Exact analysis and elastic interaction of multi-soliton for a two-dimensional Gross-Pitaevskii equation in the Bose-Einstein condensation

Introduction: The Gross-Pitaevskii equation is a class of the nonlinear Schrodinger equation, whose exact solution, especially soliton solution, is proposed for understanding and studying Bose-Einstein condensate and some nonlinear phenomena occurring in the intersection field of Bose-Einstein condensate with some other fields. It is an important subject to investigate their exact solutions. Objectives: We give multi-soliton of a two-dimensional Gross-Pitaevskii system which contains the time-varying trapping potential with a few interactions of multi-soliton. Through analytical and graphical analysis, we obtain one-, two- and three-soliton which are affected by the strength of atomic interaction. The asymptotic expression of two-soliton embodies the properties of solitons. We can give some interactions of solitons of different structures including parabolic soliton, line-soliton and dromion-like structure. Methods: By constructing an appropriate Hirota bilinear form, the multi-soliton solution of the system is obtained. The soliton elastic interaction is analyzed via asymptotic analysis. Results: The results in this paper theoretically provide the analytical bright soliton solution in the two-dimensional Bose-Einstein condensation model and their interesting interaction. To our best knowledge, the discussion and results in this work are new and important in different fields. Conclusions: The study enriches the existing nonlinear phenomena of the Gross-Pitaevskii model in Bose-Einstein condensation, and prove that the Hirota bilinear method and asymptotic analysis method are powerful and effective techniques in physical sciences and engineering for analyzing nonlinear mathematical-physical equations and their solutions. These provide a valuable basis and reference for the controllability of bright soliton phenomenon in experiments for high-dimensional Bose-Einstein condensation. (C) 2022 The Authors. Published by Elsevier B.V. on behalf of Cairo University.

Automated summary

This paper investigates the multi-soliton solutions of a two-dimensional Gross-Pitaevskii system with a time-varying trapping potential. Through analytical and graphical analysis, the effects of atomic interaction on one-, two-, and three-soliton solutions are studied. The asymptotic expression of the two-soliton solution reveals the properties of solitons.