构造非线性波方程sech^2-型和csch^2-型孤波解的一种统一方法  

A Unified Method for Seeking the sech^2-type and csch^2-type Solitary Wave Solutions of Nonlinear Wave Equations

作　　者：谢元喜[1] 

机构地区：[1]湖南理工学院物理与电子学院,湖南岳阳414006

出　　处：《湖南理工学院学报（自然科学版）》2013年第1期10-13,51,共5页Journal of Hunan Institute of Science and Technology(Natural Sciences)

基　　金：国家自然科学基金项目(11172093)

摘　　要：通过巧妙地引入一个变换,并选取合适的试探函数,提出了一种构造非线性波方程sech2-型和csch2-型孤波解的统一方法,并用该法求得了BBM方程、Kaup-Kupershmidt方程和广义KdV方程的sech2-型和csch2-型孤波解.本方法也可用于构造其他非线性波方程的sech2-型和csch2-型孤波解.By introducing felicitously a transformation and selecting the appropriate trial functions, this paper puts forward a unified approach to solving nonlinear wave equations. As a result, the sech2-type and csch2-type solitary wave solutions of three physically significant nonlinear wave equations which are called respectively the BBM equation, the Kaup-Kupershmidt equation and the generalized KdV equation are successfully derived in a uniform manner by means of this approach. The technique used herein can also be applied to find the sech2-type and csch2-type solitary wave solutions of other nonlinear wave equations.

关 键 词：BBM方程 Kaup-Kupershmidt方程 广义KDV方程 sech2-型孤波解 csch2-型孤波解 

分 类 号：O175.29[理学—数学] O411.1[理学—基础数学]