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

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


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.


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



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