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August  2009, 24(3): 897-907. doi: 10.3934/dcds.2009.24.897

Family of nonlinear wave equations which yield loop solutions and solitary wave solutions

Jibin Li 1,

1. 

Department of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang, 321004

Received  August 2007 Revised  December 2007 Published  April 2009

This paper gives a family of nonlinear wave equations, which can yield so called loop solution, cusp wave solution and solitary wave solution depending on the values of parameter $A$. For two third order systems, the dynamical behavior of these solutions are considered. The exact explicit parametric representations of solitary wave solutions and periodic wave solutions are given. It concerns with the properties of singular traveling wave systems.
Keywords: periodic wave solution, loop solution, exact explicit solution, nonlinear wave equation., solitary wave solution.
Mathematics Subject Classification: 34A05, 34C25-28, 34M55, 35Q51, 35Q53, 58F05, 58F14, 58F3.
Citation: Jibin Li. Family of nonlinear wave equations which yield loop solutions and solitary wave solutions. Discrete & Continuous Dynamical Systems - A, 2009, 24 (3) : 897-907. doi: 10.3934/dcds.2009.24.897
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