Nonlinear Wave in a Disc-Shaped Bose--Einstein Condensate

We discuss the possible nonlinear waves of atomic matter wave in a Bose--Einstein condensate. One and two of two-dimensional (2D) dark solitons in the Bose--Einstein condensed system are investigated. A rich dynamics is studied for the interactions between two solitons. The interaction profiles of two solitons are greatly different if the angle between them are different. If the angle is small enough, the maximum amplitude during the interaction between two solitons is even less than that of a single soliton. However, if the angle is large enough, the maximum amplitude of two solitons can gradually attend to the sum of two soliton amplitudes.