A generalized Hirota-Satsuma coupled KdV system: Darboux transformations and reductions (Q2820927)

In this paper, the authors obtain a new Darboux transformation for the generalized Hirota-Satsuma coupled KdV (gHS-KdV) system from that for the coupled Kadomtsev-Petviashvili (cKP) equation through a reduction. The feature of this Darboux transformation is that it survives in the reductions of the gHS-KdV system to three integrable systems: the Hirota-Satsuma (HS)-KdV equation, the complex coupled KdV equation and the coupled KdV system. By iterating the Darboux transformation, the authors found the compact representations expressed as Gramm-type Pfaffians for the solutions to the gHS-KdV system. Moreover, they also obtained the solitons and rational solution of the gHS-KdV system by using the compact representations.