利用改进的（G＇／G）-展开法求广义的（2＋1）维Boussinesq方程的精确解

摘要

In this paper, the improved （G＇/G）-expansion method is used to construct exact solutions of the generalized （2＋1）-dimensional Boussinesq equation. As a result, some new travelling wave solutions involving parameters, expressed by three types of functions which are the hyperbolic functions, the trigonometric functions and the rational functions, are obtained. When the parameters are taken as special values, the solitary wave solutions are derived from the hyperbolic function solutions.%利用改进的（G＇／G）-展开法，求广义的（2＋1）维Boussinesq方程的精确解，得到了该方程含有较多任意参数的用双曲函数、三角函数和有理函数表示的精确解，当双曲函数表示的行波解中参数取特殊值时，便得到广义的（2＋1）维Boussinesq方程的孤立波解．