional counterpart of the evolution equation obtained by Grimshaw and Yi [J. Fluid Mech. 229, 603 (1991)]. In the small-amplitude limit, our equation is reduced to the celebrated Kadomtsev-Petviashvili equation.

Stability and tunneling dynamics of a dark-bright soliton pair in a harmonic trap

DOE PAGES

Karamatskos, E. T.; Stockhofe, J.; Kevrekidis, P. G.; ...

2015-04-30

In this study, we consider a binary repulsive Bose-Einstein condensate in a harmonic trap in one spatial dimension and investigate particular solutions consisting of two dark-bright solitons. There are two different stationary solutions characterized by the phase difference in the bright component, in-phase and out-of-phase states. We show that above a critical particle number in the bright component, a symmetry-breaking bifurcation of the pitchfork type occurs that leads to a new asymmetric solution whereas the parental branch, i.e., the out-of-phase state, becomes unstable. These three different states support different small amplitude oscillations, characterized by an almost stationary density of themore » dark component and a tunneling of the bright component between the two dark solitons. Within a suitable effective double-well picture, these can be understood as the characteristic features of a bosonic Josephson junction (BJJ), and we show within a two-mode approach that all characteristic features of the BJJ phase space are recovered. For larger deviations from the stationary states, the simplifying double-well description breaks down due to the feedback of the bright component onto the dark one, causing the solitons to move. In this regime we observe intricate anharmonic and aperiodic dynamics, exhibiting remnants of the BJJ phase space.« less

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

Features of the Paired Soliton Interactions Within the Framework of the Gardner Equation

NASA Astrophysics Data System (ADS)

Shurgalina, E. G.

2018-02-01

We study the dynamics of the two-soliton interaction within the framework of a completely integrable model, namely, the Gardner equation with negative cubic nonlinearity, which admits the existence of a limiting soliton. The features of the soliton interaction with participation of a thick soliton are demonstrated. Special attention is paid to the nonlinear-interaction influence on the wave-field moments, which determine the skewness and the kurtosis in the theory of turbulence.

Magnetic droplet solitons generated by pure spin currents

NASA Astrophysics Data System (ADS)

Divinskiy, B.; Urazhdin, S.; Demidov, V. E.; Kozhanov, A.; Nosov, A. P.; Rinkevich, A. B.; Demokritov, S. O.

2017-12-01

Magnetic droplets are dynamical solitons that can be generated by locally suppressing the dynamical damping in magnetic films with perpendicular anisotropy. To date, droplets have been observed only in nanocontact spin-torque oscillators operated by spin-polarized electrical currents. Here, we experimentally demonstrate that magnetic droplets can be nucleated and sustained by pure spin currents in nanoconstriction-based spin Hall devices. Micromagnetic simulations support our interpretation of the data, and indicate that in addition to the stationary droplets, propagating solitons can be also generated in the studied system, which can be utilized for the information transmission in spintronic applications.

Vector nature of multi-soliton patterns in a passively mode-locked figure-eight fiber laser.

PubMed

Ning, Qiu-Yi; Liu, Hao; Zheng, Xu-Wu; Yu, Wei; Luo, Ai-Ping; Huang, Xu-Guang; Luo, Zhi-Chao; Xu, Wen-Cheng; Xu, Shan-Hui; Yang, Zhong-Min

2014-05-19

The vector nature of multi-soliton dynamic patterns was investigated in a passively mode-locked figure-eight fiber laser based on the nonlinear amplifying loop mirror (NALM). By properly adjusting the cavity parameters such as the pump power level and intra-cavity polarization controllers (PCs), in addition to the fundamental vector soliton, various vector multi-soliton regimes were observed, such as the random static distribution of vector multiple solitons, vector soliton cluster, vector soliton flow, and the state of vector multiple solitons occupying the whole cavity. Both the polarization-locked vector solitons (PLVSs) and the polarization-rotating vector solitons (PRVSs) were observed for fundamental soliton and each type of multi-soliton patterns. The obtained results further reveal the fundamental physics of multi-soliton patterns and demonstrate that the figure-eight fiber lasers are indeed a good platform for investigating the vector nature of different soliton types.

Long-range sound-mediated dark-soliton interactions in trapped atomic condensates

DOE Office of Scientific and Technical Information (OSTI.GOV)

Allen, A. J.; Jackson, D. P.; Barenghi, C. F.

2011-01-15

A long-range soliton interaction is discussed whereby two or more dark solitons interact in an inhomogeneous atomic condensate, modifying their respective dynamics via the exchange of sound waves without ever coming into direct contact. An idealized double-well geometry is shown to yield perfect energy transfer and complete periodic identity reversal of the two solitons. Two experimentally relevant geometries are analyzed which should enable the observation of this long-range interaction.

Soliton Perturbation Theory for Dispersion-Managed Optical Fibers

NASA Astrophysics Data System (ADS)

Kohl, Russell; Milovic, Daniela; Zerrad, Essaid; Biswas, Anjan

This paper studies the propagation of solitons through optical fibers with dispersion management. The adiabatic variation of the soliton parameters, due to the presence of perturbation terms, is obtained. The dynamics is studied for the case of polarization-preserving fibers, while the types of pulses that are considered here are Gaussian, super-Gaussian and supersech. The perturbation terms that are taken into consideration are both local and nonlocal.

Analytical theory of two-dimensional ring dark soliton in nonlocal nonlinear media

NASA Astrophysics Data System (ADS)

Chen, Wei; Wang, Qi; Shi, Jielong; Shen, Ming

2017-11-01

Completely stable two-dimensional ring dark soliton in nonlocal media with an arbitrary degree of nonlocality are investigated. The exact solution of the ring dark solitons is obtained with the variational method and a cylindrical nonlocal response function. The analytical results are confirmed by directly numerical simulations. We also analytically and numerically study the expansion dynamics of the gray ring dark solitons in detail.

Spherical ion acoustic waves in pair ion plasmas with nonthermal electrons

NASA Astrophysics Data System (ADS)

Selim, M. M.

2016-04-01

Propagation of nonplanar ion acoustic waves in a plasma composed of negative and positive ions and nonthermally distributed electrons is investigated using reductive perturbation theory. The spherical Kadomtsev-Petviashvili (SKP) equation which describes the dynamics of the nonlinear spherical ion acoustic waves is derived. It is found that compressive and rarefactive ion-acoustic solitary wave characteristics significantly depend on the density and mass ratios of the positive to negative ions, the nonthermal electron parameter, and the geometry factor. The possible regions for the existence of spherical ion acoustic waves are defined precisely for typical parameters of (H+, O2 -) and (H+, H-) plasmas in the D and F-regions of the Earth's ionosphere, as well as for laboratory plasma (Ar+, F-).

Multidimensional nonlinear ion-acoustic waves in a plasma in view of relativistic effects

NASA Astrophysics Data System (ADS)

Belashov, V. Yu.

2017-05-01

The structure and dynamics of ion-acoustic waves in an unmagnetized plasma, including the case of weakly relativistic collisional plasma (when it is necessary to take into account the high energy particle flows which are observed in the magnetospheric plasma), are studied analytically and numerically on the basis of a model of the Kadomtsev-Petviashvili (KP) equation. It is shown that, if the velocity of plasma particles approaches the speed of light, the relativistic effects start to strongly influence on the wave characteristics, such as its phase velocity, amplitude, and characteristic wavelength, with the propagation of the twodimensional solitary ion-acoustic wave. The results can be used in the study of nonlinear wave processes in the magnetosphere and in laser and astrophysical plasma.

Coexistence of a self-induced transparency soliton and a Bragg soliton.

PubMed

Tseng, Hong-Yih; Chi, Sien

2002-11-01

We theoretically show that a self-induced transparency (SIT) soliton and a Bragg soliton can coexist in a nonlinear photonic band gap (PBG) medium doped uniformly with inhomogeneous-broadening two-level atoms. The Maxwell-Bloch equations for the pulse propagating through such a uniformly doped PBG structure are derived first and further reduced to an effective nonlinear Schrödinger equation. This model describes an equivalent physical mechanism for a Bragg-soliton propagation resulting from the effective quadratic dispersion balancing with the effective third-order nonlinearity. Because the resonant atoms are taken into account, the original band gap can be shifted both by the dopants and the instantaneous nonlinearity response originating from an intense optical pulse. As a result, even if a SIT soliton with its central frequency deep inside the original forbidden band, it still can propagate through the resonant PBG medium as long as this SIT soliton satisfies the effective Bragg-soliton propagation. An approximate soliton solution describing such coexistence is found. We also show that the pulse width and group velocity of this soliton solution can be uniquely determined for given material parameters, atomic transition frequency, and input central frequency of the soliton. The numerical examples of the SIT soliton in a one-dimensional As2S3-based PBG structure doped uniformly with Lorentzian line-shape resonant atoms are shown. It is found that a SIT soliton with approximately 100-ps width in such a resonant PBG structure can travel with the velocity being two orders of magnitude slower than the light speed in an unprocessed host medium.

Hydrodynamic optical soliton tunneling

NASA Astrophysics Data System (ADS)

Sprenger, P.; Hoefer, M. A.; El, G. A.

2018-03-01

A notion of hydrodynamic optical soliton tunneling is introduced in which a dark soliton is incident upon an evolving, broad potential barrier that arises from an appropriate variation of the input signal. The barriers considered include smooth rarefaction waves and highly oscillatory dispersive shock waves. Both the soliton and the barrier satisfy the same one-dimensional defocusing nonlinear Schrödinger (NLS) equation, which admits a convenient dispersive hydrodynamic interpretation. Under the scale separation assumption of nonlinear wave (Whitham) modulation theory, the highly nontrivial nonlinear interaction between the soliton and the evolving hydrodynamic barrier is described in terms of self-similar, simple wave solutions to an asymptotic reduction of the Whitham-NLS partial differential equations. One of the Riemann invariants of the reduced modulation system determines the characteristics of a soliton interacting with a mean flow that results in soliton tunneling or trapping. Another Riemann invariant yields the tunneled soliton's phase shift due to hydrodynamic interaction. Soliton interaction with hydrodynamic barriers gives rise to effects that include reversal of the soliton propagation direction and spontaneous soliton cavitation, which further suggest possible methods of dark soliton control in optical fibers.

Hydrodynamic optical soliton tunneling.

PubMed

Sprenger, P; Hoefer, M A; El, G A

2018-03-01

A notion of hydrodynamic optical soliton tunneling is introduced in which a dark soliton is incident upon an evolving, broad potential barrier that arises from an appropriate variation of the input signal. The barriers considered include smooth rarefaction waves and highly oscillatory dispersive shock waves. Both the soliton and the barrier satisfy the same one-dimensional defocusing nonlinear Schrödinger (NLS) equation, which admits a convenient dispersive hydrodynamic interpretation. Under the scale separation assumption of nonlinear wave (Whitham) modulation theory, the highly nontrivial nonlinear interaction between the soliton and the evolving hydrodynamic barrier is described in terms of self-similar, simple wave solutions to an asymptotic reduction of the Whitham-NLS partial differential equations. One of the Riemann invariants of the reduced modulation system determines the characteristics of a soliton interacting with a mean flow that results in soliton tunneling or trapping. Another Riemann invariant yields the tunneled soliton's phase shift due to hydrodynamic interaction. Soliton interaction with hydrodynamic barriers gives rise to effects that include reversal of the soliton propagation direction and spontaneous soliton cavitation, which further suggest possible methods of dark soliton control in optical fibers.

Bright and dark solitons in the normal dispersion regime of inhomogeneous optical fibers: Soliton interaction and soliton control

DOE Office of Scientific and Technical Information (OSTI.GOV)

Liu Wenjun; Tian Bo, E-mail: tian.bupt@yahoo.com.c; State Key Laboratory of Software Development Environment, Beijing University of Aeronautics and Astronautics, Beijing 100191

2010-08-15

Symbolically investigated in this paper is a nonlinear Schroedinger equation with the varying dispersion and nonlinearity for the propagation of optical pulses in the normal dispersion regime of inhomogeneous optical fibers. With the aid of the Hirota method, analytic one- and two-soliton solutions are obtained. Relevant properties of physical and optical interest are illustrated. Different from the previous results, both the bright and dark solitons are hereby derived in the normal dispersion regime of the inhomogeneous optical fibers. Moreover, different dispersion profiles of the dispersion-decreasing fibers can be used to realize the soliton control. Finally, soliton interaction is discussed withmore » the soliton control confirmed to have no influence on the interaction. The results might be of certain value for the study of the signal generator and soliton control.« less

Soliton creation, propagation, and annihilation in aeromechanical arrays of one-way coupled bistable elements

NASA Astrophysics Data System (ADS)

Rosenberger, Tessa; Lindner, John F.

We study the dynamics of mechanical arrays of bistable elements coupled one-way by wind. Unlike earlier hydromechanical unidirectional arrays, our aeromechanical one-way arrays are simpler, easier to study, and exhibit a broader range of phenomena. Soliton-like waves propagate in one direction at speeds proportional to wind speeds. Periodic boundaries enable solitons to annihilate in pairs in even arrays where adjacent elements are attracted to opposite stable states. Solitons propagate indefinitely in odd arrays where pairing is frustrated. Large noise spontaneously creates soliton- antisoliton pairs, as predicted by prior computer simulations. Soliton annihilation times increase quadratically with initial separations, as expected for random walk models of soliton collisions.

Helmholtz dark solitons.

PubMed

Chamorro-Posada, P; McDonald, G S

2003-05-15

A general dark-soliton solution of the Helmholtz equation (with defocusing Kerr nonlinearity) that has on- and off-axis, gray and black, paraxial and Helmholtz solitons as particular solutions, is reported. Modifications to soliton transverse velocity, width, phase period, and existence conditions are derived and explained in geometrical terms. Simulations verify analytical predictions and also demonstrate spontaneous formation of Helmholtz solitons and transparency of their interactions.

Quadratic spatial soliton interactions

NASA Astrophysics Data System (ADS)

Jankovic, Ladislav

Quadratic spatial soliton interactions were investigated in this Dissertation. The first part deals with characterizing the principal features of multi-soliton generation and soliton self-reflection. The second deals with two beam processes leading to soliton interactions and collisions. These subjects were investigated both theoretically and experimentally. The experiments were performed by using potassium niobate (KNBO 3) and periodically poled potassium titanyl phosphate (KTP) crystals. These particular crystals were desirable for these experiments because of their large nonlinear coefficients and, more importantly, because the experiments could be performed under non-critical-phase-matching (NCPM) conditions. The single soliton generation measurements, performed on KNBO3 by launching the fundamental component only, showed a broad angular acceptance bandwidth which was important for the soliton collisions performed later. Furthermore, at high input intensities multi-soliton generation was observed for the first time. The influence on the multi-soliton patterns generated of the input intensity and beam symmetry was investigated. The combined experimental and theoretical efforts indicated that spatial and temporal noise on the input laser beam induced multi-soliton patterns. Another research direction pursued was intensity dependent soliton routing by using of a specially engineered quadratically nonlinear interface within a periodically poled KTP sample. This was the first time demonstration of the self-reflection phenomenon in a system with a quadratic nonlinearity. The feature investigated is believed to have a great potential for soliton routing and manipulation by engineered structures. A detailed investigation was conducted on two soliton interaction and collision processes. Birth of an additional soliton resulting from a two soliton collision was observed and characterized for the special case of a non-planar geometry. A small amount of spiraling, up to 30

One- and two-dimensional gap solitons and dynamics in the PT-symmetric lattice potential and spatially-periodic momentum modulation

NASA Astrophysics Data System (ADS)

Chen, Yong; Yan, Zhenya; Li, Xin

2018-02-01

The influence of spatially-periodic momentum modulation on beam dynamics in parity-time (PT) symmetric optical lattice is systematically investigated in the one- and two-dimensional nonlinear Schrödinger equations. In the linear regime, we demonstrate that the momentum modulation can alter the first and second PT thresholds of the classical lattice, periodically or regularly change the shapes of the band structure, rotate and split the diffraction patterns of beams leading to multiple refraction and emissions. In the Kerr-nonlinear regime for one-dimension (1D) case, a large family of fundamental solitons within the semi-infinite gap can be found to be stable, even beyond the second PT threshold; it is shown that the momentum modulation can shrink the existing range of fundamental solitons and not change their stability. For two-dimension (2D) case, most solitons with higher intensities are relatively unstable in their existing regions which are narrower than those in 1D case, but we also find stable fundamental solitons corroborated by linear stability analysis and direct beam propagation. More importantly, the momentum modulation can also utterly change the direction of the transverse power flow and control the energy exchange among gain or loss regions.

Quantum noise in bright soliton matterwave interferometry

NASA Astrophysics Data System (ADS)

Haine, Simon A.

2018-03-01

There has been considerable recent interest in matterwave interferometry with bright solitons in quantum gases with attractive interactions, for applications such as rotation sensing. We model the quantum dynamics of these systems and find that the attractive interactions required for the presence of bright solitons causes quantum phase-diffusion, which severely impairs the sensitivity. We propose a scheme that partially restores the sensitivity, but find that in the case of rotation sensing, it is still better to work in a regime with minimal interactions if possible.

Solitons in a one-dimensional Wigner crystal

DOE PAGES

Pustilnik, M.; Matveev, K. A.

2015-04-16

In one-dimensional quantum systems with strong long-range repulsion particles arrange in a quasi-periodic chain, the Wigner crystal. Here, we demonstrate that besides the familiar phonons, such one-dimensional Wigner crystal supports an additional mode of elementary excitations, which can be identified with solitons in the classical limit. Furthermore, we compute the corresponding excitation spectrum and argue that the solitons have a parametrically small decay rate at low energies. Finally, we discuss implications of our results for the behavior of the dynamic structure factor.

Nonautonomous discrete bright soliton solutions and interaction management for the Ablowitz-Ladik equation.

PubMed

Yu, Fajun

2015-03-01

We present the nonautonomous discrete bright soliton solutions and their interactions in the discrete Ablowitz-Ladik (DAL) equation with variable coefficients, which possesses complicated wave propagation in time and differs from the usual bright soliton waves. The differential-difference similarity transformation allows us to relate the discrete bright soliton solutions of the inhomogeneous DAL equation to the solutions of the homogeneous DAL equation. Propagation and interaction behaviors of the nonautonomous discrete solitons are analyzed through the one- and two-soliton solutions. We study the discrete snaking behaviors, parabolic behaviors, and interaction behaviors of the discrete solitons. In addition, the interaction management with free functions and dynamic behaviors of these solutions is investigated analytically, which have certain applications in electrical and optical systems.

N-soliton interactions: Effects of linear and nonlinear gain and loss

NASA Astrophysics Data System (ADS)

Carretero-González, R.; Gerdjikov, V. S.; Todorov, M. D.

2017-10-01

We analyze the dynamical behavior of the N-soliton train in the adiabatic approximation of the nonlinear Schrödinger equation perturbed simultaneously by linear and nonlinear gain/loss terms. We derive the corresponding perturbed complex Toda chain in the case of a combination of linear, cubic, and/or quintic terms. We show that the soliton interactions dynamics for this reduced PCTC model compares favorably to full numerical results of the original perturbed nonlinear Schrödinger equation.

Optical analogue of relativistic Dirac solitons in binary waveguide arrays

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tran, Truong X., E-mail: truong.tran@mpl.mpg.de; Max Planck Institute for the Science of Light, Günther-Scharowsky str. 1, 91058 Erlangen; Longhi, Stefano

2014-01-15

We study analytically and numerically an optical analogue of Dirac solitons in binary waveguide arrays in the presence of Kerr nonlinearity. Pseudo-relativistic soliton solutions of the coupled-mode equations describing dynamics in the array are analytically derived. We demonstrate that with the found soliton solutions, the coupled mode equations can be converted into the nonlinear relativistic 1D Dirac equation. This paves the way for using binary waveguide arrays as a classical simulator of quantum nonlinear effects arising from the Dirac equation, something that is thought to be impossible to achieve in conventional (i.e. linear) quantum field theory. -- Highlights: •An opticalmore » analogue of Dirac solitons in nonlinear binary waveguide arrays is suggested. •Analytical solutions to pseudo-relativistic solitons are presented. •A correspondence of optical coupled-mode equations with the nonlinear relativistic Dirac equation is established.« less

Evolution of separate screening soliton pairs in a biased series photorefractive crystal circuit.

PubMed

Liu, Jinsong; Hao, Zhonghua

2002-06-01

This paper presents calculations for an idea in photorefractive spatial soliton, namely, screening solitons form in a biased series photorefractive crystal circuit consisting of two photorefractive crystals connected electronically by electrode leads in a chain with a voltage source. A system of two coupled equations is derived under appropriate conditions for two-beam propagation in the crystal circuit. The possibility of obtaining steady-state bright and dark screening soliton solutions is investigated in one dimension and, the existence of dark-dark, bright-dark, and bright-bright separate screening soliton pairs in such a circuit is proved. The numerical results show that the two solitons in a soliton pair can affect each other by the light-induced current and their coupling can affect their spatial profiles, dynamical evolutions, stabilities, and self-deflection. Under the limit in which the optical wave has a spatial extent much less than the width of the crystal, only the dark soliton can affect the other soliton by the light-induced current, but the bright soliton cannot. For a bright-dark or dark-dark soliton pair, the dark soliton in a weak input intensity can be obtained for a larger nonlinearity than for a stronger input intensity. For a bright-dark soliton pair, increasing the input intensity of the dark soliton can increase the bending angle of the bright soliton. Some potential applications are discussed.

Role of nonthermal electron on the dynamics of relativistic electromagnetic soliton in the interaction of laser-plasma

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rostampooran, Shabnam; Dorranian, Davoud, E-mail: doran@srbiau.ac.ir

A system of nonlinear one-dimensional equations of the electron hydrodynamics with Maxwell's equations was developed to describe electromagnetic (EM) solitons in plasma with nonthermal electrons. Equation of vector potential was derived in relativistic regime by implementing the multiple scales technique, and their solitonic answers were introduced. The allowed regions for bright and dark electromagnetic solitons were discussed in detail. Roles of number density of nonthermal electrons, temperature of electrons, and frequency of fast participate of vector potential on the Sagdeev potential and properties of EM soliton were investigated. Results show that with increasing the number of nonthermal electrons, the amplitudemore » of vector potential of bright solitons increases. By increasing the number of nonthermal electrons, dark EM solitons may be changed to bright solitons. Increasing the energy of nonthermal electrons leads to generation of high amplitude solitons.« less

A unified view of acoustic-electrostatic solitons in complex plasmas

NASA Astrophysics Data System (ADS)

McKenzie, J. F.; Doyle, T. B.

2003-03-01

A fluid dynamic approach is used in a unified fully nonlinear treatment of the properties of the dust-acoustic, ion-acoustic and Langmuir-acoustic solitons. The analysis, which is carried out in the wave frame of the soliton, is based on total momentum conservation and Bernoulli-like energy equations for each of the particle species in each wave type, and yields the structure equation for the `heavy' species flow speed in each case. The heavy (cold or supersonic) species is always compressed in the soliton, requiring concomitant contraints on the potential and on the flow speed of the electrons and protons in the wave. The treatment clearly elucidates the crucial role played by the heavy species sonic point in limiting the collective species Mach number, which determines the upper limit for the existence of the soliton and its amplitude, and also shows the essentially similar nature of each soliton type. An exact solution, which highlights these characteristic properties, shows that the three acoustic solitons are in fact the same mathematical entity in different physical disguises.

Neutron scattering on solitons in quasi-one-dimensional systems

NASA Astrophysics Data System (ADS)

Fedyanin, V. K.

1983-05-01

In the framework of the model of an ideal lattice gas of solitons, we obtain the following general formula for the dynamic neutron scattering form factor: S(q, w) = N¯S 1(q, w) , S(q, w) = {p‧(ν 0)δ 22}/{2πqZ 1h }f 2(qδ(ν 0 Here q = k‧ - k and w = E‧ - E are the neutron momentum and energy transfer, respectively, ν0 = wq-1, δ(ν) is the soliton width of velocity ν, p‧( ν0) = d p/d ν| ν0 , p(ν) is the soliton momentum, E(p(ν)) is the soliton energy, N¯ is the average number of solitons at θ = kδT = β-1 and is constructed from the soliton non-linear differential equations. The derivation of the formula is essentially based on (i) specific dependence of these solutions on ξ = x - vt, and (ii) generalization of the averaging over the soliton ensemble, proposed in ref. [1]. The specifi properties of the scattering spectra of polypeptides, DNA molecules and magnetics as functions of the temperature and interaction parameters and of external fields are discussed on the basis of this formula. The contribution to S(q, w) for “slow” solitons in magnetics has been calculated in [2, 3]. (For each concrete model the authors were forced to formulate anew the way of calculation, to assume the small size of ν, etc.)

Why the soliton wavelet transform is useful for nonlinear dynamic phenomena

NASA Astrophysics Data System (ADS)

Szu, Harold H.

1992-10-01

If signal analyses were perfect without noise and clutters, then any transform can be equally chosen to represent the signal without any loss of information. However, if the analysis using Fourier transform (FT) happens to be a nonlinear dynamic phenomenon, the effect of nonlinearity must be postponed until a later time when a complicated mode-mode coupling is attempted without the assurance of any convergence. Alternatively, there exists a new paradigm of linear transforms called wavelet transform (WT) developed for French oil explorations. Such a WT enjoys the linear superposition principle, the computational efficiency, and the signal/noise ratio enhancement for a nonsinusoidal and nonstationary signal. Our extensions to a dynamic WT and furthermore to an adaptive WT are possible due to the fact that there exists a large set of square-integrable functions that are special solutions of the nonlinear dynamic medium and could be adopted for the WT. In order to analyze nonlinear dynamics phenomena in ocean, we are naturally led to the construction of a soliton mother wavelet. This common sense of 'pay the nonlinear price now and enjoy the linearity later' is certainly useful to probe any nonlinear dynamics. Research directions in wavelets, such as adaptivity, and neural network implementations are indicated, e.g., tailoring an active sonar profile for explorations.

Experimental Observation of Dark Solitons on Water Surface

DTIC Science & Technology

2016-06-13

Experimental observation of dark solitons on water surface A. Chabchoub1,∗, O. Kimmoun2, H. Branger3, N. Hoffmann1, D. Proment4, M. Onorato4,5, and N...The shape and width of the soliton depend on the water depth, carrier frequency and the amplitude of the background wave. The experimental data...partic- ular, the governing equation describing the dynamics of weakly nonlinear and quasi -monochromatic waves prop- agating on the surface of water with

Dark soliton decay due to trap anharmonicity in atomic Bose-Einstein condensates

DOE Office of Scientific and Technical Information (OSTI.GOV)

Parker, N. G.; Department of Physics and Astronomy, McMaster University, Hamilton, Ontario L8S 4M1; School of Food Science and Nutrition, University of Leeds, Leeds LS2 9JT

2010-03-15

A number of recent experiments with nearly pure atomic Bose-Einstein condensates have confirmed the predicted dark soliton oscillations when under harmonic trapping. However, a dark soliton propagating in an inhomogeneous condensate has also been predicted to be unstable to the emission of sound waves. Although harmonic trapping supports an equilibrium between the coexisting soliton and sound, we show that the ensuing dynamics are sensitive to trap anharmonicities. Such anharmonicities can break the soliton-sound equilibrium and lead to the net decay of the soliton on a considerably shorter time scale than other dissipation mechanisms. Thus, we propose that small realistic modificationsmore » to existing experimental setups could enable the experimental observation of this decay channel.« less

Solitons and protein folding: An In Silico experiment

NASA Astrophysics Data System (ADS)

Ilieva, N.; Dai, J.; Sieradzan, A.; Niemi, A.

2015-10-01

Protein folding [1] is the process of formation of a functional 3D structure from a random coil — the shape in which amino-acid chains leave the ribosome. Anfinsen's dogma states that the native 3D shape of a protein is completely determined by protein's amino acid sequence. Despite the progress in understanding the process rate and the success in folding prediction for some small proteins, with presently available physics-based methods it is not yet possible to reliably deduce the shape of a biologically active protein from its amino acid sequence. The protein-folding problem endures as one of the most important unresolved problems in science; it addresses the origin of life itself. Furthermore, a wrong fold is a common cause for a protein to lose its function or even endanger the living organism. Soliton solutions of a generalized discrete non-linear Schrödinger equation (GDNLSE) obtained from the energy function in terms of bond and torsion angles κ and τ provide a constructive theoretical framework for describing protein folds and folding patterns [2]. Here we study the dynamics of this process by means of molecular-dynamics simulations. The soliton manifestation is the pattern helix-loop-helix in the secondary structure of the protein, which explains the importance of understanding loop formation in helical proteins. We performed in silico experiments for unfolding one subunit of the core structure of gp41 from the HIV envelope glycoprotein (PDB ID: 1AIK [3]) by molecular-dynamics simulations with the MD package GROMACS. We analyzed 80 ns trajectories, obtained with one united-atom and two different all-atom force fields, to justify the side-chain orientation quantification scheme adopted in the studies and to eliminate force-field based artifacts. Our results are compatible with the soliton model of protein folding and provide first insight into soliton-formation dynamics.

Pure-quartic solitons

PubMed Central

Blanco-Redondo, Andrea; Martijn, de Sterke C.; Sipe, J.E.; Krauss, Thomas F.; Eggleton, Benjamin J.; Husko, Chad

2016-01-01

Temporal optical solitons have been the subject of intense research due to their intriguing physics and applications in ultrafast optics and supercontinuum generation. Conventional bright optical solitons result from the interaction of anomalous group-velocity dispersion and self-phase modulation. Here we experimentally demonstrate a class of bright soliton arising purely from the interaction of negative fourth-order dispersion and self-phase modulation, which can occur even for normal group-velocity dispersion. We provide experimental and numerical evidence of shape-preserving propagation and flat temporal phase for the fundamental pure-quartic soliton and periodically modulated propagation for the higher-order pure-quartic solitons. We derive the approximate shape of the fundamental pure-quartic soliton and discover that is surprisingly Gaussian, exhibiting excellent agreement with our experimental observations. Our discovery, enabled by precise dispersion engineering, could find applications in communications, frequency combs and ultrafast lasers. PMID:26822758

Ultrashort dark solitons interactions and nonlinear tunneling in the modified nonlinear Schrödinger equation with variable coefficient

NASA Astrophysics Data System (ADS)

Musammil, N. M.; Porsezian, K.; Nithyanandan, K.; Subha, P. A.; Tchofo Dinda, P.

2017-09-01

We present the study of the dark soliton dynamics in an inhomogeneous fiber by means of a variable coefficient modified nonlinear Schrödinger equation (Vc-MNLSE) with distributed dispersion, self-phase modulation, self-steepening and linear gain/loss. The ultrashort dark soliton pulse evolution and interaction is studied by using the Hirota bilinear (HB) method. In particular, we give much insight into the effect of self-steepening (SS) on the dark soliton dynamics. The study reveals a shock wave formation, as a major effect of SS. Numerically, we study the dark soliton propagation in the continuous wave background, and the stability of the soliton solution is tested in the presence of photon noise. The elastic collision behaviors of the dark solitons are discussed by the asymptotic analysis. On the other hand, considering the nonlinear tunneling of dark soliton through barrier/well, we find that the tunneling of the dark soliton depends on the height of the barrier and the amplitude of the soliton. The intensity of the tunneling soliton either forms a peak or valley and retains its shape after the tunneling. For the case of exponential background, the soliton tends to compress after tunneling through the barrier/well.

Stationary and oscillatory bound states of dissipative solitons created by third-order dispersion

NASA Astrophysics Data System (ADS)

Sakaguchi, Hidetsugu; Skryabin, Dmitry V.; Malomed, Boris A.

2018-06-01

We consider the model of fiber-laser cavities near the zero-dispersion point, based on the complex Ginzburg-Landau equation with the cubic-quintic nonlinearity, including the third-order dispersion (TOD) term. It is well known that this model supports stable dissipative solitons. We demonstrate that the same model gives rise to several families of robust bound states of the solitons, which exists only in the presence of the TOD. There are both stationary and dynamical bound states, with oscillating separation between the bound solitons. Stationary states are multistable, corresponding to different values of the separation. With the increase of the TOD coefficient, the bound state with the smallest separation gives rise the oscillatory state through the Hopf bifurcation. Further growth of TOD leads to a bifurcation transforming the oscillatory limit cycle into a strange attractor, which represents a chaotically oscillating dynamical bound state. Families of multistable three- and four-soliton complexes are found too, the ones with the smallest separation between the solitons again ending by a transition to oscillatory states through the Hopf bifurcation.

Two-component dark-bright solitons in three-dimensional atomic Bose-Einstein condensates.

PubMed

Wang, Wenlong; Kevrekidis, P G

2017-03-01

In the present work, we revisit two-component Bose-Einstein condensates in their fully three-dimensional (3D) form. Motivated by earlier studies of dark-bright solitons in the 1D case, we explore the stability of these structures in their fully 3D form in two variants. In one the dark soliton is planar and trapping a planar bright (disk) soliton. In the other case, a dark spherical shell soliton creates an effective potential in which a bright spherical shell of atoms is trapped in the second component. We identify these solutions as numerically exact states (up to a prescribed accuracy) and perform a Bogolyubov-de Gennes linearization analysis that illustrates that both structures can be dynamically stable in suitable intervals of sufficiently low chemical potentials. We corroborate this finding theoretically by analyzing the stability via degenerate perturbation theory near the linear limit of the system. When the solitary waves are found to be unstable, we explore their dynamical evolution via direct numerical simulations which, in turn, reveal wave forms that are more robust. Finally, using the SO(2) symmetry of the model, we produce multi-dark-bright planar or shell solitons involved in pairwise oscillatory motion.

Broadband dynamic phase matching of high-order harmonic generation by a high-peak-power soliton pump field in a gas-filled hollow photonic-crystal fiber.

PubMed

Serebryannikov, Evgenii E; von der Linde, Dietrich; Zheltikov, Aleksei M

2008-05-01

Hollow-core photonic-crystal fibers are shown to enable dynamically phase-matched high-order harmonic generation by a gigawatt soliton pump field. With a careful design of the waveguide structure and an appropriate choice of input-pulse and gas parameters, a remarkably broadband phase matching can be achieved for a soliton pump field and a large group of optical harmonics in the soft-x-ray-extreme-ultraviolet spectral range.

Surface dark screening solitons.

PubMed

Chen, W Q; Yang, X; Zhong, S Y; Yan, Z; Zhang, T H; Tian, J G; Xu, J J

2011-10-01

We report on the existence of surface dark screening solitons at the interface between a dielectric medium (air) and a self-defocusing nonlinear material, taking advantage of photorefractive diffusion and drift nonlinearities. It is very interesting that a surface dark soliton is just like half of a dark soliton in bulk, but not a whole dark soliton propagating along surface. The excitation, propagation, and stability of this type of soliton are studied by using the beam-propagation method. Another interesting thing is that this type of dark soliton can be excited by a planar light beam without a necessary dark notch. © 2011 Optical Society of America

Soliton trapping in fiber lasers.

PubMed

Zhao, L M; Tang, D Y; Zhang, H; Wu, X; Xiang, N

2008-06-23

We report on the soliton trapping in a fiber ring laser modelocked with a SESAM. It was observed that solitons along the two orthogonal polarization directions of the cavity with fairly large difference in central frequency and energy could be coupled together to form a group velocity locked vector soliton. In particular, due to that each of the coupled solitons forms its own soliton sidebands, two sets of soliton sidebands could be observed on the vector soliton spectrum. Numerical simulations have well confirmed the experimental observations.

Nonlinear ion acoustic waves scattered by vortexes

NASA Astrophysics Data System (ADS)

Ohno, Yuji; Yoshida, Zensho

2016-09-01

The Kadomtsev-Petviashvili (KP) hierarchy is the archetype of infinite-dimensional integrable systems, which describes nonlinear ion acoustic waves in two-dimensional space. This remarkably ordered system resides on a singular submanifold (leaf) embedded in a larger phase space of more general ion acoustic waves (low-frequency electrostatic perturbations). The KP hierarchy is characterized not only by small amplitudes but also by irrotational (zero-vorticity) velocity fields. In fact, the KP equation is derived by eliminating vorticity at every order of the reductive perturbation. Here, we modify the scaling of the velocity field so as to introduce a vortex term. The newly derived system of equations consists of a generalized three-dimensional KP equation and a two-dimensional vortex equation. The former describes 'scattering' of vortex-free waves by ambient vortexes that are determined by the latter. We say that the vortexes are 'ambient' because they do not receive reciprocal reactions from the waves (i.e., the vortex equation is independent of the wave fields). This model describes a minimal departure from the integrable KP system. By the Painlevé test, we delineate how the vorticity term violates integrability, bringing about an essential three-dimensionality to the solutions. By numerical simulation, we show how the solitons are scattered by vortexes and become chaotic.

Nonlinear waves in subwavelength waveguide arrays: evanescent bands and the "phoenix soliton".

PubMed

Peleg, Or; Segev, Mordechai; Bartal, Guy; Christodoulides, Demetrios N; Moiseyev, Nimrod

2009-04-24

We formulate wave propagation in arrays of subwavelength waveguides with sharp index contrasts and demonstrate the collapse of bands into evanescent modes and lattice solitons with superluminal phase velocity. We find a self-reviving soliton ("phoenix soliton") comprised of coupled forward- and backward-propagating light, originating solely from evanescent bands. In the linear regime, all Bloch waves comprising this beam decay, whereas a proper nonlinearity assembles them into a propagating self-trapped beam. Finally, we simulate the dynamics of such a beam and observe breakup into temporal pulses, indicating a new kind of slow-light gap solitons, trapped in time and in one transverse dimension.

Stokes solitons in optical microcavities

NASA Astrophysics Data System (ADS)

Yang, Qi-Fan; Yi, Xu; Yang, Ki Youl; Vahala, Kerry

2017-01-01

Solitons are wave packets that resist dispersion through a self-induced potential well. They are studied in many fields, but are especially well known in optics on account of the relative ease of their formation and control in optical fibre waveguides. Besides their many interesting properties, solitons are important to optical continuum generation, in mode-locked lasers, and have been considered as a natural way to convey data over great distances. Recently, solitons have been realized in microcavities, thereby bringing the power of microfabrication methods to future applications. This work reports a soliton not previously observed in optical systems, the Stokes soliton. The Stokes soliton forms and regenerates by optimizing its Raman interaction in space and time within an optical potential well shared with another soliton. The Stokes and the initial soliton belong to distinct transverse mode families and benefit from a form of soliton trapping that is new to microcavities and soliton lasers in general. The discovery of a new optical soliton can impact work in other areas of photonics, including nonlinear optics and spectroscopy.

Topics Associated with Nonlinear Evolution Equations and Inverse Scattering in Multidimensions,

DTIC Science & Technology

1987-03-01

significant that these concepts can be generalized to 2 spatial plus one time dimension. Here the prototype equation is the Kadomtsev - Petviashvili (K-P...O-193 32 ? T TOPICS ASSOCIATED WITH NONLINEAR E VOLUTION EQUATIONS / AND INVERSE SCATTER! .(U) CLARKSON UNIV POTSDAM NY INST...8217 - Evolution Equations and L Inverse Scattering in Multi- dimensions by _i A ,’I Mark J. Ablowi ClrsnUiest PosaNwYr/37 LaRMFOMON* .F-5 Anwo~~~d kr /ua

Transverse instability of periodic and generalized solitary waves for a fifth-order KP model

NASA Astrophysics Data System (ADS)

Haragus, Mariana; Wahlén, Erik

2017-02-01

We consider a fifth-order Kadomtsev-Petviashvili equation which arises as a two-dimensional model in the classical water-wave problem. This equation possesses a family of generalized line solitary waves which decay exponentially to periodic waves at infinity. We prove that these solitary waves are transversely spectrally unstable and that this instability is induced by the transverse instability of the periodic tails. We rely upon a detailed spectral analysis of some suitably chosen linear operators.

A numerical study of the 3-periodic wave solutions to KdV-type equations

NASA Astrophysics Data System (ADS)

Zhang, Yingnan; Hu, Xingbiao; Sun, Jianqing

2018-02-01

In this paper, by using the direct method of calculating periodic wave solutions proposed by Akira Nakamura, we present a numerical process to calculate the 3-periodic wave solutions to several KdV-type equations: the Korteweg-de Vries equation, the Sawada-Koterra equation, the Boussinesq equation, the Ito equation, the Hietarinta equation and the (2 + 1)-dimensional Kadomtsev-Petviashvili equation. Some detailed numerical examples are given to show the existence of the three-periodic wave solutions numerically.

Dark incoherent soliton splitting and "phase-memory" effects: Theory and experiment.

PubMed

Coskun, T H; Christodoulides, D N; Chen, Z; Segev, M

1999-05-01

We report on an experimental observation of dark incoherent soliton Y splitting. The effects of incoherence on the evolution of incoherent dark soliton doublets are investigated both theoretically and experimentally. We show that the dynamics of these incoherent self-trapped entities are associated with strong "phase-memory" effects that are otherwise absent in the linear regime.

Separate spatial Holographic-Hamiltonian soliton pairs and solitons interaction in an unbiased series photorefractive crystal circuit.

PubMed

Cai, Xin; Liu, Jinsong; Wang, Shenglie

2009-02-16

This paper presents calculations for an idea in photorefractive spatial soliton, namely, a dissipative holographic soliton and a Hamiltonian soliton in one dimension form in an unbiased series photorefractive crystal circuit consisting of two photorefractive crystals of which at least one must be photovoltaic. The two solitons are known collectively as a separate Holographic-Hamiltonian spatial soliton pair and there are two types: dark-dark and bright-dark if only one crystal of the circuit is photovoltaic. The numerical results show that the Hamiltonian soliton in a soliton pair can affect the holographic one by the light-induced current whereas the effect of the holographic soliton on the Hamiltonian soliton is too weak to be ignored, i.e., the holographic soliton cannot affect the Hamiltonian one.

Toda-Lattice Solitons in α-Helical Proteins

NASA Astrophysics Data System (ADS)

Yomosa, Shigeo

1984-10-01

We propose a theory of Toda-lattice soliton in α-helical proteins which enables us to elucidate the molecular dynamics of muscle contraction. One-dimensional chain of peptide groups jointed together by H-bonds, which stabilizes α-helical structure of proteins, can be regarded as a Toda-lattice where the potential of H-bonding interaction between peptide groups has a remarkable nonlinearity. By using the results of theoretical studies for Toda-lattice soliton and for the initial value problem, we can describe the molecular mechanism of the transformation of the chemical energy to the mechanical work in the process of the muscle contraction.

Dynamics of charges and solitons

NASA Astrophysics Data System (ADS)

Barros, Manuel; Ferrández, Ángel; Garay, Óscar J.

2018-02-01

We first show that trajectories traced by charges moving in rotational magnetic fields are, basically, the non-parallel geodesics of surfaces of revolution with coincident axis. Thus, people living in a surface of revolution are not able to sense the magnetic Hall effect induced by the surrounding magnetic field and perceive charges as influenced, exclusively, by the gravity action on the surface of revolution. Secondly, the extended Hasimoto transformations are introduced and then used to identify trajectories of charges moving through a Killing rotational magnetic field in terms of non-circular elastic curves. As a consequence, we see that in this case charges evolve along trajectories which are obtained as extended Hasimoto transforms of solitons of the filament equation.

Observation of soliton compression in silicon photonic crystals

PubMed Central

Blanco-Redondo, A.; Husko, C.; Eades, D.; Zhang, Y.; Li, J.; Krauss, T.F.; Eggleton, B.J.

2014-01-01

Solitons are nonlinear waves present in diverse physical systems including plasmas, water surfaces and optics. In silicon, the presence of two photon absorption and accompanying free carriers strongly perturb the canonical dynamics of optical solitons. Here we report the first experimental demonstration of soliton-effect pulse compression of picosecond pulses in silicon, despite two photon absorption and free carriers. Here we achieve compression of 3.7 ps pulses to 1.6 ps with <10 pJ energy. We demonstrate a ~1-ps free-carrier-induced pulse acceleration and show that picosecond input pulses are critical to these observations. These experiments are enabled by a dispersion-engineered slow-light photonic crystal waveguide and an ultra-sensitive frequency-resolved electrical gating technique to detect the ultralow energies in the nanostructured device. Strong agreement with a nonlinear Schrödinger model confirms the measurements. These results further our understanding of nonlinear waves in silicon and open the way to soliton-based functionalities in complementary metal-oxide-semiconductor-compatible platforms. PMID:24423977

Core filling and snaking instability of dark solitons in spin-imbalanced superfluid Fermi gases

NASA Astrophysics Data System (ADS)

Reichl, Matthew D.; Mueller, Erich J.

2017-05-01

We use the time-dependent Bogoliubov-de Gennes equations to study dark solitons in three-dimensional spin-imbalanced superfluid Fermi gases. We explore how the shape and dynamics of dark solitons are altered by the presence of excess unpaired spins which fill their low-density core. The unpaired particles broaden the solitons and suppress the transverse snake instability. We discuss ways of observing these phenomena in cold-atom experiments.

Observation of subfemtosecond fluctuations of the pulse separation in a soliton molecule.

PubMed

Shi, Haosen; Song, Youjian; Wang, Chingyue; Zhao, Luming; Hu, Minglie

2018-04-01

In this work, we study the timing instability of a scalar twin-pulse soliton molecule generated by a passively mode-locked Er-fiber laser. Subfemtosecond precision relative timing jitter characterization between the two solitons composing the molecule is enabled by the balanced optical cross-correlation (BOC) method. Jitter spectral density reveals a short-term (on the microsecond to millisecond timescale) random fluctuation of the pulse separation even in the robust stationary soliton molecules. The root-mean-square (rms) timing jitter is on the order of femtoseconds depending on the pulse separation and the mode-locking regime. The lowest rms timing jitter is 0.83 fs, which is observed in the dispersion managed mode-locking regime. Moreover, the BOC method has proved to be capable of resolving the soliton interaction dynamics in various vibrating soliton molecules.

Breather-to-soliton transformation rules in the hierarchy of nonlinear Schrödinger equations.

PubMed

Chowdury, Amdad; Krolikowski, Wieslaw

2017-06-01

We study the exact first-order soliton and breather solutions of the integrable nonlinear Schrödinger equations hierarchy up to fifth order. We reveal the underlying physical mechanism which transforms a breather into a soliton. Furthermore, we show how the dynamics of the Akhmediev breathers which exist on a constant background as a result of modulation instability, is connected with solitons on a zero background. We also demonstrate that, while a first-order rogue wave can be directly transformed into a soliton, higher-order rogue wave solutions become rational two-soliton solutions with complex collisional structure on a background. Our results will have practical implications in supercontinuum generation, turbulence, and similar other complex nonlinear scenarios.

Solitons with Gaussian tails in dispersion-managed communication systems using gratings

NASA Astrophysics Data System (ADS)

Mezentsev, Vladimir K.; Turitsyn, Sergei K.

1997-02-01

We examine the transmission of optical pulses in fibre communication systems with dispersion management. It is shown that solitons with Gaussian tails may be formed by the adoption of gratings to periodically compensate a pulse chirp. Fast decaying Gaussian tails allow us to provide denser information packing in comparison with sech-type soliton transmission. The discovered pulse is an attractive candidate for use as information carrier in optical transmission systems with an ultra-large capacity of around 100 Gbit/s. It is shown that a variational method can be effectively used to describe the dynamics of the breathing soliton.

The kink-soliton and antikink-soliton in quasi-one-dimensional nonlinear monoatomic lattice

NASA Astrophysics Data System (ADS)

Xu, Quan; Tian, Qiang

2005-04-01

The quasi-one-dimensional nonlinear monoatomic lattice is analyzed. The kink-soliton and antikink-soliton are presented. When the interaction of the lattice is strong in the x-direction and weak in the y-direction, the two-dimensional (2D) lattice changes to a quasi-one-dimensional lattice. Taking nearest-neighbor interaction into account, the vibration equation can be transformed into the KPI, KPII and MKP equation. Considering the cubic nonlinear potential of the vibration in the lattice, the kink-soliton solution is presented. Considering the quartic nonlinear potential and the cubic interaction potential, the kink-soliton and antikink-soliton solutions are presented.

Cavity solitons and localized patterns in a finite-size optical cavity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kozyreff, G.; Gelens, L.

2011-08-15

In appropriate ranges of parameters, laser-driven nonlinear optical cavities can support a wide variety of optical patterns, which could be used to carry information. The intensity peaks appearing in these patterns are called cavity solitons and are individually addressable. Using the Lugiato-Lefever equation to model a perfectly homogeneous cavity, we show that cavity solitons can only be located at discrete points and at a minimal distance from the edges. Other localized states which are attached to the edges are identified. By interpreting these patterns in an information coding frame, the information capacity of this dynamical system is evaluated. The resultsmore » are explained analytically in terms of the the tail characteristics of the cavity solitons. Finally, the influence of boundaries and of cavity imperfections on cavity solitons are compared.« less

KP Equation in a Three-Dimensional Unmagnetized Warm Dusty Plasma with Variable Dust Charge

NASA Astrophysics Data System (ADS)

El-Shorbagy, Kh. H.; Mahassen, Hania; El-Bendary, Atef Ahmed

2017-12-01

In this work, we investigate the propagation of three-dimensional nonlinear dust-acoustic and dust-Coulomb waves in an unmagnetized warm dusty plasma consisting of electrons, ions, and charged dust particles. The grain charge fluctuation is incorporated through the current balance equation. Using the perturbation method, a Kadomtsev-Petviashvili (KP) equation is obtained. It has been shown that the charge fluctuation would modify the wave structures, and the waves in such systems are unstable due to high-order long wave perturbations.

Nonlinear Ocean Waves

DTIC Science & Technology

1994-01-06

for all of this work is the fact that the Kadomtsev - Petviashvili equation , a1(atu + ui)xU + a.3u) + ay2u = 0, (KP) describes approximately the evolution...the contents of these two papers. (a) Numerically induced chaos The cubic-nonlinear Schrtdinger equation in one dimension, iatA +,2V + 21i,1 =0, (NLS...arises in several physical contexts, including the evolution of nearly monochromatic, one-dimensional waves in deep water. The equation is known to be

Exactly Solvable Multidimensional Nonlinear Equations and Inverse Scattering,

DTIC Science & Technology

1986-12-01

time dimension. Here the prototype euQation is 1 the Kadomtsev - Petviashvili (K-P) equation : .0 6u , x , x - )3,:’u ,’ which is the cop,patliil ity...AD-R193 274 EXACTLY SOLVABLE MULTIDIMENSIONAL NONLINEAR EQUATIONS L/1 AND INVERSE SCATTERING(U) CLARKSON UNIV POTSDAM MY A J MBLOUITZ DEC 86 NSOSI4...ecuations by associating thnm with appropriate compatible linear equations , -ne of which is identified as a Scattering prooD,, ne others(s) serves to

Loss-less propagation, elastic and inelastic interaction of electromagnetic soliton in an anisotropic ferromagnetic nanowire

NASA Astrophysics Data System (ADS)

Senthil Kumar, V.; Kavitha, L.; Boopathy, C.; Gopi, D.

2017-10-01

Nonlinear interaction of electromagnetic solitons leads to a plethora of interesting physical phenomena in the diverse area of science that include magneto-optics based data storage industry. We investigate the nonlinear magnetization dynamics of a one-dimensional anisotropic ferromagnetic nanowire. The famous Landau-Lifshitz-Gilbert equation (LLG) describes the magnetization dynamics of the ferromagnetic nanowire and the Maxwell's equations govern the propagation dynamics of electromagnetic wave passing through the axis of the nanowire. We perform a uniform expansion of magnetization and magnetic field along the direction of propagation of electromagnetic wave in the framework of reductive perturbation method. The excitation of magnetization of the nanowire is restricted to the normal plane at the lowest order of perturbation and goes out of plane for higher orders. The dynamics of the ferromagnetic nanowire is governed by the modified Korteweg-de Vries (mKdV) equation and the perturbed modified Korteweg-de Vries (pmKdV) equation for the lower and higher values of damping respectively. We invoke the Hirota bilinearization procedure to mKdV and pmKdV equation to construct the multi-soliton solutions, and explicitly analyze the nature of collision phenomena of the co-propagating EM solitons for the above mentioned lower and higher values of Gilbert-damping due to the precessional motion of the ferromagnetic spin. The EM solitons appearing in the higher damping regime exhibit elastic collision thus yielding the fascinating state restoration property, whereas those of lower damping regime exhibit inelastic collision yielding the solitons of suppressed intensity profiles. The propagation of EM soliton in the nanoscale magnetic wire has potential technological applications in optimizing the magnetic storage devices and magneto-electronics.

Topological solitons in helical strings

NASA Astrophysics Data System (ADS)

Nisoli, Cristiano; Balatsky, Alexander V.

2015-06-01

The low-energy physics of (quasi)degenerate one-dimensional systems is typically understood as the particle-like dynamics of kinks between stable, ordered structures. Such dynamics, we show, becomes highly nontrivial when the ground states are topologically constrained: a dynamics of the domains rather than on the domains which the kinks separate. Motivated by recently reported observations of charged polymers physio-adsorbed on nanotubes, we study kinks between helical structures of a string wrapping around a cylinder. While their motion cannot be disentangled from domain dynamics, and energy and momentum is not concentrated in the solitons, the dynamics of the domains can be folded back into a particle-like description of the local excitations.

Real-Time Observation of Internal Motion within Ultrafast Dissipative Optical Soliton Molecules

NASA Astrophysics Data System (ADS)

Krupa, Katarzyna; Nithyanandan, K.; Andral, Ugo; Tchofo-Dinda, Patrice; Grelu, Philippe

2017-06-01

Real-time access to the internal ultrafast dynamics of complex dissipative optical systems opens new explorations of pulse-pulse interactions and dynamic patterns. We present the first direct experimental evidence of the internal motion of a dissipative optical soliton molecule generated in a passively mode-locked erbium-doped fiber laser. We map the internal motion of a soliton pair molecule by using a dispersive Fourier-transform imaging technique, revealing different categories of internal pulsations, including vibrationlike and phase drifting dynamics. Our experiments agree well with numerical predictions and bring insights to the analogy between self-organized states of lights and states of the matter.

Rogue wave and a pair of resonance stripe solitons to a reduced (3+1)-dimensional Jimbo-Miwa equation

NASA Astrophysics Data System (ADS)

Zhang, Xiaoen; Chen, Yong

2017-11-01

In this paper, a combination of stripe soliton and lump soliton is discussed to a reduced (3+1)-dimensional Jimbo-Miwa equation, in which such solution gives rise to two different excitation phenomena: fusion and fission. Particularly, a new combination of positive quadratic functions and hyperbolic functions is considered, and then a novel nonlinear phenomenon is explored. Via this method, a pair of resonance kink stripe solitons and rogue wave is studied. Rogue wave is triggered by the interaction between lump soliton and a pair of resonance kink stripe solitons. It is exciting that rogue wave must be attached to the stripe solitons from its appearing to disappearing. The whole progress is completely symmetry, the rogue wave starts itself from one stripe soliton and lose itself in another stripe soliton. The dynamic properties of the interaction between one stripe soliton and lump soliton, rogue wave are discussed by choosing appropriate parameters.

Soliton cellular automaton associated with Dn(1)-crystal B2,s

NASA Astrophysics Data System (ADS)

Misra, Kailash C.; Wilson, Evan A.

2013-04-01

A solvable vertex model in ferromagnetic regime gives rise to a soliton cellular automaton which is a discrete dynamical system in which site variables take on values in a finite set. We study the scattering of a class of soliton cellular automata associated with the U_q(D_n^{(1)})-perfect crystal B2, s. We calculate the combinatorial R matrix for all elements of B2, s ⊗ B2, 1. In particular, we show that the scattering rule for our soliton cellular automaton can be identified with the combinatorial R matrix for U_q(A_1^{(1)}) oplus U_q(D_{n-2}^{(1)})-crystals.

On solitons: the biomolecular nonlinear transmission line models with constant and time variable coefficients

NASA Astrophysics Data System (ADS)

Raza, Nauman; Murtaza, Isma Ghulam; Sial, Sultan; Younis, Muhammad

2018-07-01

The article studies the dynamics of solitons in electrical microtubule ? model, which describes the propagation of waves in nonlinear dynamical system. Microtubules are not only a passive support of a cell but also they have highly dynamic structures involved in cell motility, intracellular transport and signaling. The underlying model has been considered with constant and variable coefficients of time function. The solitary wave ansatz has been applied successfully to extract these solitons. The corresponding integrability criteria, also known as constraint conditions, naturally emerge from the analysis of these models.

Dynamics of coupled mode solitons in bursting neural networks

NASA Astrophysics Data System (ADS)

Nfor, N. Oma; Ghomsi, P. Guemkam; Moukam Kakmeni, F. M.

2018-02-01

Using an electrically coupled chain of Hindmarsh-Rose neural models, we analytically derived the nonlinearly coupled complex Ginzburg-Landau equations. This is realized by superimposing the lower and upper cutoff modes of wave propagation and by employing the multiple scale expansions in the semidiscrete approximation. We explore the modified Hirota method to analytically obtain the bright-bright pulse soliton solutions of our nonlinearly coupled equations. With these bright solitons as initial conditions of our numerical scheme, and knowing that electrical signals are the basis of information transfer in the nervous system, it is found that prior to collisions at the boundaries of the network, neural information is purely conveyed by bisolitons at lower cutoff mode. After collision, the bisolitons are completely annihilated and neural information is now relayed by the upper cutoff mode via the propagation of plane waves. It is also shown that the linear gain of the system is inextricably linked to the complex physiological mechanisms of ion mobility, since the speeds and spatial profiles of the coupled nerve impulses vary with the gain. A linear stability analysis performed on the coupled system mainly confirms the instability of plane waves in the neural network, with a glaring example of the transition of weak plane waves into a dark soliton and then static kinks. Numerical simulations have confirmed the annihilation phenomenon subsequent to collision in neural systems. They equally showed that the symmetry breaking of the pulse solution of the system leaves in the network static internal modes, sometime referred to as Goldstone modes.

Dynamics of coupled mode solitons in bursting neural networks.

PubMed

Nfor, N Oma; Ghomsi, P Guemkam; Moukam Kakmeni, F M

2018-02-01

Using an electrically coupled chain of Hindmarsh-Rose neural models, we analytically derived the nonlinearly coupled complex Ginzburg-Landau equations. This is realized by superimposing the lower and upper cutoff modes of wave propagation and by employing the multiple scale expansions in the semidiscrete approximation. We explore the modified Hirota method to analytically obtain the bright-bright pulse soliton solutions of our nonlinearly coupled equations. With these bright solitons as initial conditions of our numerical scheme, and knowing that electrical signals are the basis of information transfer in the nervous system, it is found that prior to collisions at the boundaries of the network, neural information is purely conveyed by bisolitons at lower cutoff mode. After collision, the bisolitons are completely annihilated and neural information is now relayed by the upper cutoff mode via the propagation of plane waves. It is also shown that the linear gain of the system is inextricably linked to the complex physiological mechanisms of ion mobility, since the speeds and spatial profiles of the coupled nerve impulses vary with the gain. A linear stability analysis performed on the coupled system mainly confirms the instability of plane waves in the neural network, with a glaring example of the transition of weak plane waves into a dark soliton and then static kinks. Numerical simulations have confirmed the annihilation phenomenon subsequent to collision in neural systems. They equally showed that the symmetry breaking of the pulse solution of the system leaves in the network static internal modes, sometime referred to as Goldstone modes.

Traveling wave and soliton solutions of coupled nonlinear Schrödinger equations with harmonic potential and variable coefficients.

PubMed

Zhong, Wei-Ping; Belić, Milivoj

2010-10-01

Exact traveling wave and soliton solutions, including the bright-bright and dark-dark soliton pairs, are found for the system of two coupled nonlinear Schrödinger equations with harmonic potential and variable coefficients, by employing the homogeneous balance principle and the F-expansion technique. A kind of shape-changing soliton collision is identified in the system. The collision is essentially elastic between the two solitons with opposite velocities. Our results demonstrate that the dynamics of solitons can be controlled by selecting the diffraction, nonlinearity, and gain coefficients.

Nonlinear femtosecond pump-probe spectroscopy using a power-encoded soliton delay line.

PubMed

Saint-Jalm, Sarah; Andresen, Esben Ravn; Bendahmane, Abdelkrim; Kudlinski, Alexandre; Rigneault, Hervé

2016-01-01

We show femtosecond time-resolved nonlinear pump-probe spectroscopy using a fiber soliton as the probe pulse. Furthermore, we exploit soliton dynamics to record an entire transient trace with a power-encoded delay sweep. The power-encoded delay line takes advantage of the dependency of the soliton trajectory in the (λ,z) space upon input power; the difference in accumulated group delay between trajectories converts a fast power sweep into a fast delay sweep. We demonstrate the concept by performing transient absorption spectroscopy in a test sample and validate it against a conventional pump-probe setup.

Soliton Gases and Generalized Hydrodynamics

NASA Astrophysics Data System (ADS)

Doyon, Benjamin; Yoshimura, Takato; Caux, Jean-Sébastien

2018-01-01

We show that the equations of generalized hydrodynamics (GHD), a hydrodynamic theory for integrable quantum systems at the Euler scale, emerge in full generality in a family of classical gases, which generalize the gas of hard rods. In this family, the particles, upon colliding, jump forward or backward by a distance that depends on their velocities, reminiscent of classical soliton scattering. This provides a "molecular dynamics" for GHD: a numerical solver which is efficient, flexible, and which applies to the presence of external force fields. GHD also describes the hydrodynamics of classical soliton gases. We identify the GHD of any quantum model with that of the gas of its solitonlike wave packets, thus providing a remarkable quantum-classical equivalence. The theory is directly applicable, for instance, to integrable quantum chains and to the Lieb-Liniger model realized in cold-atom experiments.

Kadomtsev−Petviashvili equation for a flow of highly nonisothermal collisionless plasma

DOE Office of Scientific and Technical Information (OSTI.GOV)

Movsesyants, Yu. B., E-mail: yumovsesyants@gmail.com; Rukhadze, A. A., E-mail: rukh@fpl.gpi.ru; Tyuryukanov, P. M.

2016-01-15

It is shown that the equations of two-fluid electrodynamics for a cold ions flow and Boltzmann electrons in the vicinity of the ion-sound point can be reduced to the Kadomtsev−Petviashvili equation. Examples of two-dimensional equilibria with pole singularities obtained by exactly solving the equations are presented. An exact self-similar solution describing a two-dimensional transonic flow and having no pole singularities is found.

Coupling effects for separate spatial solitons in a biased series centrosymmetric photorefractive crystal circuit considering grey solitons

NASA Astrophysics Data System (ADS)

Katti, Aavishkar; Yadav, Ram Anjore

2018-02-01

The existence and coupling of grey-grey, grey-bright and grey-dark separate spatial solitons in a biased series centrosymmetric photorefractive crystal circuit is investigated for the first time. The numerical solution of the separate spatial solitons is presented. The coupling between the two separate spatial solitons is analysed for all three cases of separate coupled solitons, namely grey-grey, grey-bright, and grey-dark. Changing the intensity of the soliton in one crystal affects the soliton in both crystals due to flow of the light induced current through the circuit. The effect of the background intensity of each crystal on both the spatial solitons is investigated. Also, the effect of changing the temperature of one crystal affects the soliton in both crystals due to the coupling effect. The soliton width dependence on the temperature is different for each crystal.

Accessible solitons of fractional dimension

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhong, Wei-Ping, E-mail: zhongwp6@126.com; Texas A&M University at Qatar, P.O. Box 23874, Doha; Belić, Milivoj

We demonstrate that accessible solitons described by an extended Schrödinger equation with the Laplacian of fractional dimension can exist in strongly nonlocal nonlinear media. The soliton solutions of the model are constructed by two special functions, the associated Legendre polynomials and the Laguerre polynomials in the fraction-dimensional space. Our results show that these fractional accessible solitons form a soliton family which includes crescent solitons, and asymmetric single-layer and multi-layer necklace solitons. -- Highlights: •Analytic solutions of a fractional Schrödinger equation are obtained. •The solutions are produced by means of self-similar method applied to the fractional Schrödinger equation with parabolic potential.more » •The fractional accessible solitons form crescent, asymmetric single-layer and multilayer necklace profiles. •The model applies to the propagation of optical pulses in strongly nonlocal nonlinear media.« less

Topological switching and orbiting dynamics of colloidal spheres dressed with chiral nematic solitons.

PubMed

Porenta, T; Copar, S; Ackerman, P J; Pandey, M B; Varney, M C M; Smalyukh, I I; Žumer, S

2014-12-05

Metastable configurations formed by defects, inclusions, elastic deformations and topological solitons in liquid crystals are a promising choice for building photonic crystals and metamaterials with a potential for new optical applications. Local optical modification of the director or introduction of colloidal inclusions into a moderately chiral nematic liquid crystal confined to a homeotropic cell creates localized multistable chiral solitons. Here we induce solitons that "dress" the dispersed spherical particles treated for tangential degenerate boundary conditions, and perform controlled switching of their state using focused optical beams. Two optically switchable distinct metastable states, toron and hopfion, bound to colloidal spheres into structures with different topological charges are investigated. Their structures are examined using Q-tensor based numerical simulations and compared to the profiles reconstructed from the experiments. A topological explanation of observed multistability is constructed.

Dark solitons at nonlinear interfaces.

PubMed

Sánchez-Curto, Julio; Chamorro-Posada, Pedro; McDonald, Graham S

2010-05-01

The refraction of dark solitons at a planar boundary separating two defocusing Kerr media is simulated and analyzed, for the first time (to our knowledge). Analysis is based on the nonlinear Helmholtz equation and is thus valid for any angle of incidence. A new law, governing refraction of black solitons, is combined with one describing bright soliton refraction to yield a generalized Snell's law whose validity is verified numerically. The complexity of gray soliton refraction is also analyzed, and illustrated by a change from external to internal refraction on varying the soliton contrast parameter.

Observation of surface dark photovoltaic solitons.

PubMed

Yang, Xi; Chen, Weiqiang; Yao, Peng; Zhang, Tianhao; Tian, Jianguo; Xu, Jingjun

2013-02-25

Surface dark solitons in photovoltaic nonlinear media are reported. Taking advantage of diffusion and photovoltaic nonlinearities we demonstrated the surface dark solitons and their behaviors near surface theoretically and experimentally in LiNbO₃ crystal. It is very interesting that surface dark soliton is just half of dark soliton in bulk. Another interesting thing is that transverse modulation instability can be perfectly suppressed by surface dark soliton in virtue of surface. In addition, surface waveguides were written successfully utilizing surface dark soliton.

Role of Multiple Soliton Interactions in the Generation of Rogue Waves: The Modified Korteweg-de Vries Framework.

PubMed

Slunyaev, A V; Pelinovsky, E N

2016-11-18

The role of multiple soliton and breather interactions in the formation of very high waves is disclosed within the framework of the integrable modified Korteweg-de Vries (MKdV) equation. Optimal conditions for the focusing of many solitons are formulated explicitly. Namely, trains of ordered solitons with alternate polarities evolve to huge strongly localized transient waves. The focused wave amplitude is exactly the sum of the focusing soliton heights; the maximum wave inherits the polarity of the fastest soliton in the train. The focusing of several solitary waves or/and breathers may naturally occur in a soliton gas and will lead to rogue-wave-type dynamics; hence, it represents a new nonlinear mechanism of rogue wave generation. The discovered scenario depends crucially on the soliton polarities (phases), and is not taken into account by existing kinetic theories. The performance of the soliton mechanism of rogue wave generation is shown for the example of the focusing MKdV equation, when solitons possess "frozen" phases (certain polarities), though the approach is efficient in some other integrable systems which admit soliton and breather solutions.

Role of Multiple Soliton Interactions in the Generation of Rogue Waves: The Modified Korteweg-de Vries Framework

NASA Astrophysics Data System (ADS)

Slunyaev, A. V.; Pelinovsky, E. N.

2016-11-01

The role of multiple soliton and breather interactions in the formation of very high waves is disclosed within the framework of the integrable modified Korteweg-de Vries (MKdV) equation. Optimal conditions for the focusing of many solitons are formulated explicitly. Namely, trains of ordered solitons with alternate polarities evolve to huge strongly localized transient waves. The focused wave amplitude is exactly the sum of the focusing soliton heights; the maximum wave inherits the polarity of the fastest soliton in the train. The focusing of several solitary waves or/and breathers may naturally occur in a soliton gas and will lead to rogue-wave-type dynamics; hence, it represents a new nonlinear mechanism of rogue wave generation. The discovered scenario depends crucially on the soliton polarities (phases), and is not taken into account by existing kinetic theories. The performance of the soliton mechanism of rogue wave generation is shown for the example of the focusing MKdV equation, when solitons possess "frozen" phases (certain polarities), though the approach is efficient in some other integrable systems which admit soliton and breather solutions.

Double Wronskian Solution and Soliton Properties of the Nonisospectral BKP Equation

NASA Astrophysics Data System (ADS)

Wang, Deng-Shan; Li, Xiang-Gui; Chan, C. K.; Zhou, Jian

2016-03-01

Based on the Wronskian technique and Lax pair, double Wronskian solution of the nonisospectral BKP equation is presented explicitly. The speed and dynamical influence of the one soliton are discussed. Soliton resonances of two soliton are shown by means of density distributions. Soliton properties are also investigated in the inhomogeneous media. Supported by the Research Committee of The Hong Kong Polytechnic University under Grant No. G-YM37, the AMSS-PolyU Joint Research Institute for Engineering and Management Mathematics under Grant No. 1-ZVA8, National Natural Science Foundation of China under Grant Nos. 11271362 and 11375030, Beijing Natural Science Fund Project and Beijing City Board of Education Science and Technology Key Project under Grant No. KZ201511232034, Beijing Natural Science Foundation under Grant No. 1153004, Beijing Nova Program No. Z131109000413029, and Beijing Finance Funds of Natural Science Program for Excellent Talents under Grant No. 2014000026833ZK19

Gauge transformation and symmetries of the commutative multicomponent BKP hierarchy

NASA Astrophysics Data System (ADS)

Li, Chuanzhong

2016-01-01

In this paper, we defined a new multi-component B type Kadomtsev-Petviashvili (BKP) hierarchy that takes values in a commutative subalgebra of {gl}(N,{{C}}). After this, we give the gauge transformation of this commutative multicomponent BKP (CMBKP) hierarchy. Meanwhile, we construct a new constrained CMBKP hierarchy that contains some new integrable systems, including coupled KdV equations under a certain reduction. After this, the quantum torus symmetry and quantum torus constraint on the tau function of the commutative multi-component BKP hierarchy will be constructed.

Finite-amplitude strain waves in laser-excited plates.

PubMed

Mirzade, F Kh

2008-07-09

The governing equations for two-dimensional finite-amplitude longitudinal strain waves in isotropic laser-excited solid plates are derived. Geometric and weak material nonlinearities are included, and the interaction of longitudinal displacements with the field of concentration of non-equilibrium laser-generated atomic defects is taken into account. An asymptotic approach is used to show that the equations are reducible to the Kadomtsev-Petviashvili-Burgers nonlinear evolution equation for a longitudinal self-consistent strain field. It is shown that two-dimensional shock waves can propagate in plates.

Solutions of the KPI equation with smooth initial data

NASA Astrophysics Data System (ADS)

Boiti, M.; Pempinelli, F.; Pogrebkov, A.

1994-06-01

The solution $u(t,x,y)$ of the Kadomtsev--Petviashvili I (KPI) equation with given initial data $u(0,x,y)$ belonging to the Schwartz space is considered. No additional special constraints, usually considered in literature, as $\\int\\!dx\\,u(0,x,y)=0$ are required to be satisfied by the initial data. The problem is completely solved in the framework of the spectral transform theory and it is shown that $u(t,x,y)$ satisfies a special evolution version of the KPI equation and that, in general, $\\partial_t u(t,x,y)$ has different left and right limits at the initial time $t=0$. The conditions of the type $\\int\\!dx\\,u(t,x,y)=0$, $\\int\\!dx\\,xu_y(t,x,y)=0$ and so on (first, second, etc. `constraints') are dynamically generated by the evolution equation for $t\

A New Class of Almost Ricci Solitons and Their Physical Interpretation

PubMed Central

2016-01-01

We establish a link between a connection symmetry, called conformal collineation, and almost Ricci soliton (in particular Ricci soliton) in reducible Ricci symmetric semi-Riemannian manifolds. As a physical application, by investigating the kinematic and dynamic properties of almost Ricci soliton manifolds, we present a physical model of imperfect fluid spacetimes. This model gives a general relation between the physical quantities (u, μ, p, α, η, σ ij) of the matter tensor of the field equations and does not provide any exact solution. Therefore, we propose further study on finding exact solutions of our viscous fluid physical model for which it is required that the fluid velocity vector u be tilted. We also suggest two open problems. PMID:28044145

Topological Switching and Orbiting Dynamics of Colloidal Spheres Dressed with Chiral Nematic Solitons

PubMed Central

Porenta, T.; Čopar, S.; Ackerman, P. J.; Pandey, M. B.; Varney, M. C. M.; Smalyukh, I. I.; Žumer, S.

2014-01-01

Metastable configurations formed by defects, inclusions, elastic deformations and topological solitons in liquid crystals are a promising choice for building photonic crystals and metamaterials with a potential for new optical applications. Local optical modification of the director or introduction of colloidal inclusions into a moderately chiral nematic liquid crystal confined to a homeotropic cell creates localized multistable chiral solitons. Here we induce solitons that “dress” the dispersed spherical particles treated for tangential degenerate boundary conditions, and perform controlled switching of their state using focused optical beams. Two optically switchable distinct metastable states, toron and hopfion, bound to colloidal spheres into structures with different topological charges are investigated. Their structures are examined using Q-tensor based numerical simulations and compared to the profiles reconstructed from the experiments. A topological explanation of observed multistability is constructed. PMID:25477195

Uniform strongly interacting soliton gas in the frame of the Nonlinear Schrodinger Equation

NASA Astrophysics Data System (ADS)

Gelash, Andrey; Agafontsev, Dmitry

2017-04-01

The statistical properties of many soliton systems play the key role in the fundamental studies of integrable turbulence and extreme sea wave formation. It is well known that separated solitons are stable nonlinear coherent structures moving with constant velocity. After collisions with each other they restore the original shape and only acquire an additional phase shift. However, at the moment of strong nonlinear soliton interaction (i.e. when solitons are located close) the wave field are highly complicated and should be described by the theory of inverse scattering transform (IST), which allows to integrate the KdV equation, the NLSE and many other important nonlinear models. The usual approach of studying the dynamics and statistics of soliton wave field is based on relatively rarefied gas of solitons [1,2] or restricted by only two-soliton interactions [3]. From the other hand, the exceptional role of interacting solitons and similar coherent structures - breathers in the formation of rogue waves statistics was reported in several recent papers [4,5]. In this work we study the NLSE and use the most straightforward and general way to create many soliton initial condition - the exact N-soliton formulas obtained in the theory of the IST [6]. We propose the recursive numerical scheme for Zakharov-Mikhailov variant of the dressing method [7,8] and discuss its stability with respect to increasing the number of solitons. We show that the pivoting, i.e. the finding of an appropriate order for recursive operations, has a significant impact on the numerical accuracy. We use the developed scheme to generate statistical ensembles of 32 strongly interacting solitons, i.e. solve the inverse scattering problem for the high number of discrete eigenvalues. Then we use this ensembles as initial conditions for numerical simulations in the box with periodic boundary conditions and study statics of obtained uniform strongly interacting gas of NLSE solitons. Author thanks the

General multicomponent Yajima-Oikawa system: Painlevé analysis, soliton solutions, and energy-sharing collisions.

PubMed

Kanna, T; Sakkaravarthi, K; Tamilselvan, K

2013-12-01

We consider the multicomponent Yajima-Oikawa (YO) system and show that the two-component YO system can be derived in a physical setting of a three-coupled nonlinear Schrödinger (3-CNLS) type system by the asymptotic reduction method. The derivation is further generalized to the multicomponent case. This set of equations describes the dynamics of nonlinear resonant interaction between a one-dimensional long wave and multiple short waves. The Painlevé analysis of the general multicomponent YO system shows that the underlying set of evolution equations is integrable for arbitrary nonlinearity coefficients which will result in three different sets of equations corresponding to positive, negative, and mixed nonlinearity coefficients. We obtain the general bright N-soliton solution of the multicomponent YO system in the Gram determinant form by using Hirota's bilinearization method and explicitly analyze the one- and two-soliton solutions of the multicomponent YO system for the above mentioned three choices of nonlinearity coefficients. We also point out that the 3-CNLS system admits special asymptotic solitons of bright, dark, anti-dark, and gray types, when the long-wave-short-wave resonance takes place. The short-wave component solitons undergo two types of energy-sharing collisions. Specifically, in the two-component YO system, we demonstrate that two types of energy-sharing collisions-(i) energy switching with opposite nature for a particular soliton in two components and (ii) similar kind of energy switching for a given soliton in both components-result for two different choices of nonlinearity coefficients. The solitons appearing in the long-wave component always exhibit elastic collision whereas those of short-wave components exhibit standard elastic collisions only for a specific choice of parameters. We have also investigated the collision dynamics of asymptotic solitons in the original 3-CNLS system. For completeness, we explore the three-soliton interaction

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.

Collisions between coaxial vortex solitons in the three-dimensional cubic-quintic complex Ginzburg-Landau equation

NASA Astrophysics Data System (ADS)

Mihalache, D.; Mazilu, D.; Lederer, F.; Leblond, H.; Malomed, B. A.

2008-03-01

We present generic outcomes of collisions between stable solitons with intrinsic vorticity S=1 or S=2 in the complex Ginzburg-Landau equation with the cubic-quintic nonlinearity, for the axially symmetric configuration. An essential ingredient of the complex Ginzburg-Landau equation is an effective transverse diffusivity (which is known in models of laser cavities), as vortex solitons cannot be stable without it. For the sake of comparison, results are also included for fundamental three-dimensional solitons, with S=0 . Depending on the collision momentum, χ , three generic outcomes are identified: merger of the solitons into a single one, at small χ ; quasielastic interaction, at large χ ; and creation of an extra soliton, in an intermediate region. In addition to the final outcomes, we also highlight noteworthy features of the transient dynamics.

Designing magnetic droplet soliton nucleation employing spin polarizer

NASA Astrophysics Data System (ADS)

Mohseni, Morteza; Mohseni, Majid

2018-04-01

We show by means of micromagnetic simulations that spin polarizer in nano-contact (NC) spin torque oscillators as the representative of the fixed layer in an orthogonal pseudo-spin valve can be employed to design and to control magnetic droplet soliton nucleation and dynamics. We found that using a tilted spin polarizer layer decreases the droplet nucleation time which is more suitable for high speed applications. However, a tilted spin polarizer increases the nucleation current and decreases the frequency stability of the droplet. Additionally, by driving the magnetization inhomogenously at the NC region, it is found that a tilted spin polarizer reduces the precession angle of the droplet and through an interplay with the Oersted field of the DC current, it breaks the spatial symmetry of the droplet profile. Our findings explore fundamental insight into nano-scale magnetic droplet soliton dynamics with potential tunability parameters for future microwave electronics.

Soliton formation from a noise-like pulse during extreme events in a fibre ring laser

NASA Astrophysics Data System (ADS)

Pottiez, O.; Ibarra-Villalon, H. E.; Bracamontes-Rodriguez, Y.; Minguela-Gallardo, J. A.; Garcia-Sanchez, E.; Lauterio-Cruz, J. P.; Hernandez-Garcia, J. C.; Bello-Jimenez, M.; Kuzin, E. A.

2017-10-01

We study experimentally the interactions between soliton and noise-like pulse (NLP) components in a mode-locked fibre ring laser operating in a hybrid soliton-NLP regime. For proper polarization adjustments, one NLP and multiple packets of solitons coexist in the cavity, at 1530 nm and 1558 nm, respectively. By examining time-domain sequences measured using a 16 GHz real-time oscilloscope, we unveil the process of soliton genesis: they are produced during extreme-intensity episodes affecting the NLP. These extreme events can emerge sporadically, appear in small groups or even form quasi-periodic sequences. Once formed, the wavelength-shifted soliton packet drifts away from the NLP in the dispersive cavity, and eventually vanishes after a variable lifetime. Evidence of the inverse process, through which NLP formation is occasionally seeded by an extreme-intensity event affecting a bunch of solitons, is also provided. The quasi-stationary dynamics described here constitutes an impressive illustration of the connections and interactions between NLPs, extreme events and solitons in passively mode-locked fibre lasers.

Collective coordinates theory for discrete soliton ratchets in the sine-Gordon model

NASA Astrophysics Data System (ADS)

Sánchez-Rey, Bernardo; Quintero, Niurka R.; Cuevas-Maraver, Jesús; Alejo, Miguel A.

2014-10-01

A collective coordinate theory is developed for soliton ratchets in the damped discrete sine-Gordon model driven by a biharmonic force. An ansatz with two collective coordinates, namely the center and the width of the soliton, is assumed as an approximated solution of the discrete nonlinear equation. The dynamical equations of these two collective coordinates, obtained by means of the generalized travelling wave method, explain the mechanism underlying the soliton ratchet and capture qualitatively all the main features of this phenomenon. The numerical simulation of these equations accounts for the existence of a nonzero depinning threshold, the nonsinusoidal behavior of the average velocity as a function of the relative phase between the harmonics of the driver, the nonmonotonic dependence of the average velocity on the damping, and the existence of nontransporting regimes beyond the depinning threshold. In particular, it provides a good description of the intriguing and complex pattern of subspaces corresponding to different dynamical regimes in parameter space.

Collective coordinates theory for discrete soliton ratchets in the sine-Gordon model.

PubMed

Sánchez-Rey, Bernardo; Quintero, Niurka R; Cuevas-Maraver, Jesús; Alejo, Miguel A

2014-10-01

A collective coordinate theory is developed for soliton ratchets in the damped discrete sine-Gordon model driven by a biharmonic force. An ansatz with two collective coordinates, namely the center and the width of the soliton, is assumed as an approximated solution of the discrete nonlinear equation. The dynamical equations of these two collective coordinates, obtained by means of the generalized travelling wave method, explain the mechanism underlying the soliton ratchet and capture qualitatively all the main features of this phenomenon. The numerical simulation of these equations accounts for the existence of a nonzero depinning threshold, the nonsinusoidal behavior of the average velocity as a function of the relative phase between the harmonics of the driver, the nonmonotonic dependence of the average velocity on the damping, and the existence of nontransporting regimes beyond the depinning threshold. In particular, it provides a good description of the intriguing and complex pattern of subspaces corresponding to different dynamical regimes in parameter space.

Direct observation and imaging of a spin-wave soliton with p-like symmetry

NASA Astrophysics Data System (ADS)

Bonetti, S.; Kukreja, R.; Chen, Z.; Macià, F.; Hernàndez, J. M.; Eklund, A.; Backes, D.; Frisch, J.; Katine, J.; Malm, G.; Urazhdin, S.; Kent, A. D.; Stöhr, J.; Ohldag, H.; Dürr, H. A.

2015-11-01

Spin waves, the collective excitations of spins, can emerge as nonlinear solitons at the nanoscale when excited by an electrical current from a nanocontact. These solitons are expected to have essentially cylindrical symmetry (that is, s-like), but no direct experimental observation exists to confirm this picture. Using a high-sensitivity time-resolved magnetic X-ray microscopy with 50 ps temporal resolution and 35 nm spatial resolution, we are able to create a real-space spin-wave movie and observe the emergence of a localized soliton with a nodal line, that is, with p-like symmetry. Micromagnetic simulations explain the measurements and reveal that the symmetry of the soliton can be controlled by magnetic fields. Our results broaden the understanding of spin-wave dynamics at the nanoscale, with implications for the design of magnetic nanodevices.

Solitonic Dispersive Hydrodynamics: Theory and Observation

NASA Astrophysics Data System (ADS)

Maiden, Michelle D.; Anderson, Dalton V.; Franco, Nevil A.; El, Gennady A.; Hoefer, Mark A.

2018-04-01

Ubiquitous nonlinear waves in dispersive media include localized solitons and extended hydrodynamic states such as dispersive shock waves. Despite their physical prominence and the development of thorough theoretical and experimental investigations of each separately, experiments and a unified theory of solitons and dispersive hydrodynamics are lacking. Here, a general soliton-mean field theory is introduced and used to describe the propagation of solitons in macroscopic hydrodynamic flows. Two universal adiabatic invariants of motion are identified that predict trapping or transmission of solitons by hydrodynamic states. The result of solitons incident upon smooth expansion waves or compressive, rapidly oscillating dispersive shock waves is the same, an effect termed hydrodynamic reciprocity. Experiments on viscous fluid conduits quantitatively confirm the soliton-mean field theory with broader implications for nonlinear optics, superfluids, geophysical fluids, and other dispersive hydrodynamic media.

Drift ion acoustic shock waves in an inhomogeneous two-dimensional quantum magnetoplasma

DOE Office of Scientific and Technical Information (OSTI.GOV)

Masood, W.; Siddiq, M.; Karim, S.

2009-04-15

Linear and nonlinear propagation characteristics of drift ion acoustic waves are investigated in an inhomogeneous quantum plasma with neutrals in the background employing the quantum hydrodynamics (QHD) model. In this regard, a quantum Kadomtsev-Petviashvili-Burgers (KPB) equation is derived for the first time. It is shown that the ion acoustic wave couples with the drift wave if the parallel motion of ions is taken into account. Discrepancies in the earlier works on drift solitons and shocks in inhomogeneous plasmas are also pointed out and a correct theoretical framework is presented to study the one-dimensional as well as the two-dimensional propagation ofmore » shock waves in an inhomogeneous quantum plasma. Furthermore, the solution of KPB equation is presented using the tangent hyperbolic (tanh) method. The variation of the shock profile with the quantum Bohm potential, collision frequency, and ratio of drift to shock velocity in the comoving frame, v{sub *}/u, are also investigated. It is found that increasing the number density and collision frequency enhances the strength of the shock. It is also shown that the fast drift shock (i.e., v{sub *}/u>0) increases, whereas the slow drift shock (i.e., v{sub *}/u<0) decreases the strength of the shock. The relevance of the present investigation with regard to dense astrophysical environments is also pointed out.« less

Stably accessing octave-spanning microresonator frequency combs in the soliton regime.

PubMed

Li, Qing; Briles, Travis C; Westly, Daron A; Drake, Tara E; Stone, Jordan R; Ilic, B Robert; Diddams, Scott A; Papp, Scott B; Srinivasan, Kartik

2017-02-01

Microresonator frequency combs can be an enabling technology for optical frequency synthesis and timekeeping in low size, weight, and power architectures. Such systems require comb operation in low-noise, phase-coherent states such as solitons, with broad spectral bandwidths (e.g., octave-spanning) for self-referencing to detect the carrier-envelope offset frequency. However, accessing such states is complicated by thermo-optic dispersion. For example, in the Si 3 N 4 platform, precisely dispersion-engineered structures can support broadband operation, but microsecond thermal time constants often require fast pump power or frequency control to stabilize the solitons. In contrast, here we consider how broadband soliton states can be accessed with simple pump laser frequency tuning, at a rate much slower than the thermal dynamics. We demonstrate octave-spanning soliton frequency combs in Si 3 N 4 microresonators, including the generation of a multi-soliton state with a pump power near 40 mW and a single-soliton state with a pump power near 120 mW. We also develop a simplified two-step analysis to explain how these states are accessed without fast control of the pump laser, and outline the required thermal properties for such operation. Our model agrees with experimental results as well as numerical simulations based on a Lugiato-Lefever equation that incorporates thermo-optic dispersion. Moreover, it also explains an experimental observation that a member of an adjacent mode family on the red-detuned side of the pump mode can mitigate the thermal requirements for accessing soliton states.

Stably accessing octave-spanning microresonator frequency combs in the soliton regime

PubMed Central

Li, Qing; Briles, Travis C.; Westly, Daron A.; Drake, Tara E.; Stone, Jordan R.; Ilic, B. Robert; Diddams, Scott A.; Papp, Scott B.; Srinivasan, Kartik

2017-01-01

Microresonator frequency combs can be an enabling technology for optical frequency synthesis and timekeeping in low size, weight, and power architectures. Such systems require comb operation in low-noise, phase-coherent states such as solitons, with broad spectral bandwidths (e.g., octave-spanning) for self-referencing to detect the carrier-envelope offset frequency. However, accessing such states is complicated by thermo-optic dispersion. For example, in the Si3N4 platform, precisely dispersion-engineered structures can support broadband operation, but microsecond thermal time constants often require fast pump power or frequency control to stabilize the solitons. In contrast, here we consider how broadband soliton states can be accessed with simple pump laser frequency tuning, at a rate much slower than the thermal dynamics. We demonstrate octave-spanning soliton frequency combs in Si3N4 microresonators, including the generation of a multi-soliton state with a pump power near 40 mW and a single-soliton state with a pump power near 120 mW. We also develop a simplified two-step analysis to explain how these states are accessed without fast control of the pump laser, and outline the required thermal properties for such operation. Our model agrees with experimental results as well as numerical simulations based on a Lugiato-Lefever equation that incorporates thermo-optic dispersion. Moreover, it also explains an experimental observation that a member of an adjacent mode family on the red-detuned side of the pump mode can mitigate the thermal requirements for accessing soliton states. PMID:28603754

Fredholm and Wronskian representations of solutions to the KPI equation and multi-rogue waves

NASA Astrophysics Data System (ADS)

Gaillard, Pierre

2016-06-01

We construct solutions to the Kadomtsev-Petviashvili equation (KPI) in terms of Fredholm determinants. We deduce solutions written as a quotient of Wronskians of order 2N. These solutions, called solutions of order N, depend on 2N - 1 parameters. When one of these parameters tends to zero, we obtain N order rational solutions expressed as a quotient of two polynomials of degree 2N(N + 1) in x, y, and t depending on 2N - 2 parameters. So we get with this method an infinite hierarchy of solutions to the KPI equation.

Effects of dust size distribution on dust acoustic waves in two-dimensional unmagnetized dusty plasma

DOE Office of Scientific and Technical Information (OSTI.GOV)

He Guangjun; Duan Wenshan; Tian Duoxiang

2008-04-15

For unmagnetized dusty plasma with many different dust grain species containing both hot isothermal electrons and ions, both the linear dispersion relation and the Kadomtsev-Petviashvili equation for small, but finite amplitude dust acoustic waves are obtained. The linear dispersion relation is investigated numerically. Furthermore, the variations of amplitude, width, and propagation velocity of the nonlinear solitary wave with an arbitrary dust size distribution function are studied as well. Moreover, both the power law distribution and the Gaussian distribution are approximately simulated by using appropriate arbitrary dust size distribution functions.

Hierarchies of Manakov-Santini Type by Means of Rota-Baxter and Other Identities

NASA Astrophysics Data System (ADS)

Szablikowski, Błażej

2016-02-01

The Lax-Sato approach to the hierarchies of Manakov-Santini type is formalized in order to extend it to a more general class of integrable systems. For this purpose some linear operators are introduced, which must satisfy some integrability conditions, one of them is the Rota-Baxter identity. The theory is illustrated by means of the algebra of Laurent series, the related hierarchies are classified and examples, also new, of Manakov-Santini type systems are constructed, including those that are related to the dispersionless modified Kadomtsev-Petviashvili equation and so called dispersionless r-th systems.

Anisotropic spectra of acoustic type turbulence

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kuznetsov, E.; P.N. Lebedev Physical Institute, 53 Leninsky Ave., 119991 Moscow; Krasnoselskikh, V.

2008-06-15

The problem of spectra for acoustic type of turbulence generated by shocks being randomly distributed in space is considered. It is shown that for turbulence with a weak anisotropy, such spectra have the same dependence in k-space as the Kadomtsev-Petviashvili spectrum: E(k){approx}k{sup -2}. However, the frequency spectrum has always the falling {approx}{omega}{sup -2}, independent of anisotropy. In the strong anisotropic case the energy distribution relative to wave vectors takes anisotropic dependence, forming in the large-k region spectra of the jet type.

Vibron Solitons and Soliton-Induced Infrared Spectra of Crystalline Acetanilide

NASA Astrophysics Data System (ADS)

Takeno, S.

1986-01-01

Red-shifted infrared spectra at low temperatures of amide I (C=O stretching) vibrations of crystalline acetanilide measured by Careri et al. are shown to be due to vibron solitons, which are nonlinearity-induced localized modes of vibrons arising from their nonlinear interactions with optic-type phonons. A nonlinear eigenvalue equation giving the eigenfrequency of stationary solitons is solved approximately by introducing lattice Green's functions, and the obtained result is in good agreement with the experimental result. Inclusion of interactions with acoustic phonons yields the Debye-Waller factor in the zero-phonon line spectrum of vibron solitons, in a manner analogous to the case of impurity-induced localized harmonic phonon modes in alkali halides.

Soliton excitations and interactions for the three-coupled fourth-order nonlinear Schrödinger equations in the alpha helical proteins

NASA Astrophysics Data System (ADS)

Sun, Wen-Rong; Tian, Bo; Wang, Yu-Feng; Zhen, Hui-Ling

2015-06-01

Three-coupled fourth-order nonlinear Schrödinger equations describe the dynamics of alpha helical proteins with the interspine coupling at the higher order. Through symbolic computation and binary Bell-polynomial approach, bilinear forms and N-soliton solutions for such equations are constructed. Key point lies in the introduction of auxiliary functions in the Bell-polynomial expression. Asymptotic analysis is applied to investigate the elastic interaction between the two solitons: two solitons keep their original amplitudes, energies and velocities invariant after the interaction except for the phase shifts. Soliton amplitudes are related to the energy distributed in the solitons of the three spines. Overtaking interaction, head-on interaction and bound-state solitons of two solitons are given. Bound states of three bright solitons arise when all of them propagate in parallel. Elastic interaction between the bound-state solitons and one bright soliton is shown. Increase of the lattice parameter can lead to the increase of the soliton velocity, that is, the interaction period becomes shorter. The solitons propagating along the neighbouring spines are found to interact elastically. Those solitons, exhibited in this paper, might be viewed as a possible carrier of bio-energy transport in the protein molecules.

Direct observation and imaging of a spin-wave soliton with p-like symmetry

DOE PAGES

Bonetti, S.; Kukreja, R.; Chen, Z.; ...

2015-11-16

Spin waves, the collective excitations of spins, can emerge as nonlinear solitons at the nanoscale when excited by an electrical current from a nanocontact. These solitons are expected to have essentially cylindrical symmetry (that is, s-like), but no direct experimental observation exists to confirm this picture. Using a high-sensitivity time-resolved magnetic X-ray microscopy with 50 ps temporal resolution and 35 nm spatial resolution, we are able to create a real-space spin-wave movie and observe the emergence of a localized soliton with a nodal line, that is, with p-like symmetry. Moreover, micromagnetic simulations explain the measurements and reveal that the symmetrymore » of the soliton can be controlled by magnetic fields. Our results broaden the understanding of spin-wave dynamics at the nanoscale, with implications for the design of magnetic nanodevices.« less

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.

Chladni solitons and the onset of the snaking instability for dark solitons in confined superfluids.

PubMed

Muñoz Mateo, A; Brand, J

2014-12-19

Complex solitary waves composed of intersecting vortex lines are predicted in a channeled superfluid. Their shapes in a cylindrical trap include a cross, spoke wheels, and Greek Φ, and trace the nodal lines of unstable vibration modes of a planar dark soliton in analogy to Chladni's figures of membrane vibrations. The stationary solitary waves extend a family of solutions that include the previously known solitonic vortex and vortex rings. Their bifurcation points from the dark soliton indicating the onset of new unstable modes of the snaking instability are predicted from scale separation for Bose-Einstein condensates (BECs) and superfluid Fermi gases across the BEC-BCS crossover, and confirmed by full numerical calculations. Chladni solitons could be observed in ultracold gas experiments by seeded decay of dark solitons.

Chladni Solitons and the Onset of the Snaking Instability for Dark Solitons in Confined Superfluids

NASA Astrophysics Data System (ADS)

Muñoz Mateo, A.; Brand, J.

2014-12-01

Complex solitary waves composed of intersecting vortex lines are predicted in a channeled superfluid. Their shapes in a cylindrical trap include a cross, spoke wheels, and Greek Φ , and trace the nodal lines of unstable vibration modes of a planar dark soliton in analogy to Chladni's figures of membrane vibrations. The stationary solitary waves extend a family of solutions that include the previously known solitonic vortex and vortex rings. Their bifurcation points from the dark soliton indicating the onset of new unstable modes of the snaking instability are predicted from scale separation for Bose-Einstein condensates (BECs) and superfluid Fermi gases across the BEC-BCS crossover, and confirmed by full numerical calculations. Chladni solitons could be observed in ultracold gas experiments by seeded decay of dark solitons.

New Double-Periodic Soliton Solutions for the (2+1)-Dimensional Breaking Soliton Equation

NASA Astrophysics Data System (ADS)

Liu, Jian-Guo; Tian, Yu

2018-05-01

Under investigation is the (2+1)-dimensional breaking soliton equation. Based on a special ansätz functions and the bilinear form, some entirely new double-periodic soliton solutions for the (2+1)-dimensional breaking soliton equation are presented. With the help of symbolic computation software Mathematica, many important and interesting properties for these obtained solutions are revealed with some figures. Supported by National Natural Science Foundation of China under Grant No. 61377067

Defocusing complex short-pulse equation and its multi-dark-soliton solution.

PubMed

Feng, Bao-Feng; Ling, Liming; Zhu, Zuonong

2016-05-01

In this paper, we propose a complex short-pulse equation of both focusing and defocusing types, which governs the propagation of ultrashort pulses in nonlinear optical fibers. It can be viewed as an analog of the nonlinear Schrödinger (NLS) equation in the ultrashort-pulse regime. Furthermore, we construct the multi-dark-soliton solution for the defocusing complex short-pulse equation through the Darboux transformation and reciprocal (hodograph) transformation. One- and two-dark-soliton solutions are given explicitly, whose properties and dynamics are analyzed and illustrated.

Polariton condensation in solitonic gap states in a one-dimensional periodic potential

PubMed Central

Tanese, D.; Flayac, H.; Solnyshkov, D.; Amo, A.; Lemaître, A.; Galopin, E.; Braive, R.; Senellart, P.; Sagnes, I.; Malpuech, G.; Bloch, J.

2013-01-01

Manipulation of nonlinear waves in artificial periodic structures leads to spectacular spatial features, such as generation of gap solitons or onset of the Mott insulator phase transition. Cavity exciton–polaritons are strongly interacting quasiparticles offering large possibilities for potential optical technologies. Here we report their condensation in a one-dimensional microcavity with a periodic modulation. The resulting mini-band structure dramatically influences the condensation process. Contrary to non-modulated cavities, where condensates expand, here, we observe spontaneous condensation in localized gap soliton states. Depending on excitation conditions, we access different dynamical regimes: we demonstrate the formation of gap solitons either moving along the ridge or bound to the potential created by the reservoir of uncondensed excitons. We also find Josephson oscillations of gap solitons triggered between the two sides of the reservoir. This system is foreseen as a building block for polaritonic circuits, where propagation and localization are optically controlled and reconfigurable. PMID:23612290

Formation of matter-wave soliton trains by modulational instability

NASA Astrophysics Data System (ADS)

Nguyen, Jason H. V.; Luo, De; Hulet, Randall G.

2017-04-01

Nonlinear systems can exhibit a rich set of dynamics that are inherently sensitive to their initial conditions. One such example is modulational instability, which is believed to be one of the most prevalent instabilities in nature. By exploiting a shallow zero-crossing of a Feshbach resonance, we characterize modulational instability and its role in the formation of matter-wave soliton trains from a Bose-Einstein condensate. We examine the universal scaling laws exhibited by the system and, through real-time imaging, address a long-standing question of whether the solitons in trains are created with effectively repulsive nearest-neighbor interactions or rather evolve into such a structure.

Optical spatial solitons: historical overview and recent advances.

PubMed

Chen, Zhigang; Segev, Mordechai; Christodoulides, Demetrios N

2012-08-01

Solitons, nonlinear self-trapped wavepackets, have been extensively studied in many and diverse branches of physics such as optics, plasmas, condensed matter physics, fluid mechanics, particle physics and even astrophysics. Interestingly, over the past two decades, the field of solitons and related nonlinear phenomena has been substantially advanced and enriched by research and discoveries in nonlinear optics. While optical solitons have been vigorously investigated in both spatial and temporal domains, it is now fair to say that much soliton research has been mainly driven by the work on optical spatial solitons. This is partly due to the fact that although temporal solitons as realized in fiber optic systems are fundamentally one-dimensional entities, the high dimensionality associated with their spatial counterparts has opened up altogether new scientific possibilities in soliton research. Another reason is related to the response time of the nonlinearity. Unlike temporal optical solitons, spatial solitons have been realized by employing a variety of noninstantaneous nonlinearities, ranging from the nonlinearities in photorefractive materials and liquid crystals to the nonlinearities mediated by the thermal effect, thermophoresis and the gradient force in colloidal suspensions. Such a diversity of nonlinear effects has given rise to numerous soliton phenomena that could otherwise not be envisioned, because for decades scientists were of the mindset that solitons must strictly be the exact solutions of the cubic nonlinear Schrödinger equation as established for ideal Kerr nonlinear media. As such, the discoveries of optical spatial solitons in different systems and associated new phenomena have stimulated broad interest in soliton research. In particular, the study of incoherent solitons and discrete spatial solitons in optical periodic media not only led to advances in our understanding of fundamental processes in nonlinear optics and photonics, but also had a

Evolution of a dark soliton in a parabolic potential: Application to Bose-Einstein condensates

DOE Office of Scientific and Technical Information (OSTI.GOV)

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

2003-10-01

Evolution of a dark soliton in a one-dimensional Bose-Einstein condensate trapped by a harmonic potential is studied analytically and numerically. In the case of a deep soliton, main characteristics of its motion such as frequency and amplitude of oscillations are calculated by means of the perturbation theory which in the leading order results in a Newtonian dynamics, corrections to which are computed as well.

Soliton-mediated conduit flow: Deep Hawaiian magma migration

NASA Astrophysics Data System (ADS)

Ryan, M.; Stanley, B.

2006-12-01

Solitons have first-order attributes that include shape- and volume-conserving packets of fluid that migrate with characteristic wavelengths, amplitudes, wave numbers, and pulse durations. For ascent in dike-like magma- filled fractures, the soliton pulse duration is directly proportional to the conduit wall region viscosity and inversely proportional to the density contrast that drives the flow. Second-order effects that modify pathways include heat loss to conduit wall rocks, and progressive crystallization episodes along conduit walls. Long-lived (and intermediate duration) historical eruption episodes of Kilauea volcano, Hawai'i, include the 1959 Kilauea summit series at Kilauea Iki, the 1969-1974 series at Mauna Ulu and the 1983-to-present series at Pu'u `O'o-Kupaianaha. For each locale, the eruptions display a variable time-series in their erupted volumes, as well as fountain heights and vent flow rates. Inter-episode repose periods, however, often show broad regularity over extended periods. We suggest that these dynamics represent serendipitous windows into the characteristic system dynamics of deep magma migration beneath Hawai'i: all made possible by the chance clearance of mechanical obstructions allowing virtually open-system behavior. The rhythmic `beat' of eruptive episodes within a long-lived series (and their roughly regular repose periods) arise directly from the soliton migration mechanism. For non-summit locales such as Mauna Ulu and Pu'u `O'o-Kupaianaha, the fluid contents of the sub-caldera reservoir and the shallow molten rift zone core modulate the observed intrusion- eruption dynamics as volumetric displacements transmit down-rift the pressure pulses first felt beneath Halemaumau and the summit caldera. Analytic calculations of wave speed, wave length, batch volume, parcel shapes and repose periods reveal the dependence on material properties appropriate for Kilauea intrusions and eruptions. Analogue laboratory experiments using stiff

Generation of dark and bright spin wave envelope soliton trains through self-modulational instability in magnetic films.

PubMed

Wu, Mingzhong; Kalinikos, Boris A; Patton, Carl E

2004-10-08

The generation of dark spin wave envelope soliton trains from a continuous wave input signal due to spontaneous modulational instability has been observed for the first time. The dark soliton trains were formed from high dispersion dipole-exchange spin waves propagated in a thin yttrium iron garnet film with pinned surface spins at frequencies situated near the dipole gaps in the dipole-exchange spin wave spectrum. Dark and bright soliton trains were generated for one and the same film through placement of the input carrier frequency in regions of negative and positive dispersion, respectively. Two unreported effects in soliton dynamics, hysteresis and period doubling, were also observed.

Interaction of solitons with a string of coupled quantum dots

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kumar, Vijendra, E-mail: vsmedphysics@gmail.com; Swami, O. P., E-mail: omg1789@gmail.com; Nagar, A. K., E-mail: ajaya.nagar@gmail.com

2016-05-06

In this paper, we develop a theory for discrete solitons interaction with a string of coupled quantum dots in view of the local field effects. Discrete nonlinear Schrodinger (DNLS) equations are used to describe the dynamics of the string. Numerical calculations are carried out and results are analyzed with the help of matlab software. With the help of numerical solutions we demonstrate that in the quantum dots string, Rabi oscillations (RO) are self trapped into stable bright Rabi solitons. The Rabi oscillations in different types of nanostructures have potential applications to the elements of quantum logic and quantum memory.

Light-driven dynamic Archimedes spirals and periodic oscillatory patterns of topological solitons in anisotropic soft matter

DOE PAGES

Martinez, Angel; Smalyukh, Ivan I.

2015-02-12

Oscillatory and excitable systems very commonly exhibit formation of dynamic non-equilibrium patterns. For example, rotating spiral patterns are observed in biological, chemical, and physical systems ranging from organization of slime mold cells to Belousov-Zhabotinsky reactions, and to crystal growth from nuclei with screw dislocations. Here we describe spontaneous formation of spiral waves and a large variety of other dynamic patterns in anisotropic soft matter driven by low-intensity light. The unstructured ambient or microscope light illumination of thin liquid crystal films in contact with a self-assembled azobenzene monolayer causes spontaneous formation, rich spatial organization, and dynamics of twisted domains and topologicalmore » solitons accompanied by the dynamic patterning of azobenzene group orientations within the monolayer. Linearly polarized incident light interacts with the twisted liquid crystalline domains, mimicking their dynamics and yielding patterns in the polarization state of transmitted light, which can be transformed to similar dynamic patterns in its intensity and interference color. This shows that the delicate light-soft-matter interaction can yield complex self-patterning of both. Finally, we uncover underpinning physical mechanisms and discuss potential uses.« less

Many-body matter-wave dark soliton.

PubMed

Delande, Dominique; Sacha, Krzysztof

2014-01-31

The Gross-Pitaevskii equation--which describes interacting bosons in the mean-field approximation--possesses solitonic solutions in dimension one. For repulsively interacting particles, the stationary soliton is dark, i.e., is represented by a local density minimum. Many-body effects may lead to filling of the dark soliton. Using quasiexact many-body simulations, we show that, in single realizations, the soliton appears totally dark although the single particle density tends to be uniform.

Dark and grey compressional dispersive Alfven solitons in plasmas

DOE Office of Scientific and Technical Information (OSTI.GOV)

Shukla, P. K.; Eliasson, B.; Stenflo, L.

2011-06-15

The amplitude modulation of compressional dispersive Alfven (CDA) waves in a low-{beta} plasma is considered. It is shown that the dynamics of modulated CDA waves is governed by a cubic nonlinear Schroedinger equation, which depicts the formation of a dark/grey envelope CDA soliton.

Vector rogue waves and dark-bright boomeronic solitons in autonomous and nonautonomous settings.

PubMed

Mareeswaran, R Babu; Charalampidis, E G; Kanna, T; Kevrekidis, P G; Frantzeskakis, D J

2014-10-01

In this work we consider the dynamics of vector rogue waves and dark-bright solitons in two-component nonlinear Schrödinger equations with various physically motivated time-dependent nonlinearity coefficients, as well as spatiotemporally dependent potentials. A similarity transformation is utilized to convert the system into the integrable Manakov system and subsequently the vector rogue and dark-bright boomeronlike soliton solutions of the latter are converted back into ones of the original nonautonomous model. Using direct numerical simulations we find that, in most cases, the rogue wave formation is rapidly followed by a modulational instability that leads to the emergence of an expanding soliton train. Scenarios different than this generic phenomenology are also reported.

(2 + 1)-dimensional bright optical solitons in metamaterials with Kerr, power and parabolic law nonlinearities

NASA Astrophysics Data System (ADS)

Boubir, Badreddine

2018-06-01

In this paper, we investigate the dynamics of bright optical solitons in nonlinear metamaterials governed by a (2 + 1)-dimensional nonlinear Schrödinger equation. Three types of nonlinearities have been considered, Kerr law, power law and parabolic law. We based on the solitary wave ansatz method to find these optical soliton solutions. All necessary parametric conditions for their existence are driven.

Few-cycle solitons in the medium with permanent dipole moment under conditions of the induced birefringence

NASA Astrophysics Data System (ADS)

Sazonov, S. V.

2016-12-01

Propagation of electromagnetic pulse in the birefringent medium consisting of symmetric and asymmetrical molecules is investigated. Stationary quantum states of asymmetrical molecules have the permanent dipole moment. Under considered conditions the ordinary pulse component excites quantum transitions between stationary states. The extraordinary component, besides, causes a dynamic chirp of frequencies of these transitions. The new solitonic modes of propagation of the half- and single-period pulses are found. The solitonic mechanism of simultaneous generation of the second and zero harmonics in the modes of "bright" and "dark" solitons is analyzed.

Correlations, soliton modes, and non-Hermitian linear mode transmutation in the one-dimensional noisy Burgers equation.

PubMed

Fogedby, Hans C

2003-08-01

Using the previously developed canonical phase space approach applied to the noisy Burgers equation in one dimension, we discuss in detail the growth morphology in terms of nonlinear soliton modes and superimposed linear modes. We moreover analyze the non-Hermitian character of the linear mode spectrum and the associated dynamical pinning, and mode transmutation from diffusive to propagating behavior induced by the solitons. We discuss the anomalous diffusion of growth modes, switching and pathways, correlations in the multisoliton sector, and in detail the correlations and scaling properties in the two-soliton sector.

Solitons and ionospheric modification

NASA Technical Reports Server (NTRS)

Sheerin, J. P.; Nicholson, D. R.; Payne, G. L.; Hansen, P. J.; Weatherall, J. C.; Goldman, M. V.

1982-01-01

The possibility of Langmuir soliton formation and collapse during ionospheric modification is investigated. Parameters characterizing former facilities, existing facilities, and planned facilities are considered, using a combination of analytical and numerical techniques. At a spatial location corresponding to the exact classical reflection point of the modifier wave, the Langmuir wave evolution is found to be dominated by modulational instability followed by soliton formation and three-dimensional collapse. The earth's magnetic field is found to affect the shape of the collapsing soliton. These results provide an alternative explanation for some recent observations.

Universality of the Peregrine Soliton in the Focusing Dynamics of the Cubic Nonlinear Schrödinger Equation

NASA Astrophysics Data System (ADS)

Tikan, Alexey; Billet, Cyril; El, Gennady; Tovbis, Alexander; Bertola, Marco; Sylvestre, Thibaut; Gustave, Francois; Randoux, Stephane; Genty, Goëry; Suret, Pierre; Dudley, John M.

2017-07-01

We report experimental confirmation of the universal emergence of the Peregrine soliton predicted to occur during pulse propagation in the semiclassical limit of the focusing nonlinear Schrödinger equation. Using an optical fiber based system, measurements of temporal focusing of high power pulses reveal both intensity and phase signatures of the Peregrine soliton during the initial nonlinear evolution stage. Experimental and numerical results are in very good agreement, and show that the universal mechanism that yields the Peregrine soliton structure is highly robust and can be observed over a broad range of parameters.

Noncommuting Momenta of Topological Solitons

NASA Astrophysics Data System (ADS)

Watanabe, Haruki; Murayama, Hitoshi

2014-05-01

We show that momentum operators of a topological soliton may not commute among themselves when the soliton is associated with the second cohomology H2 of the target space. The commutation relation is proportional to the winding number, taking a constant value within each topological sector. The noncommutativity makes it impossible to specify the momentum of a topological soliton, and induces a Magnus force.

Gap solitons in Ginzburg-Landau media.

PubMed

Sakaguchi, Hidetsugu; Malomed, Boris A

2008-05-01

We introduce a model combining basic elements of conservative systems which give rise to gap solitons, i.e., a periodic potential and self-defocusing cubic nonlinearity, and dissipative terms corresponding to the complex Ginzburg-Landau (CGL) equation of the cubic-quintic type. The model may be realized in optical cavities with a periodic transverse modulation of the refractive index, self-defocusing nonlinearity, linear gain, and saturable absorption. By means of systematic simulations and analytical approximations, we find three species of stable dissipative gap solitons (DGSs), and also dark solitons. They are located in the first finite band gap, very close to the border of the Bloch band separating the finite and the semi-infinite gaps. Two species represent loosely and tightly bound solitons, in cases when the underlying Bloch band is, respectively, relatively broad or very narrow. These two families of stationary solitons are separated by a region of breathers. The loosely bound DGSs are accurately described by means of two approximations, which rely on the product of a carrier Bloch function and a slowly varying envelope, or reduce the model to CGL-Bragg equations. The former approximation also applies to dark solitons. Another method, based on the variational approximation, accurately describes tightly bound solitons. The loosely bound DGSs, as well as dark solitons, are mobile, and their collisions are quasielastic.

Dynamics of vortices followed by the collapse of ring dark solitons in a two-component Bose-Einstein condensate

NASA Astrophysics Data System (ADS)

Wang, Lin-Xue; Dai, Chao-Qing; Wen, Lin; Liu, Tao; Jiang, Hai-Feng; Saito, Hiroki; Zhang, Shou-Gang; Zhang, Xiao-Fei

2018-06-01

We explore the effects of system parameters on the dynamics of ring dark solitons (RDSs) and vortices followed by the collapse of RDSs in a two-component Bose-Einstein condensate (BEC). The system exhibits complicated dynamical behaviors, which are quite different from those in a scalar BEC. For two shallow RDSs with equal initial depths, the dynamical trajectories of generated vortex dipoles are similar to those in a scalar BEC, but the time for vortex dipoles to perform a periodic motion is increased. In particular, there exists a critical depth, above which vortex dipoles first move along the vertical direction and then preform complicated dynamics, including their rearrangement and recombination. Finally, we consider the case of unequal initial depths and find that the number of created vortices is determined by the depth of the shallow RDS, while their initial moving direction is determined by the deeper one.

Properties of an optical soliton gas

NASA Astrophysics Data System (ADS)

Schwache, A.; Mitschke, F.

1997-06-01

We consider light pulses propagating in an optical fiber ring resonator with anomalous dispersion. New pulses are fed into the resonator in synchronism with its round-trip time. We show that solitary pulse shaping leads to a formation of an ensemble of subpulses that are identified as solitons. All solitons in the ensemble are in perpetual relative motion like molecules in a fluid; thus we refer to the ensemble as a soliton gas. Properties of this soliton gas are determined numerically.

Vector solitons in coupled nonlinear Schrödinger equations with spatial stimulated scattering and inhomogeneous dispersion

NASA Astrophysics Data System (ADS)

Gromov, E. M.; Malomed, B. A.; Tyutin, V. V.

2018-01-01

The dynamics of two-component solitons is studied, analytically and numerically, in the framework of a system of coupled extended nonlinear Schrödinger equations, which incorporate the cross-phase modulation, pseudo-stimulated-Raman-scattering (pseudo-SRS), cross-pseudo-SRS, and spatially inhomogeneous second-order dispersion (SOD). The system models co-propagation of electromagnetic waves with orthogonal polarizations in plasmas. It is shown that the soliton's wavenumber downshift, caused by pseudo-SRS, may be compensated by an upshift, induced by the inhomogeneous SOD, to produce stable stationary two-component solitons. The corresponding approximate analytical solutions for stable solitons are found. Analytical results are well confirmed by their numerical counterparts. Further, the evolution of inputs composed of spatially even and odd components is investigated by means of systematic simulations, which reveal three different outcomes: formation of a breather which keeps opposite parities of the components; splitting into a pair of separating vector solitons; and spreading of the weak odd component into a small-amplitude pedestal with an embedded dark soliton.

Relation between nonlocal surface and bulk dark solitons

NASA Astrophysics Data System (ADS)

Gao, Xinghui; Zhang, Chengyun; Wang, Qing

2018-06-01

We investigate the existence and stability of nonlocal surface dark solitons at the interface formed by a nonlocal nonlinear self-defocusing medium and a linear medium. We find that nonlocal fundamental surface dark solitons are always stable in their entire existence domain, while high-order surface dark solitons are oscillatory stable. Comparing with nonlocal bulk dark solitons in amplitude and boundary conditions, nonlocal surface dark solitons can be regarded as the half of the corresponding bulk dark solitons with antisymmetrical amplitude distribution.

Dynamical formation of a hairy black hole in a cavity from the decay of unstable solitons

NASA Astrophysics Data System (ADS)

Sanchis-Gual, Nicolas; Degollado, Juan Carlos; Font, José A.; Herdeiro, Carlos; Radu, Eugen

2017-08-01

Recent numerical relativity simulations within the Einstein-Maxwell-(charged-)Klein-Gordon (EMcKG) system have shown that the non-linear evolution of a superradiantly unstable Reissner-Nordström black hole (BH) enclosed in a cavity, leads to the formation of a BH with scalar hair. Perturbative evidence for the stability of such hairy BHs has been independently established, confirming they are the true endpoints of superradiant instability. The same EMcKG system admits also charged scalar soliton-type solutions, which can be either stable or unstable. Using numerical relativity techniques, we provide evidence that the time evolution of some of these unstable solitons leads, again, to the formation of a hairy BH. In some other cases, unstable solitons evolve into a (bald) Reissner-Nordström BH. These results establish that the system admits two distinct channels to form hairy BHs at the threshold of superradiance: growing hair from an unstable (bald) BH, or growing a horizon from an unstable (horizonless) soliton. Some parallelism with the case of asymptotically flat boson stars and Kerr BHs with scalar hair is drawn.

Coalescence and Interaction of Solitons in the Coupled Korteweg-de Vries System

NASA Astrophysics Data System (ADS)

Chung, Wai Choi; Chow, Kwok Wing

2017-11-01

There are many physical systems which are governed by the classical Korteweg-de Vries equation. One of the prominent examples is the shallow water wave in fluid dynamics. In recent years, a coupled Korteweg-de Vries system has been proposed to describe fluids in a two-layer flow, and coherent structures in terms of solitons are found. We studied the coupled Korteweg-de Vries system by means of the Hirota bilinear method. Soliton and breather solutions are constructed. Localized pulses which result from the coupling of waves can be formed. The structure of the localized pulses becomes asymmetric as the control parameter varies. The coalescence and interaction of solitons in the coupled Korteweg-de Vries system will be discussed. Partial financial support has been provided by the Research Grants Council contract HKU 17200815.

Topological Vortex and Knotted Dissipative Optical 3D Solitons Generated by 2D Vortex Solitons

NASA Astrophysics Data System (ADS)

Veretenov, N. A.; Fedorov, S. V.; Rosanov, N. N.

2017-12-01

We predict a new class of three-dimensional (3D) topological dissipative optical one-component solitons in homogeneous laser media with fast saturable absorption. Their skeletons formed by vortex lines where the field vanishes are tangles, i.e., Nc knotted or unknotted, linked or unlinked closed lines and M unclosed lines that thread all the closed lines and end at the infinitely far soliton periphery. They are generated by embedding two-dimensional laser solitons or their complexes in 3D space after their rotation around an unclosed, infinite vortex line with topological charge M0 (Nc , M , and M0 are integers). With such structure propagation, the "hula-hoop" solitons form; their stability is confirmed numerically. For the solitons found, all vortex lines have unit topological charge: the number of closed lines Nc=1 and 2 (unknots, trefoils, and Solomon knots links); unclosed vortex lines are unknotted and unlinked, their number M =1 , 2, and 3.

Topological Vortex and Knotted Dissipative Optical 3D Solitons Generated by 2D Vortex Solitons.

PubMed

Veretenov, N A; Fedorov, S V; Rosanov, N N

2017-12-29

We predict a new class of three-dimensional (3D) topological dissipative optical one-component solitons in homogeneous laser media with fast saturable absorption. Their skeletons formed by vortex lines where the field vanishes are tangles, i.e., N_{c} knotted or unknotted, linked or unlinked closed lines and M unclosed lines that thread all the closed lines and end at the infinitely far soliton periphery. They are generated by embedding two-dimensional laser solitons or their complexes in 3D space after their rotation around an unclosed, infinite vortex line with topological charge M_{0} (N_{c}, M, and M_{0} are integers). With such structure propagation, the "hula-hoop" solitons form; their stability is confirmed numerically. For the solitons found, all vortex lines have unit topological charge: the number of closed lines N_{c}=1 and 2 (unknots, trefoils, and Solomon knots links); unclosed vortex lines are unknotted and unlinked, their number M=1, 2, and 3.

The dynamics of aloof baby Skyrmions

DOE PAGES

Salmi, Petja; Sutcliffe, Paul

2016-01-25

The aloof baby Skyrme model is a (2+1)-dimensional theory with solitons that are lightly bound. It is a low-dimensional analogue of a similar Skyrme model in (3+1)- dimensions, where the lightly bound solitons have binding energies comparable to nuclei. A previous study of static solitons in the aloof baby Skyrme model revealed that multi-soliton bound states have a cluster structure, with constituents that preserve their individual identities due to the short-range repulsion and long-range attraction between solitons. Furthermore, there are many different local energy minima that are all well-described by a simple binary species particle model. In this paper wemore » present the first results on soliton dynamics in the aloof baby Skyrme model. Numerical field theory simulations reveal that the lightly bound cluster structure results in a variety of exotic soliton scattering events that are novel in comparison to standard Skyrmion scattering. A dynamical version of the binary species point particle model is shown to provide a good qualitative description of the dynamics.« less

The dynamics of aloof baby Skyrmions

NASA Astrophysics Data System (ADS)

Salmi, Petja; Sutcliffe, Paul

2016-01-01

The aloof baby Skyrme model is a (2+1)-dimensional theory with solitons that are lightly bound. It is a low-dimensional analogue of a similar Skyrme model in (3+1)-dimensions, where the lightly bound solitons have binding energies comparable to nuclei. A previous study of static solitons in the aloof baby Skyrme model revealed that multi-soliton bound states have a cluster structure, with constituents that preserve their individual identities due to the short-range repulsion and long-range attraction between solitons. Furthermore, there are many different local energy minima that are all well-described by a simple binary species particle model. In this paper we present the first results on soliton dynamics in the aloof baby Skyrme model. Numerical field theory simulations reveal that the lightly bound cluster structure results in a variety of exotic soliton scattering events that are novel in comparison to standard Skyrmion scattering. A dynamical version of the binary species point particle model is shown to provide a good qualitative description of the dynamics.

Gap solitons in a nonlinear quadratic negative-index cavity.

PubMed

Scalora, Michael; de Ceglia, Domenico; D'Aguanno, Giuseppe; Mattiucci, Nadia; Akozbek, Neset; Centini, Marco; Bloemer, Mark J

2007-06-01

We predict the existence of gap solitons in a nonlinear, quadratic Fabry-Pérot negative index cavity. A peculiarity of a single negative index layer is that if magnetic and electric plasma frequencies are different it forms a photonic band structure similar to that of a multilayer stack composed of ordinary, positive index materials. This similarity also results in comparable field localization and enhancement properties that under appropriate conditions may be used to either dynamically shift the band edge, or for efficient energy conversion. We thus report that an intense, fundamental pump pulse is able to shift the band edge of a negative index cavity, and make it possible for a weak second harmonic pulse initially tuned inside the gap to be transmitted, giving rise to a gap soliton. The process is due to cascading, a well-known phenomenon that occurs far from phase matching conditions that limits energy conversion rates, it resembles a nonlinear third-order process, and causes pulse compression due to self-phase modulation. The symmetry of the equations of motion under the action of either an electric or a magnetic nonlinearity suggests that both nonlinear polarization and magnetization, or a combination of both, can lead to solitonlike pulses. More specifically, the antisymmetric localization properties of the electric and magnetic fields cause a nonlinear polarization to generate a dark soliton, while a nonlinear magnetization spawns a bright soliton.

Oblique Interaction of Dust-ion Acoustic Solitons with Superthermal Electrons in a Magnetized Plasma

NASA Astrophysics Data System (ADS)

Parveen, Shahida; Mahmood, Shahzad; Adnan, Muhammad; Qamar, Anisa

2018-01-01

The oblique interaction between two dust-ion acoustic (DIA) solitons travelling in the opposite direction, in a collisionless magnetized plasma composed of dynamic ions, static dust (positive/negative) charged particles and interialess kappa distributed electrons is investigated. By employing extended Poincaré-Lighthill-Kuo (PLK) method, Korteweg-de Vries (KdV) equations are derived for the right and left moving low amplitude DIA solitons. Their trajectories and corresponding phase shifts before and after their interaction are also obtained. It is found that in negatively charged dusty plasma above the critical dust charged to ion density ratio the positive polarity pulse is formed, while below the critical dust charged density ratio the negative polarity pulse of DIA soliton exist. However it is found that only positive polarity pulse of DIA solitons exist for the positively charged dust particles case in a magnetized nonthermal plasma. The nonlinearity coefficient in the KdV equation vanishes for the negatively charged dusty plasma case for a particular set of parameters. Therefore, at critical plasma density composition for negatively charged dust particles case, the modified Korteweg-de Vries (mKdV) equations having cubic nonlinearity coefficient of the DIA solitons, and their corresponding phase shifts are derived for the left and right moving solitons. The effects of the system parameters including the obliqueness of solitons propagation with respect to magnetic field direction, superthermality of electrons and concentration of positively/negatively static dust charged particles on the phase shifts of the colliding solitons are also discussed and presented numerically. The results are applicable to space magnetized dusty plasma regimes.

Propagation of electromagnetic soliton in a spin polarized current driven weak ferromagnetic nanowire

NASA Astrophysics Data System (ADS)

Senthil Kumar, V.; Kavitha, L.; Gopi, D.

2017-11-01

We investigate the nonlinear spin dynamics of a spin polarized current driven anisotropic ferromagnetic nanowire with Dzyaloshinskii-Moriya interaction (DMI) under the influence of electromagnetic wave (EMW) propagating along the axis of the nanowire. The magnetization dynamics and electromagnetic wave propagation in the ferromagnetic nanowire with weak anti-symmetric interaction is governed by a coupled vector Landau-Lifshitz-Gilbert and Maxwell's equations. These coupled nonlinear vector equations are recasted into the extended derivative nonlinear Schrödinger (EDNLS) equation in the framework of reductive perturbation method. As it is well known, the modulational instability is a precursor for the emergence of localized envelope structures of various kinds, we compute the instability criteria for the weak ferromagnetic nanowire through linear stability analysis. Further, we invoke the homogeneous balance method to construct kink and anti-solitonic like electromagnetic (EM) soliton profiles for the EDNLS equation. We also explore the appreciable effect of the anti-symmetric weak interaction on the magnetization components of the propagating EM soliton. We find that the combination of spin-polarized current and the anti-symmetric DMI have a profound effect on the propagating EMW in a weak ferromagnetic nanowire. Thus, the anti-symmetric DMI in a spin polarized current driven ferromagnetic nanowire supports the lossless propagation of EM solitons, which may have potential applications in magnetic data storage devices.

Versatile rogue waves in scalar, vector, and multidimensional nonlinear systems

NASA Astrophysics Data System (ADS)

Chen, Shihua; Baronio, Fabio; Soto-Crespo, Jose M.; Grelu, Philippe; Mihalache, Dumitru

2017-11-01

This review is dedicated to recent progress in the active field of rogue waves, with an emphasis on the analytical prediction of versatile rogue wave structures in scalar, vector, and multidimensional integrable nonlinear systems. We first give a brief outline of the historical background of the rogue wave research, including referring to relevant up-to-date experimental results. Then we present an in-depth discussion of the scalar rogue waves within two different integrable frameworks—the infinite nonlinear Schrödinger (NLS) hierarchy and the general cubic-quintic NLS equation, considering both the self-focusing and self-defocusing Kerr nonlinearities. We highlight the concept of chirped Peregrine solitons, the baseband modulation instability as an origin of rogue waves, and the relation between integrable turbulence and rogue waves, each with illuminating examples confirmed by numerical simulations. Later, we recur to the vector rogue waves in diverse coupled multicomponent systems such as the long-wave short-wave equations, the three-wave resonant interaction equations, and the vector NLS equations (alias Manakov system). In addition to their intriguing bright-dark dynamics, a series of other peculiar structures, such as coexisting rogue waves, watch-hand-like rogue waves, complementary rogue waves, and vector dark three sisters, are reviewed. Finally, for practical considerations, we also remark on higher-dimensional rogue waves occurring in three closely-related (2  +  1)D nonlinear systems, namely, the Davey-Stewartson equation, the composite (2  +  1)D NLS equation, and the Kadomtsev-Petviashvili I equation. As an interesting contrast to the peculiar X-shaped light bullets, a concept of rogue wave bullets intended for high-dimensional systems is particularly put forward by combining contexts in nonlinear optics.

Switching of bound vector solitons for the coupled nonlinear Schrödinger equations with nonhomogenously stochastic perturbations

NASA Astrophysics Data System (ADS)

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

2012-12-01

We investigate the dynamics of the bound vector solitons (BVSs) for the coupled nonlinear Schrödinger equations with the nonhomogenously stochastic perturbations added on their dispersion terms. Soliton switching (besides soliton breakup) can be observed between the two components of the BVSs. Rate of the maximum switched energy (absolute values) within the fixed propagation distance (about 10 periods of the BVSs) enhances in the sense of statistics when the amplitudes of stochastic perturbations increase. Additionally, it is revealed that the BVSs with enhanced coherence are more robust against the perturbations with nonhomogenous stochasticity. Diagram describing the approximate borders of the splitting and non-splitting areas is also given. Our results might be helpful in dynamics of the BVSs with stochastic noises in nonlinear optical fibers or with stochastic quantum fluctuations in Bose-Einstein condensates.

Switching of bound vector solitons for the coupled nonlinear Schrödinger equations with nonhomogenously stochastic perturbations.

PubMed

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

2012-12-01

We investigate the dynamics of the bound vector solitons (BVSs) for the coupled nonlinear Schrödinger equations with the nonhomogenously stochastic perturbations added on their dispersion terms. Soliton switching (besides soliton breakup) can be observed between the two components of the BVSs. Rate of the maximum switched energy (absolute values) within the fixed propagation distance (about 10 periods of the BVSs) enhances in the sense of statistics when the amplitudes of stochastic perturbations increase. Additionally, it is revealed that the BVSs with enhanced coherence are more robust against the perturbations with nonhomogenous stochasticity. Diagram describing the approximate borders of the splitting and non-splitting areas is also given. Our results might be helpful in dynamics of the BVSs with stochastic noises in nonlinear optical fibers or with stochastic quantum fluctuations in Bose-Einstein condensates.

Stable scalable control of soliton propagation in broadband nonlinear optical waveguides

NASA Astrophysics Data System (ADS)

Peleg, Avner; Nguyen, Quan M.; Huynh, Toan T.

2017-02-01

We develop a method for achieving scalable transmission stabilization and switching of N colliding soliton sequences in optical waveguides with broadband delayed Raman response and narrowband nonlinear gain-loss. We show that dynamics of soliton amplitudes in N-sequence transmission is described by a generalized N-dimensional predator-prey model. Stability and bifurcation analysis for the predator-prey model are used to obtain simple conditions on the physical parameters for robust transmission stabilization as well as on-off and off-on switching of M out of N soliton sequences. Numerical simulations for single-waveguide transmission with a system of N coupled nonlinear Schrödinger equations with 2 ≤ N ≤ 4 show excellent agreement with the predator-prey model's predictions and stable propagation over significantly larger distances compared with other broadband nonlinear single-waveguide systems. Moreover, stable on-off and off-on switching of multiple soliton sequences and stable multiple transmission switching events are demonstrated by the simulations. We discuss the reasons for the robustness and scalability of transmission stabilization and switching in waveguides with broadband delayed Raman response and narrowband nonlinear gain-loss, and explain their advantages compared with other broadband nonlinear waveguides.

Solitons in Bose-Einstein Condensates

NASA Astrophysics Data System (ADS)

Carr, Lincoln D.

2003-05-01

The stationary form, dynamical properties, and experimental criteria for creation of matter-wave bright and dark solitons, both singly and in trains, are studied numerically and analytically in the context of Bose-Einstein condensates [1]. The full set of stationary solutions in closed analytic form to the mean field model in the quasi-one-dimensional regime, which is a nonlinear Schrodinger equation equally relevant in nonlinear optics, is developed under periodic and box boundary conditions [2]. These solutions are extended numerically into the two and three dimensional regimes, where it is shown that dark solitons can be used to create vortex-anti-vortex pairs under realistic conditions. Specific experimental prescriptions for creating viable dark and bright solitons in the quasi-one-dimensional regime are provided. These analytic methods are then extended to treat the nonlinear Schrodinger equation with a generalized lattice potential, which models a Bose-Einstein condensate trapped in the potential generated by a standing light wave. A novel solution family is developed and stability criterion are presented. Experiments which successfully carried out these ideas are briefly discussed [3]. [1] Dissertation research completed at the University of Washington Physics Department under the advisorship of Prof. William P. Reinhardt. [2] L. D. Carr, C. W. Clark, and W. P. Reinhardt, Phys. Rev. A v. 62 p. 063610-1--10 and Phys. Rev. A v.62, p.063611-1--10 (2000). [3] L. Khaykovich, F. Schreck, T. Bourdel, J. Cubizolles, G. Ferrari, L. D. Carr, Y. Castin, and C. Salomon, Science v. 296, p.1290--1293 (2002).

Double-Wall Carbon Nanotube Hybrid Mode-Locker in Tm-doped Fibre Laser: A Novel Mechanism for Robust Bound-State Solitons Generation

NASA Astrophysics Data System (ADS)

Chernysheva, Maria; Bednyakova, Anastasia; Al Araimi, Mohammed; Howe, Richard C. T.; Hu, Guohua; Hasan, Tawfique; Gambetta, Alessio; Galzerano, Gianluca; Rümmeli, Mark; Rozhin, Aleksey

2017-03-01

The complex nonlinear dynamics of mode-locked fibre lasers, including a broad variety of dissipative structures and self-organization effects, have drawn significant research interest. Around the 2 μm band, conventional saturable absorbers (SAs) possess small modulation depth and slow relaxation time and, therefore, are incapable of ensuring complex inter-pulse dynamics and bound-state soliton generation. We present observation of multi-soliton complex generation in mode-locked thulium (Tm)-doped fibre laser, using double-wall carbon nanotubes (DWNT-SA) and nonlinear polarisation evolution (NPE). The rigid structure of DWNTs ensures high modulation depth (64%), fast relaxation (1.25 ps) and high thermal damage threshold. This enables formation of 560-fs soliton pulses; two-soliton bound-state with 560 fs pulse duration and 1.37 ps separation; and singlet+doublet soliton structures with 1.8 ps duration and 6 ps separation. Numerical simulations based on the vectorial nonlinear Schr¨odinger equation demonstrate a transition from single-pulse to two-soliton bound-states generation. The results imply that DWNTs are an excellent SA for the formation of steady single- and multi-soliton structures around 2 μm region, which could not be supported by single-wall carbon nanotubes (SWNTs). The combination of the potential bandwidth resource around 2 μm with the soliton molecule concept for encoding two bits of data per clock period opens exciting opportunities for data-carrying capacity enhancement.

Double-Wall Carbon Nanotube Hybrid Mode-Locker in Tm-doped Fibre Laser: A Novel Mechanism for Robust Bound-State Solitons Generation

PubMed Central

Chernysheva, Maria; Bednyakova, Anastasia; Al Araimi, Mohammed; Howe, Richard C. T.; Hu, Guohua; Hasan, Tawfique; Gambetta, Alessio; Galzerano, Gianluca; Rümmeli, Mark; Rozhin, Aleksey

2017-01-01

The complex nonlinear dynamics of mode-locked fibre lasers, including a broad variety of dissipative structures and self-organization effects, have drawn significant research interest. Around the 2 μm band, conventional saturable absorbers (SAs) possess small modulation depth and slow relaxation time and, therefore, are incapable of ensuring complex inter-pulse dynamics and bound-state soliton generation. We present observation of multi-soliton complex generation in mode-locked thulium (Tm)-doped fibre laser, using double-wall carbon nanotubes (DWNT-SA) and nonlinear polarisation evolution (NPE). The rigid structure of DWNTs ensures high modulation depth (64%), fast relaxation (1.25 ps) and high thermal damage threshold. This enables formation of 560-fs soliton pulses; two-soliton bound-state with 560 fs pulse duration and 1.37 ps separation; and singlet+doublet soliton structures with 1.8 ps duration and 6 ps separation. Numerical simulations based on the vectorial nonlinear Schr¨odinger equation demonstrate a transition from single-pulse to two-soliton bound-states generation. The results imply that DWNTs are an excellent SA for the formation of steady single- and multi-soliton structures around 2 μm region, which could not be supported by single-wall carbon nanotubes (SWNTs). The combination of the potential bandwidth resource around 2 μm with the soliton molecule concept for encoding two bits of data per clock period opens exciting opportunities for data-carrying capacity enhancement. PMID:28287159

Rational solitons in deep nonlinear optical Bragg grating.

PubMed

Alatas, H; Iskandar, A A; Tjia, M O; Valkering, T P

2006-06-01

We have examined the rational solitons in the Generalized Coupled Mode model for a deep nonlinear Bragg grating. These solitons are the degenerate forms of the ordinary solitons and appear at the transition lines in the parameter plane. A simple formulation is presented for the investigation of the bifurcations induced by detuning the carrier wave frequency. The analysis yields among others the appearance of in-gap dark and antidark rational solitons unknown in the nonlinear shallow grating. The exact expressions for the corresponding rational solitons are also derived in the process, which are characterized by rational algebraic functions. It is further demonstrated that certain effects in the soliton energy variations are to be expected when the frequency is varied across the values where the rational solitons appear.

Rational Ruijsenaars Schneider hierarchy and bispectral difference operators

NASA Astrophysics Data System (ADS)

Iliev, Plamen

2007-05-01

We show that a monic polynomial in a discrete variable n, with coefficients depending on time variables t1,t2,…, is a τ-function for the discrete Kadomtsev-Petviashvili hierarchy if and only if the motion of its zeros is governed by a hierarchy of Ruijsenaars-Schneider systems. These τ-functions were considered in [L. Haine, P. Iliev, Commutative rings of difference operators and an adelic flag manifold, Int. Math. Res. Not. 2000 (6) (2000) 281-323], where it was proved that they parametrize rank one solutions to a difference-differential version of the bispectral problem.

Rational solutions to the KPI equation and multi rogue waves

NASA Astrophysics Data System (ADS)

Gaillard, Pierre

2016-04-01

We construct here rational solutions to the Kadomtsev-Petviashvili equation (KPI) as a quotient of two polynomials in x, y and t depending on several real parameters. This method provides an infinite hierarchy of rational solutions written in terms of polynomials of degrees 2 N(N + 1) in x, y and t depending on 2 N - 2 real parameters for each positive integer N. We give explicit expressions of the solutions in the simplest cases N = 1 and N = 2 and we study the patterns of their modulus in the (x , y) plane for different values of time t and parameters.

Exact traveling wave solutions of the KP-BBM equation by using the new approach of generalized (G'/G)-expansion method.

PubMed

Alam, Md Nur; Akbar, M Ali

2013-01-01

The new approach of the generalized (G'/G)-expansion method is an effective and powerful mathematical tool in finding exact traveling wave solutions of nonlinear evolution equations (NLEEs) in science, engineering and mathematical physics. In this article, the new approach of the generalized (G'/G)-expansion method is applied to construct traveling wave solutions of the Kadomtsev-Petviashvili-Benjamin-Bona-Mahony (KP-BBM) equation. The solutions are expressed in terms of the hyperbolic functions, the trigonometric functions and the rational functions. By means of this scheme, we found some new traveling wave solutions of the above mentioned equation.

Soliton resonance in bose-einstein condensate

NASA Technical Reports Server (NTRS)

Zak, Michail; Kulikov, I.

2002-01-01

A new phenomenon in nonlinear dispersive systems, including a Bose-Einstein Condensate (BEC), has been described. It is based upon a resonance between an externally induced soliton and 'eigen-solitons' of the homogeneous cubic Schrodinger equation. There have been shown that a moving source of positive /negative potential induces bright /dark solitons in an attractive / repulsive Bose condensate.

Reconfigurable Network Routing with Spatial Soliton Crossbar Switches

DTIC Science & Technology

1999-01-31

Properties of Quadratic Solitons", Acta Physica Polonica , in press 32. G.I. Stegeman and M. Segev, "Bright Spatial Soliton Interactions", book chapter for...put and output poVts. the central idea is to use the solitons as a waveguide for guiding signals. Deflecting the soliton electro-optically...as reconfigurable interconnects for guiding signals between multiple input and output ports. The central idea is to use the solitons as a waveguide

Making beam splitters with dark soliton collisions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Steiglitz, Ken

2010-10-15

We show with numerical simulations that for certain simple choices of parameters, the waveguides induced by colliding dark solitons in a Kerr medium yield a complete family of beam splitters for trapped linear waves, ranging from total transmission to total deflection. The way energy is transferred from one waveguide to another is similar to that of a directional coupler, but no special fabrication is required. Dark soliton beam splitters offer potential advantages over their bright soliton counterparts: Their transfer characteristics do not depend on the relative phase or speed of the colliding solitons; dark solitons are generally more robust thanmore » bright solitons; and the probe peaks at nulls of the pump, enhancing the signal-to-noise ratio for probe detection. The last factor is especially important for possible application to quantum information processing.« less

Multifrequency Gap Solitons in Nonlinear Photonic Crystals

NASA Astrophysics Data System (ADS)

Xie, Ping; Zhang, Zhao-Qing

2003-11-01

We predict the existence of multifrequency gap solitons (MFGSs) in both one- and two-dimensional nonlinear photonic crystals. A MFGS is a single intrinsic mode possessing multiple frequencies inside the gap. Its existence is a result of synergic nonlinear coupling among solitons or soliton trains at different frequencies. Its formation can either lower the threshold fields of the respective frequency components or stabilize their excitations. These MFGSs form a new class of stable gap solitons.

Bilinearization of the generalized coupled nonlinear Schrödinger equation with variable coefficients and gain and dark-bright pair soliton solutions.

PubMed

Chakraborty, Sushmita; Nandy, Sudipta; Barthakur, Abhijit

2015-02-01

We investigate coupled nonlinear Schrödinger equations (NLSEs) with variable coefficients and gain. The coupled NLSE is a model equation for optical soliton propagation and their interaction in a multimode fiber medium or in a fiber array. By using Hirota's bilinear method, we obtain the bright-bright, dark-bright combinations of a one-soliton solution (1SS) and two-soliton solutions (2SS) for an n-coupled NLSE with variable coefficients and gain. Crucial properties of two-soliton (dark-bright pair) interactions, such as elastic and inelastic interactions and the dynamics of soliton bound states, are studied using asymptotic analysis and graphical analysis. We show that a bright 2-soliton, in addition to elastic interactions, also exhibits multiple inelastic interactions. A dark 2-soliton, on the other hand, exhibits only elastic interactions. We also observe a breatherlike structure of a bright 2-soliton, a feature that become prominent with gain and disappears as the amplitude acquires a minimum value, and after that the solitons remain parallel. The dark 2-soliton, however, remains parallel irrespective of the gain. The results found by us might be useful for applications in soliton control, a fiber amplifier, all optical switching, and optical computing.

Bound states and interactions of vortex solitons in the discrete Ginzburg-Landau equation

NASA Astrophysics Data System (ADS)

Mejía-Cortés, C.; Soto-Crespo, J. M.; Vicencio, Rodrigo A.; Molina, Mario I.

2012-08-01

By using different continuation methods, we unveil a wide region in the parameter space of the discrete cubic-quintic complex Ginzburg-Landau equation, where several families of stable vortex solitons coexist. All these stationary solutions have a symmetric amplitude profile and two different topological charges. We also observe the dynamical formation of a variety of “bound-state” solutions composed of two or more of these vortex solitons. All of these stable composite structures persist in the conservative cubic limit for high values of their power content.

Modulational instability, beak-shaped rogue waves, multi-dark-dark solitons and dynamics in pair-transition-coupled nonlinear Schrödinger equations.

PubMed

Zhang, Guoqiang; Yan, Zhenya; Wen, Xiao-Yong

2017-07-01

The integrable coupled nonlinear Schrödinger equations with four-wave mixing are investigated. We first explore the conditions for modulational instability of continuous waves of this system. Secondly, based on the generalized N -fold Darboux transformation (DT), beak-shaped higher-order rogue waves (RWs) and beak-shaped higher-order rogue wave pairs are derived for the coupled model with attractive interaction in terms of simple determinants. Moreover, we derive the simple multi-dark-dark and kink-shaped multi-dark-dark solitons for the coupled model with repulsive interaction through the generalizing DT. We explore their dynamics and classifications by different kinds of spatial-temporal distribution structures including triangular, pentagonal, 'claw-like' and heptagonal patterns. Finally, we perform the numerical simulations to predict that some dark solitons and RWs are stable enough to develop within a short time. The results would enrich our understanding on nonlinear excitations in many coupled nonlinear wave systems with transition coupling effects.

Dark Solitons for the Defocusing Cubic Nonlinear Schrödinger Equation with the Spatially Periodic Potential and Nonlinearity

NASA Astrophysics Data System (ADS)

Yan, Zhen-Ya; Yan, Fang-Chi

2015-09-01

We study the existence of dark solitons of the defocusing cubic nonlinear Schrödinger (NLS) eqaution with the spatially-periodic potential and nonlinearity. Firstly, we propose six families of upper and lower solutions of the dynamical systems arising from the stationary defocusing NLS equation. Secondly, by regarding a dark soliton as a heteroclinic orbit of the Poincaré map, we present some constraint conditions for the periodic potential and nonlinearity to show the existence of stationary dark solitons of the defocusing NLS equation for six different cases in terms of the theory of strict lower and upper solutions and the dynamics of planar homeomorphisms. Finally, we give the explicit dark solitons of the defocusing NLS equation with the chosen periodic potential and nonlinearity. Supported by the National Natural Science Foundation of China under Grant No. 61178091, the National Key Basic Research Program of China under Grant No. 2011CB302400, and the Open Project Program of State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, China under Grant No. Y4KF211CJ1

Attraction, merger, reflection, and annihilation in magnetic droplet soliton scattering

NASA Astrophysics Data System (ADS)

Maiden, M. D.; Bookman, L. D.; Hoefer, M. A.

2014-05-01

The interaction behaviors of solitons are defining characteristics of these nonlinear, coherent structures. Due to recent experimental observations, thin ferromagnetic films offer a promising medium in which to study the scattering properties of two-dimensional magnetic droplet solitons, particle-like, precessing dipoles. Here, a rich set of two-droplet interaction behaviors are classified through micromagnetic simulations. Repulsive and attractive interaction dynamics are generically determined by the relative phase and speeds of the two droplets and can be classified into four types: (1) merger into a breather bound state, (2) counterpropagation trapped along the axis of symmetry, (3) reflection, and (4) violent droplet annihilation into spin wave radiation and a breather. Utilizing a nonlinear method of images, it is demonstrated that these dynamics describe repulsive/attractive scattering of a single droplet off of a magnetic boundary with pinned/free spin boundary conditions, respectively. These results explain the mechanism by which propagating and stationary droplets can be stabilized in a confined ferromagnet.

Cylindrical ion-acoustic solitary waves in electronegative plasmas with superthermal electrons

DOE Office of Scientific and Technical Information (OSTI.GOV)

Eslami, Parvin; Mottaghizadeh, Marzieh

2012-06-15

By using the standard reductive perturbation technique, a three-dimensional cylindrical Kadomtsev-Petviashvili equation (CKPE), which governs the dynamics of ion acoustic solitary waves (IASWs), is derived for small but finite amplitude ion-acoustic waves in cylindrical geometry in a collisionless unmagnetized plasma with kappa distributed electrons, thermal positrons, and cold ions. The generalized expansion method is used to solve analytically the CKPE. The existence regions of localized pulses are investigated. It is found that the solution of the CKPE supports only compressive solitary waves. Furthermore, the effects of superthermal electrons, the ratio of the electron temperature to positron temperature, the ratio ofmore » the positron density to electron density and direction cosine of the wave propagation on the profiles of the amplitudes, and widths of the solitary structures are examined numerically. It is shown these parameters play a vital role in the formation of ion acoustic solitary waves.« less

Super-soliton dust-acoustic waves in four-component dusty plasma using non-extensive electrons and ions distributions

NASA Astrophysics Data System (ADS)

El-Wakil, S. A.; Abulwafa, Essam M.; Elhanbaly, Atalla A.

2017-07-01

Based on Sagdeev pseudo-potential and phase-portrait, the dynamics of four-component dust plasma with non-extensively distributed electrons and ions are investigated. Three distinct types of nonlinear waves, namely, soliton, double layer, and super-soliton, have been found. The basic features of such waves are high sensitivity to Mach number, non-extensive parameter, and dust temperature ratio. It is found that the multi-component plasma is a necessary condition for super-soliton's existence, having a wider amplitude and a larger width than the regular soliton. Super-solitons may also exist when the Sagdeev pseudo-potential curves admit at least four extrema and two roots. In our multi-component plasma system, the super-solitons can be found by increasing the Mach number and the non-extensive parameter beyond those of double-layers. On the contrary, the super-soliton can be produced by decreasing the dust temperature ratio. The conditions of the onset of such nonlinear waves and its merging to regular solitons have been studied. This work shows that the obtained nonlinear waves are found to exist only in the super-sonic Mach number regime. The obtained results may be of wide relevance in the field of space plasma and may also be helpful to better understand the nonlinear fluctuations in the Auroral-zone of the Earth's magnetosphere.

Soliton-induced relativistic-scattering and amplification.

PubMed

Rubino, E; Lotti, A; Belgiorno, F; Cacciatori, S L; Couairon, A; Leonhardt, U; Faccio, D

2012-01-01

Solitons are of fundamental importance in photonics due to applications in optical data transmission and also as a tool for investigating novel phenomena ranging from light generation at new frequencies and wave-trapping to rogue waves. Solitons are also moving scatterers: they generate refractive index perturbations moving at the speed of light. Here we found that such perturbations scatter light in an unusual way: they amplify light by the mixing of positive and negative frequencies, as we describe using a first Born approximation and numerical simulations. The simplest scenario in which these effects may be observed is within the initial stages of optical soliton propagation: a steep shock front develops that may efficiently scatter a second, weaker probe pulse into relatively intense positive and negative frequency modes with amplification at the expense of the soliton. Our results show a novel all-optical amplification scheme that relies on soliton induced scattering.

Vector solitons in femtosecond fibre lasers

NASA Astrophysics Data System (ADS)

Chen, W. C.; Xu, W. C.; Song, F.; Shen, M. C.; Han, D. A.; Chen, L. B.

2008-07-01

Experimental observation of spectral sideband suppression of mode-locked pulses is obtained in an erbium-doped fibre ring laser with nonlinear polarization rotation techniques. This effect may indicate the formation of a vector soliton in accordance with the theoretical work of reference [Phys. Rev. E 74, 046605 (2006)]. The 3 dB spectral bandwidth, the central wavelength and the repetition rate of the vector solitons are 24.41 nm, 1565.14 nm and 12.15 MHz, respectively. Based on the experimental observations, we propose an experimental criterion for the production of vector solitons, with spectral sideband suppression as a sign of the generation of vector solitons.

Families of stable solitons and excitations in the PT-symmetric nonlinear Schrödinger equations with position-dependent effective masses.

PubMed

Chen, Yong; Yan, Zhenya; Mihalache, Dumitru; Malomed, Boris A

2017-04-28

Since the parity-time-([Formula: see text]-) symmetric quantum mechanics was put forward, fundamental properties of some linear and nonlinear models with [Formula: see text]-symmetric potentials have been investigated. However, previous studies of [Formula: see text]-symmetric waves were limited to constant diffraction coefficients in the ambient medium. Here we address effects of variable diffraction coefficient on the beam dynamics in nonlinear media with generalized [Formula: see text]-symmetric Scarf-II potentials. The broken linear [Formula: see text] symmetry phase may enjoy a restoration with the growing diffraction parameter. Continuous families of one- and two-dimensional solitons are found to be stable. Particularly, some stable solitons are analytically found. The existence range and propagation dynamics of the solitons are identified. Transformation of the solitons by means of adiabatically varying parameters, and collisions between solitons are studied too. We also explore the evolution of constant-intensity waves in a model combining the variable diffraction coefficient and complex potentials with globally balanced gain and loss, which are more general than [Formula: see text]-symmetric ones, but feature similar properties. Our results may suggest new experiments for [Formula: see text]-symmetric nonlinear waves in nonlinear nonuniform optical media.

Black and gray Helmholtz-Kerr soliton refraction

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sanchez-Curto, Julio; Chamorro-Posada, Pedro; McDonald, Graham S.

Refraction of black and gray solitons at boundaries separating different defocusing Kerr media is analyzed within a Helmholtz framework. A universal nonlinear Snell's law is derived that describes gray soliton refraction, in addition to capturing the behavior of bright and black Kerr solitons at interfaces. Key regimes, defined by beam and interface characteristics, are identified, and predictions are verified by full numerical simulations. The existence of a unique total nonrefraction angle for gray solitons is reported; both internal and external refraction at a single interface is shown possible (dependent only on incidence angle). This, in turn, leads to the proposalmore » of positive or negative lensing operations on soliton arrays at planar boundaries.« less

Brownian motion of solitons in a Bose-Einstein condensate.

PubMed

Aycock, Lauren M; Hurst, Hilary M; Efimkin, Dmitry K; Genkina, Dina; Lu, Hsin-I; Galitski, Victor M; Spielman, I B

2017-03-07

We observed and controlled the Brownian motion of solitons. We launched solitonic excitations in highly elongated [Formula: see text] Bose-Einstein condensates (BECs) and showed that a dilute background of impurity atoms in a different internal state dramatically affects the soliton. With no impurities and in one dimension (1D), these solitons would have an infinite lifetime, a consequence of integrability. In our experiment, the added impurities scatter off the much larger soliton, contributing to its Brownian motion and decreasing its lifetime. We describe the soliton's diffusive behavior using a quasi-1D scattering theory of impurity atoms interacting with a soliton, giving diffusion coefficients consistent with experiment.

Spectral transform and orthogonality relations for the Kadomtsev-Petviashvili I equation

NASA Astrophysics Data System (ADS)

Boiti, M.; Leon, J. J.-P.; Pempinelli, F.

1989-10-01

We define a new spectral transform r(k, l) of the potential u in the time dependent Schrödinger equation (associated to the KPI equation). Orthogonality relations for the sectionally holomorphic eigenfunctions of the Schrödinger equation are used to express the spectral transform f( k, l) previously introduced by Manakov and Fokas and Ablowitz in terms of r( k, l). The main advantage of the new spectral transform r( k, l) is that its definition does not require to introduce an additional nonanalytic eigenfunction N. Characterization equations for r( k, l) are also obtained.

Soliton concepts and protein structure

NASA Astrophysics Data System (ADS)

Krokhotin, Andrei; Niemi, Antti J.; Peng, Xubiao

2012-03-01

Structural classification shows that the number of different protein folds is surprisingly small. It also appears that proteins are built in a modular fashion from a relatively small number of components. Here we propose that the modular building blocks are made of the dark soliton solution of a generalized discrete nonlinear Schrödinger equation. We find that practically all protein loops can be obtained simply by scaling the size and by joining together a number of copies of the soliton, one after another. The soliton has only two loop-specific parameters, and we compute their statistical distribution in the Protein Data Bank (PDB). We explicitly construct a collection of 200 sets of parameters, each determining a soliton profile that describes a different short loop. The ensuing profiles cover practically all those proteins in PDB that have a resolution which is better than 2.0 Å, with a precision such that the average root-mean-square distance between the loop and its soliton is less than the experimental B-factor fluctuation distance. We also present two examples that describe how the loop library can be employed both to model and to analyze folded proteins.

Soliton concepts and protein structure.

PubMed

Krokhotin, Andrei; Niemi, Antti J; Peng, Xubiao

2012-03-01

Structural classification shows that the number of different protein folds is surprisingly small. It also appears that proteins are built in a modular fashion from a relatively small number of components. Here we propose that the modular building blocks are made of the dark soliton solution of a generalized discrete nonlinear Schrödinger equation. We find that practically all protein loops can be obtained simply by scaling the size and by joining together a number of copies of the soliton, one after another. The soliton has only two loop-specific parameters, and we compute their statistical distribution in the Protein Data Bank (PDB). We explicitly construct a collection of 200 sets of parameters, each determining a soliton profile that describes a different short loop. The ensuing profiles cover practically all those proteins in PDB that have a resolution which is better than 2.0 Å, with a precision such that the average root-mean-square distance between the loop and its soliton is less than the experimental B-factor fluctuation distance. We also present two examples that describe how the loop library can be employed both to model and to analyze folded proteins.

From solitons to rogue waves in nonlinear left-handed metamaterials.

PubMed

Shen, Yannan; Kevrekidis, P G; Veldes, G P; Frantzeskakis, D J; DiMarzio, D; Lan, X; Radisic, V

2017-03-01

In the present work, we explore soliton and roguelike wave solutions in the transmission line analog of a nonlinear left-handed metamaterial. The nonlinearity is expressed through a voltage-dependent, symmetric capacitance motivated by recently developed ferroelectric barium strontium titanate thin-film capacitor designs. We develop both the corresponding nonlinear dynamical lattice and its reduction via a multiple scales expansion to a nonlinear Schrödinger (NLS) model for the envelope of a given carrier wave. The reduced model can feature either a focusing or a defocusing nonlinearity depending on the frequency (wave number) of the carrier. We then consider the robustness of different types of solitary waves of the reduced model within the original nonlinear left-handed medium. We find that both bright and dark solitons persist in a suitable parametric regime, where the reduction to the NLS model is valid. Additionally, for suitable initial conditions, we observe a rogue wave type of behavior that differs significantly from the classic Peregrine rogue wave evolution, including most notably the breakup of a single Peregrine-like pattern into solutions with multiple wave peaks. Finally, we touch upon the behavior of generalized members of the family of the Peregrine solitons, namely, Akhmediev breathers and Kuznetsov-Ma solitons, and explore how these evolve in the left-handed transmission line.

Pulse dynamics of dual-wavelength dissipative soliton resonances and domain wall solitons in a Tm fiber laser with fiber-based Lyot filter.

PubMed

Wang, Pan; Zhao, Kangjun; Xiao, Xiaosheng; Yang, Changxi

2017-11-27

We report on the first demonstration of dual-wavelength square-wave pulses in a thulium-doped fiber laser. Under appropriate cavity parameters, dual-wavelength dissipative soliton resonances (DSRs) and domain wall solitons (DWSs) are successively obtained. Meanwhile, dark pulses generation is achieved at the dual-wavelength DWSs region due to the overlap of the two domain wall pulses. The fiber-based Lyot filter, conducted by inserting PMF between an in-line PBS and a PD-ISO, facilitates the generation of dual-wavelength operation. The polarization-resolved investigation suggests that the cross coupling between two orthogonal polarization components in the high nonlinear fiber plays an important role in the square-wave pulses formation. The investigation may be helpful for further understanding the square-wave pulse formation and has potential in application filed of multi-wavelength pulsed fiber lasers.

Properties of a vector soliton laser passively mode-locked by a fiber-based semiconductor saturable absorber operating in transmission

NASA Astrophysics Data System (ADS)