Energy Scattering of a Generalized Davey-Stewartson System in Three Dimension

In this paper, we study the global scattering result of the solution for the generalized Davey-Stewartson system { i partial derivative(t)u + Delta u = vertical bar u vertical bar(2) u + uv(x1), (t,x) is an element of R x R-3, -Delta v = (vertical bar u vertical bar(2))(x1). The main difficulties are the failure of the interaction Morawetz estimate and the asymmetrical structure of nonlinearity (in particular, the nonlinearity is non-local). To compensate, we utilize the strategy derived from concentration-compactness idea, which was first introduced by Kenig and Merle