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Ufa Mathematical Journal, 2016, Volume 8, Issue 4, Pages 42–51
DOI: https://doi.org/10.13108/2016-8-4-42 (Mi ufa350) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Darboux transformations in the inverse scattering problem

M. Sh. Badakhovab, A. B. Shabatcab

a Karachay-Cherkess State University, Karachaevsk
b Institution of Russian Academy of Sciences Institute of Mathematics with Computer Center, Ufa
c L. D. Landau Institute for Theoretical Physics of Russian Academy of Sciences, Chernogolovka
English version PDF (347 kB) Citations (2) Russian version article
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DOI: https://doi.org/10.13108/2016-8-4-42
Abstract: As it is know, Darboux transformations play a key role in applications in ISP. In the paper we expose the theory of such transformations for the Schrödinger equations with compactly supported potential, which are not necessarily smooth. We study a new class of transformations connected with the zeroes of the reflection coefficient located at conjugated points in the complex plane.
Keywords: Inverse Problem, Schrödinger equation, compactly supported potentials, Darboux transformation.
Funding agency Grant number
Russian Science Foundation 15-11-20007
The research is supported by the grant of the Russian Science Foundation (project no. 15-11-20007).
Received: 27.08.2016
Bibliographic databases:
Document Type: Article
UDC: 512.5
MSC: 34L25, 35J10, 37K15
Language: English
Original paper language: Russian
Citation: M. Sh. Badakhov, A. B. Shabat, “Darboux transformations in the inverse scattering problem”, Ufa Math. J., 8:4 (2016), 42–51
Citation in format AMSBIB
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\by M.~Sh.~Badakhov, A.~B.~Shabat
\paper Darboux transformations in the inverse scattering problem
\jour Ufa Math. J.
\yr 2016
\vol 8
\issue 4
\pages 42--51
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85013379967}
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  • https://doi.org/10.13108/2016-8-4-42
  • https://www.mathnet.ru/eng/ufa/v8/i4/p43
    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Уфимский математический журнал
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    Russian version PDF:136
    English version PDF:13
    References:73
     
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