Dynamics of interacting dark soliton stripes

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. The cases of two-, three-, and four-stripe states are studied in detail. We use a recently developed adiabatic invariant formulation to derive a quasianalytical prediction for the stripe equilibrium position and for the Bogoliubov-de Gennes spectrum of excitations of stationary stripes. 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.Swedish Research Council [642-2013-7837]; Goran Gustafsson Foundation for Research in Natural Sciences and Medicine; Greek Diaspora Fellowship Program Greek Ministry of Development-GSRT;[NSF-PHY-1602994]; [NSF-PHY-1603058]; [NSF-PHY-1607243]This item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at repository@u.library.arizona.edu