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Zh. Mat. Fiz. Anal. Geom., 2015, Volume 11, Number 2, Pages 123–158 (Mi jmag613)  

This article is cited in 4 scientific papers (total in 4 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

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.

DOI: https://doi.org/10.15407/mag11.02.123

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MSC: Primary 34L25, 81U40; Secondary 34B30, 34L40
Received: 20.01.2015
Revised: 18.02.2015
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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
\Bibitem{EgoGlaLan15}
\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
\mathnet{http://mi.mathnet.ru/jmag613}
\crossref{https://doi.org/10.15407/mag11.02.123}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3442842}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000354621000002}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. K. Andreiev, I. Egorova, T. L. Lange, G. Teschl, “Rarefaction waves of the Korteweg–de Vries equation via nonlinear steepest descent”, J. Differ. Equ., 261:10 (2016), 5371–5410  crossref  mathscinet  zmath  isi  scopus
    2. I. Egorova, Z. Gladka, G. Teschl, “On the form of dispersive shock waves of the Korteweg–de Vries equation”, Zhurn. matem. fiz., anal., geom., 12:1 (2016), 3–16  mathnet  crossref  mathscinet
    3. K. Andreiev, I. Egorova, “On the long-time asymptotics for the Korteweg–de Vries equation with steplike initial data associated with rarefaction waves”, Zhurn. matem. fiz., anal., geom., 13:4 (2017), 325–343  mathnet  crossref
    4. M. J. Ablowitz, X.-D. Luo, J. T. Cole, “Solitons, the Korteweg–de Vries equation with step boundary values, and pseudo-embedded eigenvalues”, J. Math. Phys., 59:9, SI (2018), 091406  crossref  mathscinet  zmath  isi  scopus
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