Related papers: Solitons: Kinks, Collisions and Breathers
A spatially discrete version of the general kink-bearing nonlinear Klein-Gordon model in (1+1) dimensions is constructed which preserves the topological lower bound on kink energy. It is proved that, provided the lattice spacing h is…
We analyze the kinetic behavior of localized excitations - solitons, breathers and phonons - in Sine-Gordon model. Collision integrals for all type of localized excitation collision processes are constructed, and the kinetic equations are…
The ac driven sine-Gordon equation is studied analytically and numerically, with the aim of providing a full description of how soliton solutions behave. To date, there is much controversy about when ac driven dc motion is possible. Our…
The nonstationary dynamics of topological solitons (dislocations, domain walls, fluxons) and their bound states in one-dimensional systems with high dispersion are investigated. Dynamical features of a moving kink emitting radiation and…
We study collisions of two, three, and four kinks of the double sine-Gordon model. The initial conditions are taken in a special form in order to provide collision of all kinks in one point. We obtain dependences of the maximal energy…
We consider radial sine-Gordon kinks in two, three and higher dimensions. A full two dimensional simulation showing that azimuthal perturbations remain small allows to reduce the problem to the one dimensional radial sine-Gordon equation.…
It is shown that the topological discrete sine-Gordon system introduced by Speight and Ward models the dynamics of an infinite uniform chain of electric dipoles constrained to rotate in a plane containing the chain. Such a chain admits a…
Extending a recent effective theory formulation for the dynamics of kinks in the sine-Gordon model [1], we propose an analogous effective description of $\phi^4$ kinks. Three different reduced models based on the kink position, width and…
It was recently proposed a novel discretization for nonlinear Klein-Gordon field theories in which the resulting lattice preserves the topological (Bogomol'nyi) lower bound on the kink energy and, as a consequence, has no Peierls-Nabarro…
Nonperturbative, oscillatory, winding number one solutions of the Sine-Gordon equation are presented and studied numerically. We call these nonperturbative shape modes {\sl wobble} solitons. Perturbed Sine-Gordon kinks are found to decay to…
In the present Chapter, we consider two prototypical Klein-Gordon models: the integrable sine-Gordon equation and the non-integrable $\phi^4$ model. We focus, in particular, on two of their prototypical solutions, namely the kink-like…
We construct the soliton solutions in the symmetric space sine-Gordon theories. The latter are a series of integrable field theories in 1+1-dimensions which are associated to a symmetric space F/G, and are related via the Pohlmeyer…
We look at BPS systems involving two interacting Sine-Gordon like fields both when one of them has a kink solution and the second one either a kink or an antikink solution. The interaction between the two fields is controlled by a parameter…
We consider static solutions of the sine-Gordon theory defined on a cylinder, which can be either periodic or quasi-periodic in space. They are described by the different modes of a simple pendulum moving in an inverted effective potential…
We revisit the problem of the three-soliton collisions in the weakly perturbed sine-Gordon equation and develop an effective three-particle model allowing to explain many interesting features observed in numerical simulations of the soliton…
Solitons are very effective in transporting energy over great distances and collisions between them can produce high energy density spots of relevance to phase transformations, energy localization and defect formation among others. It is…
We have studied the space-reflection symmetries of some soliton solutions of deformed sine-Gordon models in the context of the quasi-integrability concept. Considering a dual pair of anomalous Lax representations of the deformed model we…
In this paper, we introduce a commensurable and non-degenerate double sine-Gordon model, in which a partial breaking of vacuum degeneracy provides a mechanism for the emergence of static multi-kinks. These multi-kinks $K_n$ are stable field…
Klein-Gordon equations describe the dynamics of waves/particles in sub-atomic scales. For nonlinear Klein-Gordon equations, their breather solutions are usually known as time periodic solutions with the vanishing spatial-boundary condition.…
We present an analytical and numerical study of the Klein-Gordon kink-soliton dynamics in inhomogeneous media. In particular, we study an external field that is almost constant for the whole system but that changes its sign at the center of…