Global Existence and Asymptotic Behavior of Solutions to Some Nonlinear Systems of Schrödinger Equations

We study the global existence and the large time behavior of solutions to the coupled system of the Schrödinger equations with cubic nonlinearities in one space dimension. We construct modified wave operators to the system for small final data

Global Existence and Asymptotic Behavior of Solutions to Some Nonlinear Systems of Schrödinger Equations

We study the global existence and the large time behavior of solutions to the coupled system of the Schrödinger equations with cubic nonlinearities in one space dimension. We construct modified wave operators to the system for small final data

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

We study the asymptotic behavior of solutions, in particular the scattering theory, for the nonlinear Schr"{o}dinger 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