Energy Scattering For The Generalized Davey-Stewartson Equations

In the theory of water waves (esp. surface waves), the 2D generalization of the usual cubic ID Schrodinger equation turns out to be the Davey-Stewartson equation.In Chapter 1, we study the scattering for a class of nonlinear Davey-Stewartson equations with three nonlinearities. We proved that their scattering operator exists in H1.In Chapter 2, We generalize its nonlinearity from the cubic case to the p-th power cases. Through considering the Cauchy problem for the generalized Davey-Stewartson equation in , we obtain its scattering theory. Of course ,the global existence and the uniqueness of the solution for the Cauchy problem are studied.