R. W. Sallatti, L. Tomio, D. E. Pelinovsky, and A. Gammal

Stability of dark solitons in a bubble Bose-Einstein condensate

Abstract:
The dynamic stability of dark solitons trapped on the surface of a two-dimensional spherical bubble is investigated. In this spherical geometry of the Bose-Einstein condensate, dark solitons are found to be unstable for the interaction parameter exceeding 8.37, since discrete angular modes drive snake instabilities, with the generation of vortex dipoles. We show analytically and numerically that, for each angular mode m >= 2, there exists exactly one unstable mode whose dominance determines the number m of vortex dipoles. Time-dependent simulations confirm the formation of vortex dipoles.

Keywords:
Gross-Pitaevskii equation, dark solitons, spherical coordinates, spectral stability, creation of vortices