新 (3+1) 维 KP 方程的退化解与相互作用解

数学物理学报 ›› 2024, Vol. 44 ›› Issue (6): 1520-1536.

新 (3+1) 维 KP 方程的退化解与相互作用解

郭艳凤^1,^*(),崔静易¹(),肖海军¹(),张景军²()

¹中国地质大学 (武汉) 数学与物理学院武汉 430074
²嘉兴大学数据科学学院浙江嘉兴 314001

收稿日期:2024-01-30 修回日期:2024-04-29 出版日期:2024-12-26 发布日期:2024-11-22
通讯作者: ^*郭艳凤,Email: guoyan_feng@163.com
作者简介:崔静易, Email: cuijingyi@cug.edu.cn;|肖海军, Email: xiaohj@cug.edu.cn;|张景军, Email: zjj_math@aliyun.com
基金资助:
国家自然科学基金(11861013);国家自然科学基金(11771183);国家自然科学基金(12261053);广西科技基地与人才专项(AD21238019)

Degeneration Behaviors of Solutions and Hybrid Solutions for the New (3+1)-Dimensional KP Equation

Guo Yanfeng^1,^*(),Cui Jingyi¹(),Xiao Haijun¹(),Zhang Jingjun²()

¹School of Mathematics and Physics, China University of Geosciences, Wuhan 430074
²College of Data Science, Jiaxing University, Zhejiang Jiaxing 314001

Received:2024-01-30 Revised:2024-04-29 Online:2024-12-26 Published:2024-11-22
Supported by:
NSFC(11861013);NSFC(11771183);NSFC(12261053);Guangxi Science and Technology Base and Talent Special Project(AD21238019)

摘要/Abstract

摘要：

该文主要研究了由 Wazwaz 于 2022 年首次提出的新 (3+1) 维 KP 方程的非线性波解. 基于 Hirota 双线性形式, 利用模共振技术由$ N $-孤子解得到 $ P $-呼吸解. 然后, 利用参数极限法, 根据参数的特殊关系, 对同宿呼吸解和 $ N $-孤子解进行退化得到了 Lump 解. 最后, 从 $ N $-孤子解的部分退化出发, 研究了由呼吸解、孤子解和 Lump 解组成的相互作用解. 该文通过可视化图形展示了这些解的动力学特性.

关键词: 新 $ (3+1) $ 维 KP 方程, $ P $-呼吸解, 退化行为, Lump 解, 相互作用解

Abstract:

We concentrate on the nonlinear wave solutions of the new (3+1)-dimensional KP equation, which was firstly proposed by Wazwaz in 2022. Based on the Hirota bilinear form, the $ P $-breathing solutions are mainly obtained from the $ N $-soliton solutions utilizing the module resonance technique. Then, using parameter limit approach, the Lump solutions are derived by degenerating behaviors of the homoclinic breathing solutions and $ N $-soliton solutions on the basis of the special relations of parameters. In addition, from the partial degeneration of the $ N $-soliton solutions, some hybrid solutions are investigated by the interaction solutions among the breathing, soliton and Lump solutions.

Key words: New (3+1)-dimensional KP equation, $ P $-Breathing solutions, Degeneration behaviors, $ Q $-Lump solutions, Hybrid solutions

中图分类号:

0175.29

郭艳凤, 崔静易, 肖海军, 张景军. 新 (3+1) 维 KP 方程的退化解与相互作用解[J]. 数学物理学报, 2024, 44(6): 1520-1536.

Guo Yanfeng, Cui Jingyi, Xiao Haijun, Zhang Jingjun. Degeneration Behaviors of Solutions and Hybrid Solutions for the New (3+1)-Dimensional KP Equation[J]. Acta mathematica scientia,Series A, 2024, 44(6): 1520-1536.

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