利用(G′/G)-展开法求分数阶Drinfel'd-Sokolov-Wilson方程精确解

Exact Solutions of Fractional Drinfel’d-Sokolov-Wilson Obtained by Using G'/G-expansion

时空分数阶方程组Drinfel'd-Sokolov-Wilson精确解在描述自然现象的理解与研究起着推动作用.故文章讨论时空分数阶方程组Drinfel'd-Sokolov-Wilson的精确解.通过用分数阶的复变换,将时空分数阶方程组Drinfel'd-Sokolov-Wilson转换成相应的常微分方程,然后利用了(G′/G)-展开法,得到了包括双曲函数解、三角函数解和有理函数解,进而丰富了解的形式,并用Maple软件验证了所得到的解的正确性.

This paper discusses the precise solution of the fractional space-time equation group Drinfel'd-Sokolov-Wilson.By using the complex transformation of fractional order,the fractional order space-time equation group Drinfel'd-Sokolov-Wilson is converted into the corresponding normal differential equation,and then the precise solution of the equation is derived by using theG'/G--expansion method,thus enriching the form of understanding,and verifying the correctness of the resulting solution Maple software.