The Davey-Stewartson System and the Bäcklund Transformations

Abstract

We consider the (coupled) Davey-Stewartson (DS) system and its B\"{a}cklund transformations (BT). Relations among the DS system, the double Kadomtsev-Petviashvili (KP) system and the Ablowitz-Ladik hierarchy (ALH) are established. The DS hierarchy and the double KP system are equivalent. The ALH is the BT of the DS system in a certain reduction. {From} the BT of coupled DS system we can obtain new coupled derivative nonlinear Schr\"{o}dinger equations.