广义Camassa-Holm方程的行波解  

THE TRAVELING WAVE SOLUTIONS OF THE GENERALIZED CAMASSA-HOLM EQUATION

作　　者：刘小华[1] 

机构地区：[1]贵州民族大学理学院,贵阳550025

出　　处：《系统科学与数学》2012年第7期852-864,共13页Journal of Systems Science and Mathematical Sciences

基　　金：贵州省教育厅自然科学基金(2010026);贵州省科学技术厅;贵州民族大学科技联合基金(LKM[2011]14);贵州省"模式识别与智能系统"重点实验室建设项目(黔科合计[2009]4002);贵州省"信息处理与模式识别"研究生教育创新基地资助课题

摘　　要：运用平面动力系统理论和方法给出了广义Camassa-Holm方程在各种参数条件下的相图与分支,分析了奇线对其行波解的影响,获得了广义Camassa-Holm方程光滑、非光滑孤立波解和周期波解的存在性及个数,求出了它的两组新周期尖波解的显式表达式.In this paper, the existence of the traveling wave solutions to the general- ized Camassa-Holm equation is investigated. For different value of the parameters, the phase diagram and branches of the generalized Camassa-Holm equation are given by the qualitative theory and method of plane dynamic system, The influence of the odd lines on traveling wave solutions of the generalized Camassa-Holm equation is analyzed, the existence and number of smooth, non-smooth solitary wave solutions and periodic wave solutions to the generalized Camassa-Holm equation are obtained. The new exact periodic cusp solutions to the generalized Camassa-Holm equation are found out.

关 键 词：孤立波解 广义CAMASSA-HOLM方程 相图与分支. 

分 类 号：O175.29[理学—数学]