在浅水波理论中,通常的具有立方项的一维Schrodinger方程推广到二维的情形即是Davey-Stewartson方程.将此立方项推广到p次幂非线性项的情形,进而考虑其初值在∑(Rn):={u∈H1(Rn):x|u∈L2(Rn)}中的Cauchy问题的解的整体存在性及惟一性,得到该方程的散射理论.

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.