Dynamics of trapped bright solitons in the presence of localized inhomogeneities

TL;DR

This paper investigates how localized impurities affect the behavior and stability of bright solitons in Bose-Einstein condensates, revealing bifurcation phenomena and providing both numerical and theoretical insights.

Contribution

It introduces a detailed analysis of steady states and bifurcations of bright solitons near impurities, combining numerical simulations with theoretical calculations.

Findings

Identification of stable and unstable steady states near impurities

Observation of saddle-node bifurcation as impurity strength varies

Good agreement between numerical results and theoretical predictions

Abstract

We examine the dynamics of a bright solitary wave in the presence of a repulsive or attractive localized ``impurity'' in Bose-Einstein condensates (BECs). We study the generation and stability of a pair of steady states in the vicinity of the impurity as the impurity strength is varied. These two new steady states, one stable and one unstable, disappear through a saddle-node bifurcation as the strength of the impurity is decreased. The dynamics of the soliton is also examined in all the cases (including cases where the soliton is offset from one of the relevant fixed points). The numerical results are corroborated by theoretical calculations which are in very good agreement with the numerical findings.