Travelling wave solutions of a generalized Camassa-Holm-Degasperis-Procesi equation  

作　　者：DENG ShengFu1, GUO BoLing2 & WANG TingChun2,3 1Department of Mathematics, Zhanjiang Normal University, Zhanjiang 524048, China 2Institute of Applied Physics and Computational Mathematics, Beijing 100088, China 3 College of Math and Physics, Nanjing University of Information Science and Technology, Nanjing 210044, China 

出　　处：《Science China Mathematics》2011年第3期555-572,共18页中国科学：数学（英文版）

基　　金：supported by China Postdoctoral Science Foundation (Grant Nos. 20100470249, 20100470254)

摘　　要：The travelling wave solutions of a generalized Camassa-Holm-Degasperis-Procesi equation ut-uxxt + (1 + b)umux = buxuxx + uuxxx are considered where b > 1 and m are positive integers. The qualitative analysis methods of planar autonomous systems yield its phase portraits. Its soliton wave solutions, kink or antikink wave solutions, peakon wave solutions, compacton wave solutions, periodic wave solutions and periodic cusp wave solutions are obtained. Some numerical simulations of these solutions are also given.The travelling wave solutions of a generalized Camassa-Holm-Degasperis-Procesi equation ut-uxxt ＋ （1 ＋ b）umux = buxuxx ＋ uuxxx are considered where b 1 and m are positive integers. The qualitative analysis methods of planar autonomous systems yield its phase portraits. Its soliton wave solutions, kink or antikink wave solutions, peakon wave solutions, compacton wave solutions, periodic wave solutions and periodic cusp wave solutions are obtained. Some numerical simulations of these solutions are also given.

关 键 词：homoclinic orbits heteroclinic orbits peakon wave solutions compacton wave solutions periodic cusp wave solutions 

分 类 号：O241.8[理学—计算数学]