Bifurcation analysis and exact traveling wave solutions for (2+1)-dimensional generalized modified dispersive water wave equation

doi:10.1088/1674-1056/ab9f27

中国物理B ›› 2020, Vol. 29 ›› Issue (10): 100206-.doi: 10.1088/1674-1056/ab9f27

Ming Song(宋明)¹^,†(), Beidan Wang(王贝丹)¹, Jun Cao(曹军)²

收稿日期:2020-04-28 修回日期:2020-06-05 接受日期:2020-06-23 出版日期:2020-10-05 发布日期:2020-10-05
通讯作者: Ming Song(宋明)

Bifurcation analysis and exact traveling wave solutions for (2+1)-dimensional generalized modified dispersive water wave equation

Ming Song(宋明)^1,†, Beidan Wang(王贝丹)¹, and Jun Cao(曹军)²

¹ Department of Mathematics, Shaoxing University, Shaoxing 312000, China
² Department of Mathematics, Yuxi Normal University, Yuxi 653100, China

Received:2020-04-28 Revised:2020-06-05 Accepted:2020-06-23 Online:2020-10-05 Published:2020-10-05
Contact: ^†Corresponding author. E-mail: songming12_15@163.com
About author:
†Corresponding author. E-mail: songming12_15@163.com
* Project supported by the National Natural Science Foundation of China (Grant Nos. 11361069 and 11775146).

摘要/Abstract

Abstract:

We investigate (2+1)-dimensional generalized modified dispersive water wave (GMDWW) equation by utilizing the bifurcation theory of dynamical systems. We give the phase portraits and bifurcation analysis of the plane system corresponding to the GMDWW equation. By using the special orbits in the phase portraits, we analyze the existence of the traveling wave solutions. When some parameter takes special values, we obtain abundant exact kink wave solutions, singular wave solutions, periodic wave solutions, periodic singular wave solutions, and solitary wave solutions for the GMDWW equation.

Key words: bifurcation theory, generalized modified dispersive water wave equation, traveling wave solution

中图分类号: (Bifurcation theory)

02.30.Oz

04.20.Jb (Exact solutions)

Ming Song(宋明), Beidan Wang(王贝丹), Jun Cao(曹军). [J]. 中国物理B, 2020, 29(10): 100206-.

Ming Song(宋明)†, Beidan Wang(王贝丹), and Jun Cao(曹军). Bifurcation analysis and exact traveling wave solutions for (2+1)-dimensional generalized modified dispersive water wave equation[J]. Chin. Phys. B, 2020, 29(10): 100206-.

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Bifurcation analysis and exact traveling wave solutions for (2+1)-dimensional generalized modified dispersive water wave equation

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