Higher dimensional bright solitons and their collisions in a multicomponent long wave–short wave system

Abstract

Bright plane soliton solutions of an integrable (2+1)-dimensional (n + 1)-wave system are obtained by applying Hirota's bilinearization method. First, the soliton solutions of a three-wave system consisting of two short-wave components and one long-wave component are found and then the results are generalized to the corresponding integrable (n + 1)-wave system with n short waves and a single long wave. It is shown that the solitons in the short-wave components (say S(1) and S(2)) can be amplified by merely reducing the pulse width of the long-wave component (say L). Study of the collision dynamics reveals some interesting behaviour: the solitons which split up in the short-wave components undergo shape changing collisions with intensity redistribution and amplitude-dependent phase shifts. Even though a similar type of collision is possible in (1+1)-dimensional multicomponent integrable systems, to our knowledge we report this kind of collision in (2+1) dimensions for the first time. However, solitons which appear in the long-wave component exhibit only elastic collision though they undergo amplitude-dependent phase shifts.