On the initial value problem for the Davey-Stewartson systems

Abstract

In the theory of water waves, the 2D generalisation of the usual cubic 1D Schrodinger equation turns out to be a family of systems: the Davey-Stewartson systems. For special values of the parameters characterising these systems, one obtains systems of the inverse scattering type. The authors' work addresses the very general case and their methods belong to the more standard theory of nonlinear partial differential equations. Well-posedness of the Cauchy problem and also finite-time blow-up are studied.