Dynamics of vector dark soliton of coupled nonlinear
Schrödinger equations. Application to
two-component Bose-Einstein condensates
Abstract:
We report recent studies of dynamics of dark solitons in two-component
Bose-Einstein condensates. In the case of a cigar-shaped condensate with
relatively low density the system of coupled 1D Gross-Pitaevskii equations
is reduced to the system of effective 1D coupled nonlinear Schrödinger
(CNLS) equations. As first step, we study the small amplitude limit of
the CNLS which is reduced to the coupled Korteweg-de Vries (KdV) equations.
For a specific choice of the parameters when the CNLS are reduces to the
integrable Manakov system we obtain integrable coupled KdV equations. We
find that there exist two branches of dark solitons corresponding to two
branches of the sound waves. Slow solitons, however appear to be unstable
and transform during the evolution to the stable upper branch solitons.
Oscillations of solitons in a parabolic trap are studied numerically.