A series of new exact solutions for a complex coupled KdV system

In this paper an algebraic method is devised to uniformly construct a series of exact solutions for general nonlinear equations. Compared with the existing tanh methods and Jacobi function method, the proposed method gives more general exact solutions without much extra effort. More importantly, the method provides a guideline for the classification of the solutions based on the given parameters. For illustration, we apply the proposed method to revisit a complex coupled KdV system and successfully construct a series of new exact solutions including the soliton solutions and elliptic doubly periodic solutions.