Decay estimates for Schrödinger equations (Q749780)

A class of nonlinear, nonlocal Schrödinger equations is considered; the Laplacian is replaced by a second order constant coefficient operator corresponding to a nondegenerate quadratic form. The Davey-Stewartson system belongs to this class. Adapted Sobolev spaces and a Gagliardo- Nirenberg type estimate are employed to prove global existence and optimal decay estimates in time for classical solutions.