Scattering for the non-radial 3D cubic nonlinear Schrödinger equation

Abstract

Scattering of radial H 1 solutions to the 3D focusing cubic nonlinear Schrödinger equation below a mass-energy thresholdwhere Q is the ground state, was established in Holmer-Roudenko [7].In this note, we extend the result in [7] to non-radial H 1 data.For this, we prove a non-radial profile decomposition involving a spatial translation parameter.Then, in the spirit of Kenig-Merle [10], we control via momentum conservation the rate of divergence of the spatial translation parameter and by a convexity argument based on a local virial identity deduce scattering.An application to the defocusing case is also mentioned.