一族非线性色散偏微分方程的指数函数型和三角函数型精确解  

Exact Solutions of Exp-function-Type and Trigonometric Function-Type to a Family of Nonlinear Third-Order PDEs

作　　者：张金华[1] 丁玉敏[1] 

机构地区：[1]红河学院数学系,云南蒙自661100

出　　处：《西南大学学报（自然科学版）》2012年第1期28-33,共6页Journal of Southwest University(Natural Science Edition)

基　　金：云南省自然科学基金资助项目(2008CD186)

摘　　要：利用辅助方程法和指数函数法,研究了由Degasperis,Holm和Hone 3人导出的一族非线性三阶扩散方程.借助于Maple程序的辅助计算,获得了大量的指数函数型、双曲函数型和三角函数型精确解,这些精确解包括孤立波解、扭子波解和周期波解,并分析和讨论了几种典型类型的精确解的动力学性质,给出了几种代表性精确解的波形图.Using the auxiliary equation method and the exp-function method,we study a family of third-order nonlinear dispersive PDEs,given by Degasperis,Holm and Hone.By the auxiliary computation of Maple＇s programe,many exact solutions of exp-function type,hyperbolic function type and trigonometric function type are obtained,including solitary wave solutions,kink-wave solutions and periodic wave solutions.The dynamic properties of several typical exact solutions are analyzed and discussed and several typical waveforms are illustrated.

关 键 词：一族非线性三阶扩散方程 指数函数法 辅助方程法 周期波解 孤立波解 扭子波解 

分 类 号：O175.2[理学—数学]