Acta Mathematica Sinica, English Series

, Volume 24, Issue 8, pp 1319-1330

First online:

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

  • Ji Bin LiAffiliated withCenter for Nonlinear Science Studies, Kunming University of Science and TechnologyDepartment of Mathematics, Zhejiang Normal University Email author 
  • , Yi Shen LiAffiliated withDepartment of Mathematics and Center of Nonlinear Science, University of Science and Technology of China

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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 wave kink wave solution periodic wave solution breaking wave solution smoothness of wave

MR(2000) Subject Classification

34C37 34C23 74J30 58Z05