广义 b 方程的孤立波解及周期波解

广义 b 方程的孤立波解及周期波解

Solitary and periodic solutions of the generalized b-equation

广义 b 方程的孤立波解及周期波解

Solitary and periodic solutions of the generalized b-equation

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数学物理学报

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杨佼朋¹,梁勇²

1. 广东外语外贸大学数学与统计学院
2. 华南理工大学数学学院

收稿日期:2023-11-21 出版日期:2024-01-26 发布日期:2024-01-26
通讯作者: 梁勇
基金资助:
国家自然科学基金;广东省青年创新人才项目;广州市基础与应用基础研究项目

¹,Yong LIANG²

1.
2. School of Mathematics，South China University of Technology

Received:2023-11-21 Online:2024-01-26 Published:2024-01-26
Contact: Yong LIANG

摘要： 对于广义 b 方程的研究主要集中在 b >= 0 的情况，该文利用分方法研究了 b=-3 这类特殊广义 b 方程的分支、非线性波解及动力学特征. 在一定参数条件下，得到了该方程的分支相图,还发现了不同于 b > 0 情况的新现象,在行波系统中有无限多周期轨穿过奇异直线 \varphi = c. 同时，给出了光滑孤立波解和光滑周期波解的存在性及其精确表达式，共获得了 15 个非线性波解的显式表达式.

关键词: 广义 b 方程, 定性理论, 分支方法, 孤立波解, 周期波解

Abstract: The research of generalized b-equation mainly focuses on the case of b >= 0. This paper uses the bifurcation method to investigate the bifurcation, nonlinear wave solutions and dynamical characteristics of generalized b-equation with b = -3. Under certain parameter conditions, one obtains the bifurcation phase diagram of the equation. Meanwhile, a new phenomenon is found different from the case of b > 0, in which an infinite number of periodic trajectories in the traveling wave system cross the singular line \varphi = c. The existence of solitary and periodic solutions is given, and the 15 exact expressions for nonlinear wave solutions are obtained.

Key words: Generalized b-equations, Qualitative theory, Bifurcation method, Solitary solutions, Periodic solutions.

中图分类号:

O175.2

杨佼朋梁勇. 广义 b 方程的孤立波解及周期波解[J]. 数学物理学报, 0, (): 0-0.

Yong LIANG. Solitary and periodic solutions of the generalized b-equation[J]. Acta mathematica scientia,Series A, 0, (): 0-0.

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