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

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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