Zhurnal Matematicheskoi Fiziki, Analiza, Geometrii [Journal of Mathematical Physics, Analysis, Geometry]
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Zhurnal Matematicheskoi Fiziki, Analiza, Geometrii [Journal of Mathematical Physics, Analysis, Geometry], 2015, Volume 11, Number 2, Pages 123–158
DOI: https://doi.org/10.15407/mag11.02.123 (Mi jmag613) 		 
This article is cited in 11 scientific papers (total in 11 papers)

Inverse Scattering Theory for Schrödinger Operators with Steplike Potentials

I. Egorovaab, Z. Gladkaa, T. L. Langeb, G. Teschlbc

a B. Verkin Institute for Low Temperature Physics and Engineering, National Academy of Sciences of Ukraine, 47 Lenin Ave., Kharkiv 61103, Ukraine
b Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, Wien 1090, Austria
c International Erwin Schrödinger Institute for Mathematical Physics, Boltzmanngasse 9, Wien 1090, Austria
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DOI: https://doi.org/10.15407/mag11.02.123
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 its asymptotics. Our results generalize all previous known results and are important for solving the Korteweg–de Vries equation via the inverse scattering transform.
Key words and phrases: Schrödinger operator, inverse scattering theory, steplike potential.
Received: 20.01.2015
Revised: 18.02.2015
Bibliographic databases:
Document Type: Article
MSC: Primary 34L25, 81U40; Secondary 34B30, 34L40
Language: English
Citation: I. Egorova, Z. Gladka, T. L. Lange, G. Teschl, “Inverse Scattering Theory for Schrödinger Operators with Steplike Potentials”, Zh. Mat. Fiz. Anal. Geom., 11:2 (2015), 123–158
Citation in format AMSBIB
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\by I.~Egorova, Z.~Gladka, T.~L.~Lange, G.~Teschl
\paper Inverse Scattering Theory for Schr\"odinger Operators with Steplike Potentials
\jour Zh. Mat. Fiz. Anal. Geom.
\yr 2015
\vol 11
\issue 2
\pages 123--158
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\crossref{https://doi.org/10.15407/mag11.02.123}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3442842}
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    • This publication is cited in the following 11 articles:
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