利用(g′/g^2)展开法求解KdV-Burgers方程和KdV-Burgers-Kuramoto方程

Solutions of KdV-Burgers and KdV-Burgers-Kuramoto equations by(g′/g^2) expansion method

根据(g′/g^2)展开法求得KdV-Burgers方程和KdV-Burgers-Kuramoto方程的精确解,在不同的条件下,得出双曲函数通解、三角函数通解以及有理函数通解.双曲函数通解中的常数项取特殊值时,得出孤立波解.(g′/g^2)展开法求解KdV-Burgers方程和KdV-Burgers-Kuramoto方程,比(g′/g)展开等方法,具有简便、易于计算的特点,是求解非线性方程的较好选择.

Exact solutions of KdV-Burgers equation and KdV-Burgers-Kuramoto equation are obtained by(g′/g^2)expansion method.Three different types of solutions can be deduced:Hyperbolic function solutions,trigonometric functionsolutions,and rational functional solutions.Solitary wave solution can be calculated when special values of the hyperbolic function solution are properly chosen.From the solving of both equations,it can be concluded that the(g′/g^2)expansion method is a good choice of solving nonlinear equations which is more convenient,and easy-calculating than(g′/g)expansion method and other methods mentioned before.