Modified wave operators for nonlinear Schrodinger equations in one and two dimensions

Abstract

We study the asymptotic behavior of solutions, in particular the scattering theory, for the nonlinear Schrodinger equations with cubic and quadratic nonlinearities in one or two space dimensions. The nonlinearities are summation of gauge invariant term and non-gauge invariant terms. The scattering problem of these equations belongs to the long range case. We prove the existence of the modified wave operators to those equations for small final data. Our result is an improvement of the previous work [13].