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Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia, 2023, Volume 513, Pages 93–98
DOI: https://doi.org/10.31857/S2686954323600477
(Mi danma421)
 

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

MATHEMATICS

Optimization spectral problem for the Sturm–Liouville operator in the space of vector functions

V. A. Sadovnichiiab, Ya. T. Sultanaevbc, N. F. Valeevd

a Lomonosov Moscow State University, Moscow, Russian Federation
b Moscow Center for Fundamental and Applied Mathematics, Moscow, Russian Federation
c Bashkir State Pedagogical University n.a. M. Akmulla, Ufa, Russian Federation
d Institute of Mathematics with Computing Centre, Ufa, Russian Federation
Citations (2)
References:
Abstract: An inverse spectral optimization problem is considered: for a given matrix potential $Q_0(x)$ it is required to find the matrix function $\hat{Q}(x)$ closest to it, such that the $k$-th eigenvalue of the Sturm–Liouville matrix operator with potential $\hat{Q}(x)$ matched the given value $\lambda^*$. The main result of the paper is the proof of existence and uniqueness theorems. Explicit formulas for the optimal potential are established through solutions to systems of nonlinear differential equations of the second order, known in mathematical physics as systems of nonlinear Schrödinger equations
Keywords: inverse spectral problem, optimization problem, vector Sturm–Liouville operator, non-linear system of Schrödinger equations.
Funding agency Grant number
Russian Science Foundation 23-21-00225
Sultanaev’s work was supported by the Russian Science Foundation, grant no. 23-21-00225.
Received: 05.06.2023
Revised: 02.09.2023
Accepted: 21.09.2023
English version:
Doklady Mathematics, 2023, Volume 108, Issue 2, Pages 406–410
DOI: https://doi.org/10.1134/S1064562423701284
Bibliographic databases:
Document Type: Article
UDC: 517.4+519.71
Language: Russian
Citation: V. A. Sadovnichii, Ya. T. Sultanaev, N. F. Valeev, “Optimization spectral problem for the Sturm–Liouville operator in the space of vector functions”, Dokl. RAN. Math. Inf. Proc. Upr., 513 (2023), 93–98; Dokl. Math., 108:2 (2023), 406–410
Citation in format AMSBIB
\Bibitem{SadSulVal23}
\by V.~A.~Sadovnichii, Ya.~T.~Sultanaev, N.~F.~Valeev
\paper Optimization spectral problem for the Sturm--Liouville operator in the space of vector functions
\jour Dokl. RAN. Math. Inf. Proc. Upr.
\yr 2023
\vol 513
\pages 93--98
\mathnet{http://mi.mathnet.ru/danma421}
\crossref{https://doi.org/10.31857/S2686954323600477}
\elib{https://elibrary.ru/item.asp?id=56716601}
\transl
\jour Dokl. Math.
\yr 2023
\vol 108
\issue 2
\pages 406--410
\crossref{https://doi.org/10.1134/S1064562423701284}
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  • This publication is cited in the following 2 articles:
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    Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia
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