Exact solutions to fractional Drinfel'd-Sokolov-Wilson equations

In this paper, the complete discrimination system for polynomial method is applied to retrieve the exact traveling wave solutions of time-fractional coupled Drinfel'd-Sokolov-Wilson equations. All of the possible exact traveling wave solutions which consist of the rational function type solutions, solitary wave solutions, triangle function type periodic solutions and Jacobian elliptic functions solutions are obtained, and some of them are new solutions. Moreover, the concrete examples are presented to ensure the existences of obtained solutions. In addition, four types of representative solutions are depicted to show the nature of solutions.