Abstract
An inverse spectral optimization problem is considered: given a matrix potential \({{Q}_{0}}(x)\) and a value \(\lambda {\kern 1pt} \text{*}\), find a matrix function \(\hat {Q}(x)\) closest to \({{Q}_{0}}(x)\) such that the kth eigenvalue of the Sturm–Liouville matrix operator with potential \(\hat {Q}(x)\) matches \(\lambda {\kern 1pt} \text{*}\). 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 second-order nonlinear differential equations known in mathematical physics as systems of nonlinear Schrödinger equations.
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Funding
Sultanaev’s work was supported by the Russian Science Foundation, grant no. 23-21-00225.
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Translated by I. Ruzanova
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Sadovnichii, V.A., Sultanaev, Y.T. & Valeev, N.F. Optimization Spectral Problem for the Sturm–Liouville Operator in a Vector Function Space. Dokl. Math. 108, 406–410 (2023). https://doi.org/10.1134/S1064562423701284
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DOI: https://doi.org/10.1134/S1064562423701284