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 new Weierstrass elliptic function solutions via Weierstrass elliptic function ℘(ξ; g2, g3) and its first-order derivative ℘′(ξ; g2, g3). Moreover, the corresponding new Jacobi elliptic function solutions and solitary wave solutions are also presented, and when ξ → ∞, these solitary wave solutions approach to some constants.