Low Energy Scattering for Nonlinear Schrödinger Equations in Fractional Order Sobolev Spaces

Abstract

We consider the scattering problem for the nonlinear Schrödinger equations with interactions behaving as a power p at zero. In the critical and subcritical cases (s≥n/2-2/(p-1)≥0), we prove the existence and asymptotic completeness of wave operators in the sense of Sobolev norm of order s on a set of asymptotic states with small homogeneous norm of order n/2-2/(p-1) in space dimension n≥1.