Matter-Wave Solitons in the Presence of Collisional Inhomogeneities: Perturbation theory and the impact of derivative terms

TL;DR

This paper investigates how spatially varying nonlinearities affect matter-wave solitons, using perturbation theory to analyze the dynamics and the influence of derivative terms in the nonlinear Schrödinger equation.

Contribution

The study introduces a transformation approach to handle inhomogeneous nonlinearities and develops perturbation theory for solitons with derivative terms, especially in cases with inverse square spatial dependence.

Findings

Perturbation theory accurately predicts soliton dynamics in inhomogeneous media.

Derivative terms significantly influence soliton behavior in spatially varying nonlinearities.

The approach applies to both attractive and repulsive interactions.

Abstract

We study the dynamics of bright and dark matter-wave solitons in the presence of a spatially varying nonlinearity. When the spatial variation does not involve zero crossings, a transformation is used to bring the problem to a standard nonlinear Schrodinger form, but with two additional terms: an effective potential one and a non-potential term. We illustrate how to apply perturbation theory of dark and bright solitons to the transformed equations. We develop the general case, but primarily focus on the non-standard special case whereby the potential term vanishes, for an inverse square spatial dependence of the nonlinearity. In both cases of repulsive and attractive interactions, appropriate versions of the soliton perturbation theory are shown to accurately describe the soliton dynamics.