Bifurcations, Exact Peakon, Periodic Peakons and Solitary Wave Solutions of Generalized Camassa–Holm–Degasperis–Procosi Type Equation

Author:

Sun Xianbo1,Li Jibin23ORCID,Chen Guanrong4

Affiliation:

1. Department of Mathematics, Hangzhou Normal University, Hangzhou 311121, P. R. China

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

3. School of Mathematical Science, Huaqiao University, Quanzhou, Fujian 362021, P. R. China

4. Department of Electrical Engineering, City University of Hong Kong, Hong Kong SAR, P. R. China

Abstract

For the generalized Camassa–Holm–Degasperis–Procosi (CH–DP) type equation, by using the techniques from dynamical systems and singular traveling wave theory developed by Li and Chen [2007] to analyze its corresponding traveling wave systems, which depend on four parameters, it is found that under different parameter conditions its bifurcation portraits exhibit all possible exact explicit bounded solutions, such as solitary wave solutions, periodic wave solutions, peakon as well as periodic peakons. A total of 30 explicit exact parametric representations of the traveling wave system of the CH–DP type equation are presented.

Publisher

World Scientific Pub Co Pte Ltd

Subject

Applied Mathematics,Modeling and Simulation,Engineering (miscellaneous)

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