Large Time Asymptotics for a Cubic Nonlinear Schrödinger System in One Space Dimension

Abstract

We consider a two-component system of cubic nonlinear Schrödinger equations in one space dimension. We show that each component of the solutions to this system behaves like a free solution in the large time and that the scattering profiles satisfy a crucially restricted condition. This restriction results from non-trivial long-range nonlinear interactions.