Two-dimensional vector solitons in Bose-Einstein-condensate mixtures

We derive two decoupled KP-I equations from the system of two-dimensional (2D) Gross-Pitaevskii equations for a two -component Bose-Einstein condensate (BEC), using the multiple -scale expansion method. We produce asymptotic analytical vector-soliton solutions, viz., dark -dark (DD) and dark-antidark (DAD) one-soliton and two-soliton states, by tuning coupling constants and norms of species, and address their evolution numerically under the action of the harmonic -oscillator (HO) trap, in the local -density approximation. We find that shallow single -line DD and DAD solitons are stable, while single -lump DAD solutions (weakly localized truly -2D states) split and lead to nucleation of two half -vortices. We also find that the BEC mixture placed in the HO trap admits stable asymptotic multi-soliton solutions, e.g., two-line DD and DAD solitons and two -lump DD ones, which were not reported before. In particular, the two -lump solutions describe inelastic collisions between the lumps. The analysis developed in this work may also be applied to systems with spin -orbit coupling and gauge fields, which have been realized in atomic BEC.