Science in China Series A: Mathematics

, Volume 50, Issue 6, pp 773–785

Dynamical understanding of loop soliton solution for several nonlinear wave equations

  • Ji-bin Li
Article

DOI: 10.1007/s11425-007-0039-y

Cite this article as:
Li, J. SCI CHINA SER A (2007) 50: 773. doi:10.1007/s11425-007-0039-y

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.

Keywords

planar dynamical systemhomoclinic orbitsolitary wave solutionone-loop soliton solutionperiodic wave solutionbifurcationnonlinear wave equation

MSC(2000)

34C3734C2374J3058Z05

Copyright information

© Science in China Press 2007

Authors and Affiliations

  • Ji-bin Li
    • 1
    • 2
  1. 1.Department of MathematicsZhejiang Normal UniversityJinhuaChina
  2. 2.Kunming University of Science and TechnologyKunmingChina