Weierstrass semi-rational expansion method and new doubly periodic solutions of the generalized Hirota-Satsuma coupled KdV system

In the paper, with the aid of symbolic computation, we investigate the generalized Hirota–Satsuma coupled KdV system via our Weierstrass semi-rational expansion method presented recently using the rational expansion of Weierstrass elliptic function and its first-order derivative. As a consequence, three families of newWeierstrass elliptic function solutions via Weierstrass elliptic function }(n;g2,g3) and its first-order derivative } (n;g2,g3). Moreover, the corresponding new Jacobi elliptic function solutions and solitary wave solutions are also presented, and when n ! 1, these solitary wave solutions approach to some constants. 2005 Elsevier Inc. All rights reserved.