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arXiv · 1510.01835

Inverse scattering theory for Schr\"odinger operators with steplike potentials

Iryna Egorova·Zoya Gladka·Till Luc Lange·Gerald Teschl
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Abstract

We study the direct and inverse scattering problem for the one-dimensional Schr\"odinger 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.

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Iryna Egorova, Zoya Gladka, Till Luc Lange, Gerald Teschl. 2015-10-07. Inverse scattering theory for Schr\"odinger operators with steplike potentials. https://doi.org/10.15407/mag11.02.123

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