Sobolev mapping properties of the scattering transform for the Schrödinger equation

Abstract

We consider the scattering transform for the Schrödinger equation with a singular potential and no bound states. Using the Riccati representation for real-valued potentials on the line, we obtain invertibility and Lipschitz continuity of the scattering transform between weighted and Sobolev spaces. Our approach exploits the connection between scattering theory for the Schrödinger equation and scattering theory for the ZS-AKNS system

15 pages, uses "conm-p-l.cls" class file