Sobolev mapping properties of the scattering transform for the Schrödinger equation

Details Sobolev mapping properties of the scattering transform for the Schrödinger equation Sobolev mapping properties of the scattering transform for the Schrödinger equation

2010-02-02

arxiv.org/abs/1002.0540v1

Physics

Mathematical Physics

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

Scientific paper

We consider the scattering transform for the Schr\"odinger 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 Schr\"odinger equation and scattering theory for the ZS-AKNS system

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