Scattering for NLS with a potential on the line

Abstract

We show the $H^1$ scattering for a one dimensional nonlinear Schrödinger equation with a non-negative, repulsive potential $V$ such that $V,xV\in W^{1,1}$, and a mass-supercritical non-linearity. We follow the approach of concentration-compacity/rigidity first introduced by Kenig and Merle.

References in corpus (3)

• Global well-posedness, scattering and blow-up for the energy-critical, focusing, non-linear Schrodinger equation in the radial case
• A sharp condition for scattering of the radial 3d cubic nonlinear Schroedinger equation
• Dispersive estimates for Schrodinger operators in dimensions one and three