Excitation of high-amplitude localized nonlinear waves as a result of interaction of kink with attractive impurity in sine-Gordon equation (original) (raw)

Dynamics of sine-Gordon solitons

After reviewing a few physical examples in which the sine-Gordon equation arises as the governing dynamical equation, we discuss various solutions exhibiting multisoliton dynamics. Interaction of solitons and the corresponding velocitydependent interaction potentials are derived and discussed. Numerical experiments are carried out in order to study kink dynamics in an inhomogeneous medium. Finally, we introduce two kinds of generalized sine-Gordon equations and discuss their properties.

Radiative and inelastic effects in dynamics of double sine-gordon solitons

Physics Letters A, 1987

The dynamics ofthe so-called wobblers, i.e. 4it-kinks ofthe double sine-Gordon equation with excited internal oscillations, is studied. The rate of energy emission from a weakly excited wobbler is calculated. Then scattering of a wobbler by a localized inhomogeneity is considered and it is demonstrated that in the first approximation it results in the change ofthe wobbler's velocity only if the wobbler was excited prior to the collision. The corresponding changes of velocity and ofthe internal oscillation amplitude are calculated. Inelastic collision oftwo unexcited wobblers in the presence ofthe inhomogeneity is briefly considered too.

Self-excited soliton motion

Physical Review E, 1996

We present an extensive analytical and numerical study of the dynamics of kink solitons in Klein-Gordon systems with nonlinear damping. Particularly, the nonlinear damping could model the interaction of the solitons with an active medium. We analyze the existence and stability conditions of stationary states for the soliton. We present a different kind of bifurcation: a structure-breaking bifurcation. After this bifurcation the soliton enters a highly nonstationary state (solitonic explosion). We show the existence of self-sustained oscillations of solitons (solitonic limit cycles). Finally, we present chaotic motion of solitons similar to the Duffing–Van der Pol type.

Multisoliton Dynamics in the Sine-Gordon Model with Two Point Impurities

Brazilian Journal of Physics, 2018

Collective variables method is used to derive a set of differential equations to describe the dynamics of a kink in the sine-Gordon model with two identical point impurities taking damping into account. It is shown that the scenarios of kink interaction with the waves localized on the impurities, found from the reduced model, are similar to those obtained earlier by numerical integration of the continuous sine-Gordon equation. For the case of the kink passage through the region with the impurities, the structure and properties of the arising on impurities long-lived four-kink multisolitons are analyzed. For the approximate analytical description of the two bound impurity-localized nonlinear waves, the system of differential equations for harmonic oscillators with elastic link is obtained. The analytical model qualitatively reproduces the results of the sine-Gordon equation numerical simulation. The cases of large and small distances between impurities are analyzed. The results of our study uncover new features of the kinkimpurity interaction which is important for a number of applications where the sine-Gordon model is used.

Internal modes of sine-Gordon solitons in the presence of spatiotemporal perturbations

Physical Review E, 2002

We investigate the dynamics of the sine-Gordon solitons perturbed by spatiotemporal external forces. We prove the existence of internal ͑shape͒ modes of sine-Gordon solitons when they are in the presence of inhomogeneous space-dependent external forces, provided some conditions ͑for these forces͒ hold. Additional periodic time-dependent forces can sustain oscillations of the soliton width. We show that, in some cases, the internal mode even can become unstable, causing the soliton to decay into an antisoliton and two solitons. In general, in the presence of spatiotemporal forces the soliton behaves as a deformable ͑nonrigid͒ object. A soliton moving in an array of inhomogeneities can also present sustained oscillations of its width. There are very important phenomena ͑like the soliton-antisoliton collisions͒ where the existence of internal modes plays a crucial role.

How to excite the internal modes of sine-Gordon solitons

Chaos, Solitons and Fractals, 2003

We investigate the dynamics of the sine-Gordon solitons perturbed by spatiotemporal external forces. We prove the existence of internal (shape) modes of sine-Gordon solitons when they are in the presence of inhomogeneous space-dependent external forces, provided some conditions (for these forces) hold. Additional periodic time-dependent forces can sustain oscillations of the soliton width. We show that, in some cases, the internal mode even can become unstable, causing the soliton to decay in an antisoliton and two solitons. In general, in the presence of spatiotemporal forces the soliton behaves as a deformable (non-rigid) object. A soliton moving in an array of inhomogeneities can also present sustained oscillations of its width. There are very important phenomena (like the soliton-antisoliton collisions) where the existence of internal modes plays a crucial role. We show that, under some conditions, the dynamics of the soliton shape modes can be chaotic. A short report of some of our results has been published in [Phys. Rev. E 65 (2002) 065601(R)].

Nonlinear Waves: Classical and Quantum Aspects

NATO Science Series II: Mathematics, Physics and Chemistry, 2005

Towards algebro-geometric integration of the Gross-Pitaevskii equation V.Z. Enolskii 1 Introduction 2 Utilization of the Schrödinger equation 3 Solutions in terms of hyperelliptic functions 4 Two component Gross-Pitaevskii equation and the Manakov system 9 On modeling adiabatic N-soliton interactions V.S. Gerdjikov 1 Introduction 2 N-soliton trains of the NLS and HNLS equations 3 N-soliton trains of the MNLS equation 4 The importance of the CTC model 18 5 Dynamical regimes of the HNLS soliton trains 6 The perturbed NLS and perturbed CTC 6.1 Second order dispersion and nonlinear gain 6.2 Quadratic and periodic potentials 7 Analysis of the Perturbed CTC 8 Discussion Dynamical stabilization of nonlinear waves F. Abdullaev 1 Introduction 2 Dynamics of solitons in BEC with rapidly oscillating trap 3 Stable two dimensional bright soliton under Feschbach resonance management 4 Stable two dimensional dispersion-managed soliton 5 Conclusions v vi

Sine-Gordon solitons in the presence of a noisy potential

Physica D: Nonlinear Phenomena, 1985

We study the interaction of sine-Gordon solitons with two kinds of impurity potentials localized in space and varying randomly in time. The production of modified kink-a&kink pairs is observed with different features depending respectively on the additive or multiplicative nature of the noise

Dynamics and kinetics of solitons in the driven damped double Sine-Gordon equation

Physics Letters A, 1989

A damped double SG equation with a constant driving term describes a model of the Frenkel-Kontorova type in the case when the substrate potential contains a weak subharmonic component, and an external field is present. This equation generates three types of solitons: a 47t-kink and two sorts of 2a-kinks (with corresponding antikinks). It is demonstrated that collisions between kinks and/or antikinks give rise to various modes of annihilation and mutual conversion. Next, kinetics of a rarefied gas ofkinks are considered, and a stable equilibrium solution of the corresponding kinetic equations is found. Collision-induced radiative effects and their influence on the kinetics of the rarefied gas are analyzed too.

Interaction of Double Sine-Gordon Solitons with External Potentials: an Analytical Model

Chinese Physics Letters, 2016

Interaction of Double sine-Gordon solitons with a space dependent potential wall and also a potential well has been investigated by employing an analytical model based on the collective coordinate approach. The potential has been added to the model through a suitable nontrivial metric for the background space-time. The model is able to predict most of the features of the soliton-potential interaction. It is shown that a soliton can pass through a potential barrier if its velocity is greater than a critical velocity which is a function of soliton initial conditions and also characters of the potential. It is interesting that the solitons of the double sine-Gordon model can be trapped by a potential barrier and oscillate there. This situation is very important in applied physics. Solitonwell system has been investigated using the presented model too. Analytical results also have been compared with the results of the direct numerical solutions.