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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
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.
Received: 05.06.2023 Revised: 02.09.2023 Accepted: 21.09.2023
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
Linking options:
https://www.mathnet.ru/eng/danma421 https://www.mathnet.ru/eng/danma/v513/p93
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