Study on Integrability of (2+1)-Dimensional Bidirectional Sawada-Kotera Equation and Interaction of Lump-Type Solutions

IF 1.7 4区物理与天体物理 Q3 PHYSICS, MULTIDISCIPLINARY

International Journal of Theoretical Physics Pub Date : 2025-10-20 DOI:10.1007/s10773-025-06158-4

Jiangying Huo, Taogetusang Bao

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Abstract

In this paper, we investigate the integrability problem of the (2+1)-dimensional bidirectional Sawada-Kotera (bSK) equation. Through analyzing the model, we explore the characteristics of nonlinear dynamics. The Bell polynomial method is one of the most useful tools for studying the integrability of nonlinear evolution equations. Using this method, we derive the Bäcklund transformation, Lax pair, infinite many conservation laws, and nonlinear superposition formula of solutions for the (2+1)-dimensional bSK equation. Then, we constructed the lump-type solutions and soliton solutions of the equation respectively by utilizing its bilinear form and the nonlinear superposition formula of solutions. The dynamic behaviors of the lump-type solutions, lump-kink solutions, and interaction solutions of the model were deduced via the mathematical symbolic computation system Mathematica, the extended three-wave method, and the homo-clinic test method, with the relationship between local waves in physics being elaborated.

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（2+1）维双向Sawada-Kotera方程的可积性及块型解的相互作用研究

本文研究了（2+1）维双向Sawada-Kotera （bSK）方程的可积性问题。通过对模型的分析，探讨了非线性动力学的特点。贝尔多项式方法是研究非线性演化方程可积性的一种最有用的工具。利用这种方法，我们导出了（2+1）维bSK方程的Bäcklund变换、Lax对、无限多守恒定律和解的非线性叠加公式。然后，利用该方程的双线性形式和解的非线性叠加公式，分别构造了该方程的集解和孤子解。利用数学符号计算系统Mathematica、扩展三波法和同斜检验方法推导了模型的块型解、块结解和相互作用解的动力学行为，并阐述了物理中局域波之间的关系。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

International Journal of Theoretical Physics 物理-物理：综合

CiteScore

2.50

自引率

21.40%

发文量

258

审稿时长

3.3 months

期刊介绍： International Journal of Theoretical Physics publishes original research and reviews in theoretical physics and neighboring fields. Dedicated to the unification of the latest physics research, this journal seeks to map the direction of future research by original work in traditional physics like general relativity, quantum theory with relativistic quantum field theory,as used in particle physics, and by fresh inquiry into quantum measurement theory, and other similarly fundamental areas, e.g. quantum geometry and quantum logic, etc.