OPTIMIZATION SPECTRAL PROBLEM FOR THE STURM-LIOUVILLE OPERATOR IN THE SPACE OF VECTOR FUNCTIONS

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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 \(\lambda {\kern 1pt} *\). 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

About the authors

V. A. Sadovnichii

M.V. Lomonosov Moscow State University

Author for correspondence.
Email: info@rector.msu.ru
Russian Federation, Moscow

Ya. T. Sultanaev

Bashkir State Pedagogical University n.a. M. Akmulla; Moscow Center for Fundamental and Applied Mathematics

Author for correspondence.
Email: sultanaevyt@gmail.com
Russian Federation, Ufa; Russian Federation, Moscow

N. F. Valeev

Institute of Mathematics with Computing Centre

Author for correspondence.
Email: valeevnf@yandex.ru
Russian Federation, Ufa

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