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Vladikavkaz. Mat. Zh., 2014, Volume 16, Number 4, Pages 9–15 (Mi vmj517)  

This article is cited in 2 scientific papers (total in 2 papers)

Asymptotic behavior of generalized eigenvalues of the Schrödinger operator

M. Sh. Badakhova, O. Y. Veremeenkob, A. B. Shabatca

a Karachay-Cherkess State University, Karachaevsk, Russia
b Southern Federal University, Rostov-on-Don, Russia
c Landau Institute for Theoretical Physics, Russian Academy of Sciences, Chernogolovka, Russia

Abstract: The Schrödinger operator on the real line with compactly supported potential is considered. An asymptotic analysis of complex poles of the transmission coefficient $1/a(k)$ for some $\delta$-type potentials is fulfilled. We are planning to use these poles producing effective methods of approximate solutions of the inverse scattering problem in the one-dimensional case.

Key words: inverse scattering problem, zeros of entire functions.

Full text: PDF file (594 kB)
References: PDF file   HTML file
UDC: 517.928
Received: 05.09.2014

Citation: M. Sh. Badakhov, O. Y. Veremeenko, A. B. Shabat, “Asymptotic behavior of generalized eigenvalues of the Schrödinger operator”, Vladikavkaz. Mat. Zh., 16:4 (2014), 9–15

Citation in format AMSBIB
\Bibitem{BadVerSha14}
\by M.~Sh.~Badakhov, O.~Y.~Veremeenko, A.~B.~Shabat
\paper Asymptotic behavior of generalized eigenvalues of the Schr\"odinger operator
\jour Vladikavkaz. Mat. Zh.
\yr 2014
\vol 16
\issue 4
\pages 9--15
\mathnet{http://mi.mathnet.ru/vmj517}


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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. A. B. Shabat, “Scattering theory for delta-type potentials”, Theoret. and Math. Phys., 183:1 (2015), 540–552  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    2. A. B. Shabat, M. Sh. Badakhov, “Darboux transformations in the inverse scattering problem”, Ufa Math. J., 8:4 (2016), 42–51  mathnet  crossref  mathscinet  isi  scopus
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