Inverse scattering theory for Schrödinger operators with steplike potentials

Abstract

We study the direct and inverse scattering problem for the one-dimensional Schrödinger equation with steplike potentials. We give necessary and sufficient conditions for the scattering data to correspond to a potential with prescribed smoothness and prescribed decay to their asymptotics. These results are important for solving the Korteweg-de Vries equation via the inverse scattering transform.

28 pages

References in corpus (1)

• Inverse Scattering Theory for One-Dimensional Schroedinger Operators with Steplike Periodic Potentials

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