| Dynamical understanding of loop soliton solution for several nonlinear wave equations |
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| 作者姓名： | Ji-bin LI |
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| 作者单位： | Ji-bin LI Department of Mathematics，Zhejiang Normal University，Jinhua 321004，China; Kunming University of Science and Technology，Kunming 650093，China |
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| 基金项目： | 国家自然科学基金;云南省自然科学基金 |
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| 摘 要： | 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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| 收稿时间： | 6 November 2006 |
| 修稿时间： | 9 January 2007 |
Dynamical understanding of loop soliton solution for several nonlinear wave equations |
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| Ji-bin LI.Dynamical understanding of loop soliton solution for several nonlinear wave equations[J].Science in China(Mathematics),2007,50(6):773-785. |
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| Authors: | Ji-bin Li |
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| Institution: | Department of Mathematics, Zhejiang Normal University, Jinhua 321004, China;Kunming University of Science and Technology, Kunming 650093, China |
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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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| Keywords: | planar dynamical system homoclinic orbit solitary wave solution one-loop soliton solution periodic wave solution bifurcation nonlinear wave equation |
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