Eur. Phys. J. B 62, 485-491 (2008)
https://doi.org/10.1140/epjb/e2008-00192-y

Interactions between two solitons with an arbitrary collision direction in two-dimensional Bose-Einstein condensates

College of Physics and Electronic Engineering, Northwest Normal University, Lanzhou, 730070, P.R. China

Corresponding author: ^a duanws@nwnu.edu.cn

Received: 5 January 2008
Revised: 23 March 2008
Published online: 22 May 2008

Abstract

Interactions between two solitary waves with an arbitrary collision direction in disk-shaped Bose-Einstein condensates are investigated by using the modified Poincaré-Lighthill-Kuo (PLK) perturbation technique. The results show that the two-dimensional system have a solution of two dark solitons with small-amplitude, but finite amplitude which propagating in two different directions. This solution can be described by two Boussinesq-Korteweg-de Vries (B-KdV) equations in the respective reference frames. The solitary wave solutions and their analytical phase shifts are obtained. Moreover, the solution and its stability are discussed by numerical simulation. Particularly, it is found that the phase shifts strongly depend on the angle between two propagation directions of two solitons, which is quite different from that in one-dimensional system.