Dynamics of bright solitons and soliton arrays in the nonlinear Schrodinger equation with a combination of random and harmonic potentials

TL;DR

This paper investigates the dynamics of bright solitons and their arrays in a one-dimensional nonlinear Schrödinger equation with combined harmonic and random potentials, relevant to Bose-Einstein condensates and nonlinear optics, through systematic simulations.

Contribution

It provides a detailed analysis of soliton formation, oscillation, and stability in disordered potentials, highlighting the effects of disorder strength and correlation on soliton behavior.

Findings

Soliton arrays are generated via modulational instability from broad states.

The number and mobility of solitons depend on disorder parameters.

Single soliton survival rate varies with disorder characteristics.

Abstract

We report results of systematic simulations of the dynamics of solitons in the framework of the one-dimensional nonlinear Schr\"{o}dinger equation (NLSE), which includes the harmonic-oscillator (HO) potential and a random potential. The equation models experimentally relevant spatially disordered settings in Bose-Einstein condensates (BECs) and nonlinear optics. First, the generation of soliton arrays from a broad initial quasi-uniform state by the modulational instability (MI) is considered, following a sudden switch of the nonlinearity from repulsive to attractive. Then, we study oscillations of a single soliton in this setting, which models a recently conducted experiment in BEC. Basic characteristics of the MI-generated array, such as the number of solitons and their mobility, are reported as functions of the strength and correlation length of the disorder, and of the total norm. For the single oscillating soliton, its survival rate is found. Main features of these dependences are explained qualitatively.