Asymptotic reductions of two coupled (2 + 1)-dimensional nonlinear Schrödinger equations: application to Bose–Einstein condensates

Abstract

We consider a system of two coupled (2 + 1)-dimensional nonlinear Schrodinger equations, describing two-component disc-shaped Bose–Einstein condensates. We present three different asymptotic reductions of this system. In particular, we derive the Mel'nikov system, the Yajima–Oikawa system as well as the Davey–Stewartson system (the latter is found as a special case of the Djordjevic–Redekopp system). Conditions for integrability of the reduced systems, their soliton solutions and the asymptotic relevance of such solutions to the original system are also discussed. Numerical results pertaining to the reduction to the Davey–Stewartson system are found to be in good agreement with the analytical predictions.