Family of nonlinearwave equations which yield loop solutions and solitary wavesolutions

Jibin Li

doi:10.3934/dcds.2009.24.897

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2009, Volume 24, Issue 3: 897-907. Doi: 10.3934/dcds.2009.24.897

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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: July 31, 2007

Revised: November 30, 2007

Published: August 2009

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Abstract

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.

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Mathematics Subject Classification: 34A05, 34C25-28, 34M55, 35Q51, 35Q53, 58F05, 58F14, 58F30.

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