Soliton solutions and doubly periodic wave solutions for a new generalized Hirota–Satsuma coupled system

Abstract

In this paper, a new algebraic method with symbolic computation is presented to uniformly construct a series of exact solutions for general nonlinear equations. Compared with most existing tanh methods, the proposed method not only gives new and more general solutions, but also provides a guideline to classify the various types of the solutions according to the values of some parameters. For illustration, we apply the proposed method to solve a new generalized Hirota–Satsuma coupled system and explicitly construct a series of exact solutions which include the soliton solutions and elliptic doubly periodic solutions as special cases. In addition, the links among our proposed method, the tanh method and the extended method are also clarified generally.