Dynamics of interacting dark soliton stripes

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.