‎Using the explicit forms of eigenstates for linearized operator related to a matrix version of Nonlinear Schrödinger equation‎, ‎soliton perturbation theory is developed for the $F=1$ bright spinor Bose-Einstein condensates‎. ‎A small disturbance of the integrability condition can be considered as a small correction to the integrable equation‎. ‎By choosing appropriate perturbation‎, ‎the soli...

We present a simple approach for finding N -soliton solution and the corresponding Jost solutions of the derivative nonlinear Scrödinger equation with nonvanishing boundary conditions. Soliton perturbation theory based on the inverse scattering transform method is developed. As an application of the present theory we consider the action of the diffusive-type perturbation on a single bright/dark...

The intra-channel collision of optical solitons, with dual-power law nonlinearity, is studied in this paper by the aid of quasi-particle theory. The perturbation terms that are considered in this paper are of Hamil-tonian type. The suppression of soliton-soliton interaction, in presence of these perturbation terms, is acheived. The numerical simulations support the quasi-particle theory.

We develop a perturbation theory for bright solitons of the F=1 integrable spinor Bose-Einstein condensates BEC model. The formalism is based on using the Riemann-Hilbert problem and provides the means to analytically calculate evolution of the soliton parameters. Both rank-one and rank-two soliton solutions of the model are obtained. We prove equivalence of the rank-one soliton and the ferroma...

The adiabatic parameter dynamics of 1-soliton solution of the generalized fifth-order nonlinear equation is obtained by virtue of the soliton perturbation theory. The adiabatic change of soliton velocity is also obtained in this paper.

Department of Physics and Pre-Engineering Delaware State University, Dover, DE 19901-2277, USA Abstract The soliton perturbation theory is used to obtain adiabatic parameter dynamics of solitons due to the splitted regularized long wave equation in presence of perturbation terms. The adiabatic change of soliton velocity is also obtained in this paper. Mathematics Subject Classification: 35Q51, ...

The adiabatic parameter dynamics of solitons, due to fifth order KdV-type equations with power law nonlinearity, is obtained with the aid of soliton perturbation theory. In addition, the small change in the velocity of the soliton, in the presence of perturbation terms, is also determined in this work. c © 2007 Elsevier Ltd. All rights reserved.

A brief survey of the theory of soliton perturbations is presented. The focus is on the usefulness of the so-called Generalised Fourier Transform (GFT). This is a method that involves expansions over the complete basis of “squared solutions” of the spectral problem, associated to the soliton equation. The Inverse Scattering Transform for the corresponding hierarchy of soliton equations can be v...

For the conservatively perturbed nonlinear Schriidinger equation three-particle effects in the collision of a fast soliton with a pair of more slow ones are considered in the first order of perturbation theory. The changes of the solitons’ velocities and amplitudes, and the perturbation-induced three-particle contribution to the phase shift of the fast soliton are calculated. The total energy e...