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Dynamical understanding of loop soliton solution for several nonlinear wave equations

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Abstract

It has been found that some nonlinear wave equations have one-loop soliton solutions. What is the dynamical behavior of the so-called one-loop soliton solution? To answer this question, the travelling wave solutions for four nonlinear wave equations are discussed. Exact explicit parametric representations of some special travelling wave solutions are given. The results of this paper show that a loop solution consists of three different breaking travelling wave solutions. It is not one real loop soliton travelling wave solution.

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Authors and Affiliations

  1. Department of Mathematics, Zhejiang Normal University, Jinhua, 321004, China

    Ji-bin Li

  2. Kunming University of Science and Technology, Kunming, 650093, China

    Ji-bin Li

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  1. Ji-bin Li
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Additional information

This work was supported by the National Natural Science Foundation of China (Grant No. 10671179) and the Natural Science Foundation of Yunnan Province (Grant No. 2005A0013M)

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Li, Jb. Dynamical understanding of loop soliton solution for several nonlinear wave equations. SCI CHINA SER A 50, 773–785 (2007). https://doi.org/10.1007/s11425-007-0039-y

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  • DOI: https://doi.org/10.1007/s11425-007-0039-y

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