广义Camassa-Holm方程的对称性约化和精确解  

Symmetry reductions and exact solutions of generalized Camassa-Holm equation

作　　者：殷久利[1] 田立新[1] 桂贵龙[1] 

机构地区：[1]江苏大学非线性科学研究中心,江苏镇江212013

出　　处：《江苏大学学报（自然科学版）》2005年第4期312-315,共4页Journal of Jiangsu University：Natural Science Edition

基　　金：国家自然科学基金资助项目(10071033);江苏大学高级专业人才科研启动基金资助项目(04JDG033)

摘　　要：利用一种更直接有效的对称性约化方法(CK直接约化法),研究具有充分非线性项的广义Camassa-Holm方程C(m,n,p)的精确解以及解受非线性项影响的情况.在3种规则的要求下得到了广义Camassa-Holm方程的对称性约化,特别研究了C(m,1,1)的对称性约化,约化的结果得到了丰富的解:紧孤立波解(Compacton),尖峰孤立波解(peakon),扭结解和光滑的钟型孤立波解.Using the direct and potential symmetry reduction method (CK method), the generalized Camassa-Holm equation with full nonlinear terms, its exact solutions and the effect of nonlinear terms are studied. Under three rules, the reductions of generalized Camassa-Holm equation, particularly, the reductions of C(m,1,1) equation are obtained. The result of reductions gives rise to abundant solutions: Compacton solutions, peakon solutions,kink solutions, and bell-shaped solitary solutions.

关 键 词：广义CAMASSA-HOLM方程 直接约化法 孤立波解 紧孤立波解 尖峰孤立波解 

分 类 号：O193[理学—数学]