Scattering below ground states for a class of systems of nonlinear Schrodinger equations

Abstract

In this paper, we consider the scattering problem for a class of $N$-coupled systems of the cubic nonlinear Schrödinger equations in three space dimensions. We prove the scattering of solutions that have a mass-energy quantity less than that for the ground states. This result is previously obtained by Duyckaerts-Holmer-Roudenko for the single cubic nonlinear Schrödinger equation in three space dimensions. It turns out that the result can be extended to a wide class of $N$-coupled systems.

arXiv comment22 pages, no figure