Abstract
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; g 2, g 3) and its first-order derivative ℘′( ξ; g 2, g 3). 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.
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