广义对称正则长波方程的孤波解和周期波解及它们与Hamilton能量的关系

摘要/Abstract

摘要：

该文研究了广义对称正则长波方程的精确孤波解和周期波解，以及它们解随Hamilton能量的演化关系.首先，该文利用平面动力系统的理论和方法，对该方程的行波解对应的平面动力系统进行了详细的定性分析，根据对应系统的首次积分和待定假设法求出了该方程的两种钟状孤波解和一种扭状孤波解，以及七种精确周期波解.此外，该文建立了所求孤波解和周期波解与Hamilton能量对应关系，研究了所求周期波解和孤波解的演变关系，揭示出系统之所以会出现周期波解和孤波解，本质上是该方程所对应的Hamilton系统的能量在发挥着关键的作用.最后该文还举例给出了当Hamilton能量变化，孤波解演化到周期波解的示意图.

关键词: 广义对称正则长波方程, 平面动力系统, 孤波解, 周期波解, 演化关系

Abstract:

In this paper, we study the exact solitary wave, periodic wave solutions and their evolutionary relationship with Hamilton energy for generalized symmetric regularized long wave equation. By the planar dynamical system method, we make detailed qualitative analysis on this equation. Then we use the first integral method to obtain the exact solutions for the equation. Furthermore, by establishing the corresponding relationships between the solitary wave, periodic wave solutions and Hamilton energy h, we reveal that the value of Hamilton energy h plays an important role in the appearance of solitary wave and periodic wave solutions. The evolution processes from the periodic wave solution to the solitary wave solution and the kink wave solution are also given in this paper.

Key words: Generalized symmetric regularized long wave equation, Planar dynamical system, Solitary wave solution, Periodic wave solution, Evolutionary relationship

中图分类号:

O175.2

凌兴乾,张卫国. 广义对称正则长波方程的孤波解和周期波解及它们与Hamilton能量的关系[J]. 数学物理学报, 2021, 41(3): 603-628.

Xingqian Ling,Weiguo Zhang. Periodic Wave Solutions, Solitary Wave Solutions and Their Relationship for Generalized Symmetric Regularized Long Wave Equation with Two Nonlinear Terms[J]. Acta mathematica scientia,Series A, 2021, 41(3): 603-628.

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