一类耦合非线性波动方程的显式精确解  

Explicit and exact solutions to a coupled nonlinear wave equation

作　　者：尚亚东[1] 

机构地区：[1]西安石油学院信息科学系,陕西西安710065

出　　处：《宁夏大学学报（自然科学版）》2000年第4期290-294,共5页Journal of Ningxia University(Natural Science Edition)

基　　金：国家自然科学基金!资助项目 (199710 6 8) ;西安石油学院科研基金!资助项目 (99- 0 19)

摘　　要：研究了一类耦合非线性波动方程 ,利用两种不同的假设获得了该方程的一些新的显式精确行波解 ,包括渐近值不为零的钟状孤立波解、扭状或反扭状的孤立波解、奇异行波解和三角函数型周期波解 对参数的其他取值范围找到了几种新的精确解 ,丰富了精确解的种类 ,扩充了参数取值的范围 。A coupled nonlinear wave equation is studied in the present paper.Some new explicit and exact travelling wave solutions to the coupled nonlinear wave equation are presented through two different ansatze.These solutions include the bell shaped solitary wave solutions which have non zero asymptotic value,the kink shaped and antikink shaped solitary wave solutions,singular travelling wave solutions and periodic wave solutions of the triangular function type.Some new kind of exact solutions are found for the other range of the parameters.Some results in the literature are improved and extended not only the types of the exact solutions but also the range of the parameters.

关 键 词：孤波解 周期波解 假设方法 耦合非线性波动方程 显式精确解 奇异行波解 

分 类 号：O241.82[理学—计算数学]