相关论文: Collective coordinates for the hybrid model

An equation for the quasi-static soliton ansatz depending on an arbitrary set of collective variables is covariantly derived on the basis of the variational approach to the method of collective variables. The field configuration and the…

In this report, the various 1D single soliton and multi-soliton solutions of the Sine-Gordon equation are explored. First the topological kink solitons and their properties for the Sine-Gordon, as well as the $\phi^{4}$ model are…

This work presents an extensive exploration of scattering and tunneling involving composite objects with intrinsic degrees of freedom. We aim at exact solutions to such scattering problems. Along this path we demonstrate solution to model…

A hybrid asymptotic-numerical theory is developed to analyze the effect of different types of localized heterogeneities on the existence, linear stability, and slow dynamics of localized spot patterns for the two-component Schnakenberg…

In this paper, we study the global well-posedness and scattering problem in the energy space for both focusing and defocusing the Klein-Gordon-Hartree equation in the spatial dimension $d \geq 3$. The main difficulties are the absence of an…

We propose a unified method for the large space-time scaling limit of \emph{linear} collisional kinetic equations in the whole space. The limit is of \emph{fractional} diffusion type for heavy tail equilibria with slow enough decay, and of…

We study, both theoretically and experimentally, the scattering properties of optical dipole-mode vector solitons - radially asymmetric composite self-trapped optical beams. First, we analyze the soliton collisions in an isotropic…

The aim of this paper is to introduce the Inverse Scattering Method for later studies of some problems in nonlinear dynamics, and describe the kink solution of the Sine Gordon Equation using the Inverse Scattering Method as a methodological…

We establish the long time soliton asymptotics for the translation invariant nonlinear system consisting of the Klein-Gordon equation coupled to a charged relativistic particle. The coupled system has a six dimensional invariant manifold of…

With the help of numerical simulations we study N-soliton scattering (N=3,4) in the (2+1)-dimensional CP^1 model with periodic boundary conditions. When the solitons are scattered from symmetrical configurations the scattering angles…

In this paper we study the scattering of solitons in a binary Bose-Einstein Condensate (BEC) including SO- and Rabi-couplings. To this end, we derive a reduced ODE model in view to provide a variational description of the collisional…

Scattering and bound states for a spinless particle in the background of a kink-like smooth step potential, added with a scalar uniform background, are considered with a general mixing of vector and scalar Lorentz structures. The problem is…

The initial value problem for the general coupled Hirota system with nonzero boundary conditions at infinity is solved by reporting a rigorous theory of the inverse scattering transform. With the help of a suitable uniformization variable,…

Interaction of asymmetric $\phi^6$ kinks with a spatially localized $\mathcal{PT}$-symmetric perturbation is investigated numerically. It has been shown that when the kink (antikink) hits the defect from the gain side, a final velocity of…

The scattering of charged solitons in the complex sine-Gordon field theory is investigated. An exact factorizable S-matrix for the theory is proposed when the renormalized coupling constant takes the values $\lambda^{2}_{R}=4\pi/k$ for any…

We study a generalized $\phi^4$ model that gives rise to BPS kink/antikink configurations with compacton-like profiles. One observes that the positive parameter controlling the generalizing function promotes an infinity degenerescence of…

We study the diffusion and deformation of classical solitons coupled to thermal noise. The diffusion coefficient for kinks in the $\phi^4$ theory is predicted up to the second order in $kT$. The prediction is verified by numerical…

We characterize the soliton solutions of the nonlinear Schroedinger equation on the half line with linearizable boundary conditions. Using an extension of the solution to the whole line and the corresponding symmetries of the scattering…

We investigate the propagation of fronts in an inhomogeneous medium within the framework of the $\phi^4$ model. The inhomogeneity is modeled either as an interface separating regions with different dissipation or as a finite layer with…

We present a novel approximation method that can predict the number of solitons asymptotically appearing under arbitrary rapidly decreasing initial wave packets. The number of solitons can be estimated without integration of the original…