Acta mathematica scientia,Series A ›› 2021, Vol. 41 ›› Issue (3): 603-628.

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Periodic Wave Solutions, Solitary Wave Solutions and Their Relationship for Generalized Symmetric Regularized Long Wave Equation with Two Nonlinear Terms

Xingqian Ling1(),Weiguo Zhang2,*()   

  1. 1 Business School, University of Shanghai for Science and Technology, Shanghai 200093
    2 College of Science, University of Shanghai for Science and Technology, Shanghai 200093
  • Received:2020-06-12 Online:2021-06-26 Published:2021-06-09
  • Contact: Weiguo Zhang E-mail:1097576100@qq.com;zwgzwm@126.com
  • Supported by:
    the NSFC(11471215)

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

CLC Number: 

  • O175.2
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