Adiabatic N-soliton interactions of Bose-Einstein condensates in external potentials

TL;DR

This paper models the interactions of N-soliton trains in Bose-Einstein condensates under external potentials using a perturbed complex Toda chain, providing analytical and numerical insights into soliton dynamics and critical potential strengths.

Contribution

It introduces a perturbed complex Toda chain model for N-soliton interactions in BECs with external potentials, combining analytical and numerical methods.

Findings

The perturbed CTC accurately models soliton train dynamics.

Critical potential strengths for soliton expulsion are derived.

Existence of localized states from soliton trains under linear potentials.

Abstract

Perturbed version of the complex Toda chain (CTC) has been employed to describe adiabatic interactions within N-soliton train of the nonlinear Schrodinger equation (NLS). Perturbations induced by weak quadratic and periodic external potentials are studied by both analytical and numerical means. It is found that the perturbed CTC adequately models the N-soliton train dynamics for both types of potentials. As an application of the developed theory we consider the dynamics of a train of matter - wave solitons confined to a parabolic trap and optical lattice, as well as tilted periodic potentials. In the last case we demonstrate that there exist critical values of the strength of the linear potential for which one or more localized states can be extracted from a soliton train. An analytical expression for these critical strengths for expulsion is also derived.