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Sibirskii Zhurnal Industrial'noi Matematiki, 2021, Volume 24, Number 2, Pages 116–125
DOI: https://doi.org/10.33048/SIBJIM.2021.24.209 (Mi sjim1134) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Bäcklund transformations for the one-dimensional Schrödinger equation

M. V. Neshchadimab

a Sobolev Institute of Mathematics SB RAS, pr. Acad. Koptyuga 4, Novosibirsk 630090, Russia
b Novosibirsk State University, ul. Pirogova 1, Novosibirsk 630090, Russia
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DOI: https://doi.org/10.33048/SIBJIM.2021.24.209
Abstract: We study the system of equations which bases on the one-dimensional Schrödinger equation and connects the potential, amplitude, and phase functions. Using the methods of compatibility theory of systems of partial differential equations, we obtain the completely integrable systems that connect only two functions of the above three. As a corollary, we construct some exact solutions of the Schrödinger equation.
Keywords: Schrödinger equation, Bäcklund transformation, compatibility condition.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation 0314-2019-0011
The author was supported by the State Task of the Sobolev Institute of Mathematics (project no. 0314-2019-0011).
Received: 05.02.2021
Revised: 11.02.2021
Accepted: 15.04.2021
English version:
Journal of Applied and Industrial Mathematics, 2021, Volume 15, Issue 2, Pages 307–314
DOI: https://doi.org/10.1134/S1990478921020125
Bibliographic databases:
Document Type: Article
UDC: 517.95
Language: Russian
Citation: M. V. Neshchadim, “Bäcklund transformations for the one-dimensional Schrödinger equation”, Sib. Zh. Ind. Mat., 24:2 (2021), 116–125; J. Appl. Industr. Math., 15:2 (2021), 307–314
Citation in format AMSBIB
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\by M.~V.~Neshchadim
\paper B\"{a}cklund transformations for the one-dimensional Schr\"{o}dinger equation
\jour Sib. Zh. Ind. Mat.
\yr 2021
\vol 24
\issue 2
\pages 116--125
\mathnet{http://mi.mathnet.ru/sjim1134}
\crossref{https://doi.org/10.33048/SIBJIM.2021.24.209}
\elib{https://elibrary.ru/item.asp?id=47509023}
\transl
\jour J. Appl. Industr. Math.
\yr 2021
\vol 15
\issue 2
\pages 307--314
\crossref{https://doi.org/10.1134/S1990478921020125}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85116236772}
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    • This publication is cited in the following 1 articles:
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    		Сибирский журнал индустриальной математики
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