Periodic blow-up solutions and their limit forms for the generalized Camassa-Holm equation  

作　　者：Zhengrong Liu Boling Guo 

机构地区：[1]School of Mathematical Sciences, South China University of Technology, Cruangzhou 510640, China [2]Institute of Applied Physics and Computational Mathematics, Beijing 100088, China

出　　处：《Progress in Natural Science:Materials International》2008年第3期259-266,共8页自然科学进展·国际材料（英文版）

基　　金：supported by the National Natural Science Foundation of China(Grant No.10571062);the Natural Science Foundation of Guangdong Province(Grant No.07006552).

摘　　要：In this paper, we consider the generalized Camassa-Holm equation uι＋2kux-uxxt＋au^2ux=2uxUxx＋uuxxx. Under substitutionξ=x-ct, some new explicit periodic wave solutions and their limit forms are presented through some special phase orbits. These periodic wave solutions tend to infinity on ξ-u plane periodically. Thus we call them periodic blow-up solutions. To our knowledge, such periodic blow-up solutions have not been found in any other equations.In this paper, we consider the generalized Camassa-Holm equation u_t+2ku_x-u_(xxt)+ au^2u_x=2u_xu_(xx)+uu_(xxx) Under substitution ξ=x-ct, some new explicit periodic wave solutions and their limit forms are presented through some special phase orbits. These periodic wave solutions tend to infinity on ξ-u plane periodically. Thus we call them periodic blow-up solutions. To our knowledge, such periodic blow-up solutions have not been found in any other equations.

关 键 词：Generalized Camassa-Holm equation Explicit solutions Periodic blow-up 

分 类 号：O175.2[理学—数学]