Two-Dimensional Soliton Interaction for Multi-component Bose-Einstein Condensates

For two-component disk-shaped Bose-Einstein condensates with repulsive atom-atom interaction, the small amplitude, finite and long wavelength nonlinear waves can be described by a Kadomtsev-Petviashvili-Ⅰ equation at the lowest order from the originai coupled Gross-Pitaevskii equations. One- and two-soliton solutions of the Kadomtsev- Petviashvili-1 equation are given, therefore, the wave functions of both atomic gases are obtained as well. The instability of a soliton under higher-order long wavelength disturbance has been investigated. It is found that the instability depends on the angle between two directions of both soliton and disturbance.