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

• Published in: Journal of advanced research Vol. 38; pp. 179 - 190
• Main Authors: Wang, Haotian, Zhou, Qin, Liu, Wenjun
• Format: Journal Article
• Language: English
• Published: Egypt Elsevier B.V 01.05.2022; Elsevier
• Subjects: Asymptotic analysis; Bose-Einstein condensation; Exact bright soliton solutions; Hirota bilinear method; Mathematics, Engineering, and Computer Science; Multi-soliton interactions; Two-dimensional Gross-Pitaevskii equation; Multi-soliton interactions; Exact bright soliton solutions; Asymptotic analysis; Two-dimensional Gross-Pitaevskii equation; Hirota bilinear method; Bose-Einstein condensation
• ISSN: 2090-1232; 2090-1224
• DOI: 10.1016/j.jare.2021.09.007

Interaction of two solitons with different structures is exhibited. By adjusting the corresponding parameters, distinct solitons and their interaction can be achieved. It can also simulate a process of energy concentration of solitons at different times. [Display omitted] •We investigated a two-dimensional Gross-Pitaevskii equation with time-varying trapping potential in the Bose-Einstein condensation.•The Hirota bilinear method is established to solve the two-dimensional Gross-Pitaevskii equation and its parabolic soliton, line-soliton and dromion-like structure can be exhibited via some appropriate parameters chosen. Their interaction structures are discussed.•The interaction of two-soliton solutions is investigated through asymptotic analysis. The Gross-Pitaevskii equation is a class of the nonlinear Schrödinger 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. 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. 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. 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. 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.