New Darboux transformation for Hirota–Satsuma coupled KdV system

A new Darboux transformation (DT) is presented for the Hirota–Satsuma coupled KdV system. It is shown that this DT can be constructed by means of two methods: Painlevé analysis and reduction of a binary DT. By iteration of the DT, the Grammian type solutions are found for the coupled KdV system.