Exact solutions of the classical Drinfel'd–Sokolov–Wilson equations and the relations among the solutions

Abstract With the aid of Mathematica, and using a direct algebraic method, four kinds of exact solutions of the classical Drinfel's–Sokolov–Wilson equations (DSWEs) are presented by formula form. Then the exponential function solutions, the hyperbolic function solutions and the triangular function solutions of the classical DSWEs are obtained in a unified way. From the results one can see there are certain relations among the solutions.