Dynamical behaviors of traveling wave solutions to a Fujimoto-Watanabe equation

doi:10.1088/1674-1056/27/9/090201

Abstract

We study dynamical behaviors of traveling wave solutions to a Fujimoto-Watanabe equation using the method of dynamical systems. We obtain all possible bifurcations of phase portraits of the system in different regions of the three-dimensional parameter space. Then we show the required conditions to guarantee the existence of traveling wave solutions including solitary wave solutions, periodic wave solutions, kink-like (antikink-like) wave solutions, and compactons. Moreover, we present exact expressions and simulations of these traveling wave solutions. The dynamical behaviors of these new traveling wave solutions will greatly enrich the previews results and further help us understand the physical structures and analyze the propagation of nonlinear waves.

Keywords: dynamical behaviors traveling wave solutions Fujimoto-Watanabe equation bifurcations

Received: 26 May 2018
Revised: 24 June 2018
Accepted manuscript online:

PACS:	02.30.Hq	(Ordinary differential equations)
	02.30.Oz	(Bifurcation theory)
	05.45.Yv	(Solitons)
	05.45.-a	(Nonlinear dynamics and chaos)

Fund:

Project supported by the National Natural Science Foundation of China (Grant No. 11701191) and Subsidized Project for Cultivating Postgraduates' Innovative Ability in Scientific Research of Huaqiao University, China.

Corresponding Authors: Zhen-Shu Wen
E-mail: wenzhenshu@hqu.edu.cn

Cite this article:

Zhen-Shu Wen(温振庶), Li-Juan Shi(师利娟) Dynamical behaviors of traveling wave solutions to a Fujimoto-Watanabe equation 2018 Chin. Phys. B 27 090201

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