Adiabatic invariant analysis of dark and dark-bright soliton stripes in two-dimensional Bose-Einstein condensates

TL;DR

This paper develops an adiabatic invariant method to analyze the stability and dynamics of dark and dark-bright soliton stripes in two-dimensional Bose-Einstein condensates, providing analytical insights validated by numerical simulations.

Contribution

It introduces a novel adiabatic invariant approach for studying quasi-one-dimensional solitons in 2D BECs, including complex dark-bright structures, and predicts their stability properties.

Findings

Analytical predictions match numerical simulations.

Identified instability modes based on system parameters.

Extended understanding of soliton dynamics in BECs.

Abstract

In the present work, we develop an adiabatic invariant approach for the evolution of quasi-one-dimensional (stripe) solitons embedded in a two-dimensional Bose-Einstein condensate. The results of the theory are obtained both for the one-component case of dark soliton stripes, as well as for the considerably more involved case of the two-component dark-bright (alias "filled dark") soliton stripes. In both cases, analytical predictions regarding the stability and dynamics of these structures are obtained. One of our main findings is the determination of the instability modes of the waves as a function of the parameters of the system (such as the trap strength and the chemical potential). Our analytical predictions are favorably compared with results of direct numerical simulations.