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

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.