一类广义四阶非线性Camassa-Holm方程的行波解  

TRAVELLING WAVE SOLUTIONS IN A CLASS OF NONLINEAR FOURTH ORDER VARIANT OF A GENERALIZED CAMASSA-HOLM EQUATION

作　　者：唐亚宁[1] 徐伟[1,2] 

机构地区：[1]西北工业大学理学院数学系,西安710072 [2]西北工业大学网络与教育技术中心,西安710072

出　　处：《系统科学与数学》2008年第2期180-192,共13页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金(10332030，10472091)资助课题

摘　　要：用动力系统的分支理论研究了一类广义四阶非线性Camassa-Holm方程的动力学行为和行波解,发现方程存在一些孤立波解,周期波解和一些诸如Compacton类型的非光滑行波解.在不同的参数条件下,给出了这些解存在的条件和一些特殊条件下的精确解.By using the bifurcation theory of dynamical systems, it is shown that there exist smooth solitary wave solutions, periodic wave solutions and non-smooth solutions such as compactons for a class of generalized nonlinear fourth order Camassa-Holm equation. Under different parametric conditions, various sufficient conditions to guarantee the existence of the above solutions are given, and some exact solutions under some special conditions are obtained.

关 键 词：广义的四阶非线性Camassa-Holm方程 孤立波解 周期波解 波的不光滑性 分支理论 

分 类 号：O175.29[理学—数学] O175.8[理学—基础数学]