Bifurcations of travelling wave solutions for a two-component camassa-holm equation


DOI: 10.1007/s10114-008-6207-3

Cite this article as:
Li, J.B. & Li, Y.S. Acta. Math. Sin.-English Ser. (2008) 24: 1319. doi:10.1007/s10114-008-6207-3


By using the method of dynamical systems to the two-component generalization of the Camassa-Holm equation, the existence of solitary wave solutions, kink and anti-kink wave solutions, and uncountably infinite many breaking wave solutions, smooth and non-smooth periodic wave solutions is obtained. Under different parametric conditions, various sufficient conditions to guarantee the existence of the above solutions are given. Some exact explicit parametric representations of travelling wave solutions are listed.


solitary wavekink wave solutionperiodic wave solutionbreaking wave solutionsmoothness of wave

MR(2000) Subject Classification


Copyright information

© Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag GmbH 2008

Authors and Affiliations

  1. 1.Center for Nonlinear Science StudiesKunming University of Science and TechnologyKunmingP. R. China
  2. 2.Department of MathematicsZhejiang Normal UniversityJinhuaP. R. China
  3. 3.Department of Mathematics and Center of Nonlinear ScienceUniversity of Science and Technology of ChinaHefeiP. R. China