摘要

In this paper a new algebraic method is devised to uniformly construct a series of travelling wave solutions for a coupled Ito system. The obtained solutions include (a) kink-shaped and bell-shaped soliton solutions, (b) rational solutions, (c) triangular periodic solutions, (d) Jacobi and Weierstrass doubly periodic wave solutions. Among them, the Jacobi elliptic doubly periodic wave solutions exactly degenerate to the soliton solutions at a certain limit condition. Compared with most existing tanh methods, 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.