广义色散Camassa-Holm方程的精确解  

Exact solutions for generalized dispersive Camassa-Holm equation

作　　者：孙璐[1] 田立新[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B12期1-4,19,共5页Journal of Jiangsu University：Natural Science Edition

基　　金：国家自然科学基金资助项目(10071003);江苏省自然科学基金资助项目(2000-65-31)

摘　　要：为了研究非线性色散对Compacton和孤立波形成的作用,对非线性Camassa-Holm方程增加一色散项(ul)3x后得到广义色散Camassa-Holm方程.拟设该方程具有4种形式解,得到了丰富的精确解.讨论了在各种不同的非线性参数条件下,得到单峰、双峰Compacton解、斑图解、孤立波解、周期波解以及K ink Compacton解.研究了高维广义色散Camassa-Holm方程的精确解.结果表明,非线性和色散的相互作用是形成孤立波的关键.To understand the role of nonlinear dispersion in compacton and solitary wave formation, disprsive Camassa-Holm equation is generalized by adding a dispersive term （u＇）3x. Among four different forms of solutions, abundant solitary wave solutions are obtained. In particular, Kink Compacton solutions, solitary wave solution, periodic wave solution, solitary pattern solution and Compacton solutions with one and two peaks are developed. High dimension generalized dispersive Camassa-Holm equation are also studied. The reciprocity between nonlinearity and dispersion is the key to solitary wave formation.

关 键 词：非线性偏微分方程 CAMASSA-HOLM方程 斑图解 COMPACTON解 孤立波解 周期波解 

分 类 号：O193[理学—数学]