Abstract: In the theory of water waves(esp. Surface waves), the 2D generalization of the usual cubic 1D Schrodinger equation tums out to be the Davey-Stewartson equation. The author generalizes its nonlinearity from the cubic case to the p-th power cases. Through considering the Cauchy problem for the generalized Davey-Stew artson equation in ∑(Rn): = { u ∈ H1 (Rn): ｜ x ｜ u ∈ L2 (Rn)} , the author obtains its scattering theory. Of course, the global existence and the uniqueness of the solution for the Cauchy problem are studied.

Key words: generalized Davey-Stewartson equation, pseudo conformally invariant conservation law, scatter ing operator