Introduction

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.

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.

中文翻译：

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Bose-Einstein凝聚中二维Gross-Pitaevskii方程的多孤子精确分析和弹性相互作用

介绍

Gross-Pitaevskii方程是一类非线性薛定谔方程，提出了其精确解，尤其是孤子解，用于理解和研究玻色-爱因斯坦凝聚态以及玻色-爱因斯坦凝聚态与其他一些场的交叉场中出现的一些非线性现象. 研究它们的确切解决方案是一个重要的课题。

目标

我们给出了二维 Gross-Pitaevskii 系统的多孤子，该系统包含随时间变化的俘获势和一些多孤子的相互作用。通过分析和图形分析，我们得到了受原子相互作用强度影响的一、二和三孤子。双孤子的渐近表达式体现了孤子的性质。我们可以给出一些不同结构的孤子的相互作用，包括抛物线孤子、线孤子和dromion-like结构。

方法

通过构造适当的广田双线性形式，得到系统的多孤子解。通过渐近分析分析孤子弹性相互作用。

结果

本文的结果在理论上提供了二维玻色-爱因斯坦凝聚模型中的解析亮孤子解及其有趣的相互作用。据我们所知，这项工作的讨论和结果在不同领域都是新的和重要的。

结论

该研究丰富了现有的Gross-Pitaevskii模型在Bose-Einstein凝聚中的非线性现象，证明了Hirota双线性法和渐近分析法是物理科学和工程中分析非线性数理方程及其解的强大而有效的技术。 . 这些为高维玻色-爱因斯坦凝聚实验中亮孤子现象的可控性提供了有价值的依据和参考。