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Bifurcations of Traveling Wave Solutions of a Nonlinear Wave Model Created by Diffraction in Periodic Media

Jibin Li

Department of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang 321004, P. R. China

Department of Mathematics, Kunming University of Science and Technology, Kunming, Yunnan 650093, P. R. China

E-mail Address: lijb@zjnu.cn

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and

Fengjuan Chen

Department of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang 321004, P. R. China

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https://doi.org/10.1142/S0218127416500322Cited by:0 (Source: Crossref)

Abstract

In this paper, we consider a model created by diffraction in periodic media. The study of the traveling wave solutions for this model derives a planar dynamical system with a singular straight line. On the basis of the investigation of the dynamical behavior and bifurcations of solutions of the planar dynamical systems, we obtain all possible explicit exact parametric representations of solutions (including solitary wave solutions, periodic wave solutions, periodic peakon solutions, compactons, etc.) under different parameter conditions.

This research was partially supported by the National Natural Science Foundation of China (11471289, 11162020).

Keywords:

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