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

doi:10.1088/1674-1056/ab9f27

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.

Keywords: bifurcation theory generalized modified dispersive water wave equation traveling wave solution

Received: 28 April 2020
Revised: 05 June 2020
Accepted manuscript online: 23 June 2020

PACS:	02.30.Oz	(Bifurcation theory)
	04.20.Jb	(Exact solutions)

Corresponding Authors: ^†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).

Cite this article:

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 2020 Chin. Phys. B 29 100206

Fig. 1.

The phase portraits of system (8): (a) g < –g₀, (b) g = –g₀, (c) –g₀ < g < 0, (d) g = 0, (e) 0 < g < g₀, (f) g = g₀, (g) g > g₀.

Fig. 2.

The profiles of traveling wave solutions of Eq. (2). (a) Kink wave solution (15), (b) singular wave solution (17), (c) periodic singular wave solution (19).

Fig. 3.

The profiles of traveling wave solutions of Eq. (2). (a) Periodic wave solution (22), (b) solitary wave solution (24), (c) singular wave solution (29).

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