Darboux transformation for a generalized Hirota-Satsuma coupled Korteweg-de Vries equation.

A Darboux transformation for the generalized Hirota-Satsuma coupled Korteweg-de Vries (KdV) equation is derived with the aid of the gauge transformation between the corresponding 4x4 matrix spectral problems with three potentials, by which some explicit solutions of the generalized Hirota-Satsuma coupled KdV equation are constructed. As a reduction, a Darboux transformation of the complex coupled KdV equation and its explicit solutions are obtained.