# Dynamics of interacting dark soliton stripes

## TL;DR

This paper investigates how multiple dark soliton stripes in a 2D Bose-Einstein condensate interact and influence each other's stability, combining analytical predictions with numerical simulations to understand their dynamics and decay into vortices.

## Contribution

It introduces a quasi-analytical approach to predict the equilibrium and stability of multiple interacting dark soliton stripes, extending understanding of their collective behavior.

## Key findings

- Number of unstable modes increases with stripe count.
- Growth rates of instabilities are relatively unaffected by stripe number.
- Larger chemical potentials lead to higher maximum instability growth rates.

## Abstract

In the present work we examine the statics and dynamics of multiple parallel dark soliton stripes in a two-dimensional Bose-Einstein condensate. Our principal goal is to study the effect of the interaction between the stripes on the transverse instability of the individual stripes. We use a recently developed adiabatic invariant formulation to derive a quasi-analytical prediction for the stripe equilibrium position and for the Bogoliubov-de Gennes spectrum of excitations of stationary stripes. The cases of two-, three- and four-stripe states are studied in detail. We subsequently test our predictions against numerical simulations of the full two-dimensional Gross-Pitaevskii equation. We find that the number of unstable eigenmodes increases as the number of stripes increases due to (unstable) relative motions between the stripes. Their corresponding growth rates do not significantly change, although for large chemical potentials, the larger the stripe number, the larger the maximal instability growth rate. The instability induced dynamics of multiple stripe states and their decay into vortices are also investigated.