Bifurcations of Travelling Wave Solutions for a Two-Component Camassa-Holm Equation  

作　　者：Ji Bin LI Yi Shen LI 

机构地区：[1]Center for Nonlinear Science Studies, Kunming University of Science and Technology, Kunming 650093, P. R. China [2]Department of Mathematics, Zhejiang Normal University, Jinhua 321004, P. R. China [3]Department of Mathematics and Center of Nonlinear Science,University of Science and Technology of China, Hefei 230026, P. R. China

出　　处：《Acta Mathematica Sinica,English Series》2008年第8期1319-1330,共12页数学学报（英文版）

基　　金：the National Natural Science Foundation of China (10671179) and (10772158)

摘　　要：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.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.

关 键 词：solitary wave kink wave solution periodic wave solution breaking wave solution smooth- ness of wave 

分 类 号：O192[理学—数学] O175.1[理学—基础数学]