Dynamics of traveling wave solutions to a highly nonlinear Fujimoto-Watanabe equation

doi:10.1088/1674-1056/28/4/040201

Abstract

In this work, we apply the bifurcation method of dynamical systems to investigate the underlying complex dynamics of traveling wave solutions to a highly nonlinear Fujimoto-Watanabe equation. We identify all bifurcation conditions and phase portraits of the system in different regions of the three-dimensional parametric space, from which we present the sufficient conditions to guarantee the existence of traveling wave solutions including solitary wave solutions, periodic wave solutions, kink-like (antikink-like) wave solutions, and compactons. Furthermore, we obtain their exact expressions and simulations, which can help us understand the underlying physical behaviors of traveling wave solutions to the equation.

Keywords: highly nonlinear Fujimoto-Watanabe equation dynamics traveling wave solutions bifurcations

Received: 27 December 2018
Revised: 31 January 2019
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 Nos. 11701191 and 11871232), the Program for Innovative Research Team in Science and Technology in University of Fujian Province, Quanzhou High-Level Talents Support Plan (Grant No. 2017ZT012), and the Subsidized Project for Cultivating Postgraduates' Innovative Ability in Scientific Research of Huaqiao University.

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

Cite this article:

Li-Juan Shi(师利娟), Zhen-Shu Wen(温振庶) Dynamics of traveling wave solutions to a highly nonlinear Fujimoto-Watanabe equation 2019 Chin. Phys. B 28 040201

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Dynamics of traveling wave solutions to a highly nonlinear Fujimoto-Watanabe equation

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