On modelling adiabatic N - soliton interactions in external potentials

TL;DR

This paper develops a perturbed complex Toda chain model to accurately describe the adiabatic interactions of N-soliton trains in the nonlinear Schrödinger equation under weak external potentials, combining analytical and numerical methods.

Contribution

It introduces a novel perturbed CTC approach for modeling N-soliton interactions in external potentials, validated through analytical and numerical analysis.

Findings

Perturbed CTC effectively models soliton train dynamics.

The model applies to quadratic and periodic external potentials.

Validated with numerical simulations of matter-wave and optical lattice systems.

Abstract

We analyze perturbed version of the complex Toda chain (CTC) in an attempt to describe the adiabatic N - soliton train interactions of the perturbed nonlinear Schr\"odinger equation (NLS). We study perturbations with weak quadratic and periodic external potentials by both analytical and numerical means. 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 in a parabolic trap and optical lattice, as well as tilted periodic potential.