Article
Zh. Mat. Fiz. Anal. Geom. 11, 123-158 (2015) [DOI: 10.15407/mag11.02.123]

Inverse scattering theory for Schrödinger operators with steplike potentials

Iryna Egorova, Zoya Gladka, Till Luc Lange, and Gerald Teschl

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.

MSC2000: Primary 34L25, 81U40; Secondary 34B30, 34L40
Keywords: Schrödinger operator, inverse scattering theory, steplike potential

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