Kink-soliton explosions in generalized Klein-Gordon equations (original) (raw)

Solitons trapping for the nonlinear Klein–Gordon equation with an external excitation

Chaos, Solitons & Fractals, 2003

The asymptotic perturbation (AP) method is applied to the study of the nonlinear Klein-Gordon equation and an external periodic excitation is supposed to be in primary resonance with the frequency of a generic mode. The AP method uses two different procedures for the solutions: introducing an asymptotic temporal rescaling and balancing of the harmonic terms with a simple iteration. Amplitude and phase modulation equations and external force-response and frequency-response curves are obtained and the presence of multistabilities and solitons trapping is demonstrated. The validity of the method is highlighted by comparing the approximate solutions with results of the numerical integration.

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.

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.

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

arXiv (Cornell University), 2013

We study properties of the localized solitons to the sine-Gordon equation excited on the attractive impurity by a moving kink. The cases of one-and two-dimensional spatially extended impurities are considered. For the case of one-dimensional impurity the possibility of excitation of the first even and odd high-amplitude impurity modes by the moving kink is demonstrated. For the case of two-dimensional impurity we show the possibility of excitation of the nonlinear high-amplitude waves of new type called here breathing pulson and breathing 2D soliton. We suggest different analytical expressions to model these nonlinear excitations. The dependencies of the oscillation frequency and the amplitude of the excited impurity modes on the impurity parameters are reported.

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.

Solitons for the nonlinear Klein-Gordon equation

2007

In this paper we study existence and orbital stability for solitary waves of the nonlinear Klein-Gordon equation. The energy of these solutions travels as a localized packet, hence they are a particular type of solitons. In particular we are interested in sufficient conditions on the potential for the existence of solitons. Our proof is based on the study of the

Soliton–potential interaction in the nonlinear Klein–Gordon model

Physica Scripta, 2012

Interaction of solitons with external potentials in nonlinear Klein-Gordon field theory is investigated using an improved model. Presented model is constructed with a better approximation for adding the potential to the lagrangian through the metric of background spacetime. The results of the model are compared with the another model and the differences are discussed. *

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.

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.