OPTIMIZATION SPECTRAL PROBLEM FOR THE STURM-LIOUVILLE OPERATOR IN THE SPACE OF VECTOR FUNCTIONS-Reference-Cited by-同舟云学术

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

Published:2023-09-01 Issue:1 Volume:513 Page:93-98
ISSN:2686-9543
Container-title:Доклады Российской академии наук. Математика, информатика, процессы управления
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Short-container-title:Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ

Author:

Sadovnichii V. A.¹,Sultanaev Ya. T.²³,Valeev N. F.⁴

Affiliation:

1. M.V. Lomonosov Moscow State University

2. Bashkir State Pedagogical University n.a. M. Akmulla

3. Moscow Center for Fundamental and Applied Mathematics

4. Institute of Mathematics with Computing Centre

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

Publisher

The Russian Academy of Sciences

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