Recovery of the nearest potential field from the \(m\) observed eigenvalues
type: Item
instance of: scholarly article
title: Recovery of the nearest potential field from the \(m\) observed eigenvalues
zbMATH Open document ID: 1493.34052
author: Nur Valeev
author: Ya. Sh. Il'yasov
published in: Physica D
publication date: 2022-02-21T00:00:00Z
review text: In this work, authors consider a new class of inverse problems. An approach to a complete solution to such a problem is developed. Within the framework of this approach, they consider a model problem of recovering the potential field \(\hat{V}\) from \(m\) observed eigenvalues of the Schrödinger operator, provided that such potential field is at the minimum distance from a priori given potential \(V_{a}\). In the main result, they establish a new type of relationship between the linear spectral problems and systems of nonlinear differential equations which enables us to find a solution to the inverse optimal spectral problem and obtain novel results on the existence of solutions to nonlinear problems as well.
reviewed by: B. Keskin
Mathematics Subject Classification ID: 34A55
Mathematics Subject Classification ID: 34L40
zbMATH DE Number: 7477787
zbMATH Keywords: inverse spectral problem
zbMATH Keywords: system of nonlinear equations
zbMATH Keywords: Schrödinger equation
zbMATH Keywords: Sturm-Liouville operator
zbMATH Keywords: optimal tuning problem
MaRDI profile type: Publication
full work available at URL: j.physd.2021.132985
OpenAlex ID: W3179524333
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DOI: 10.1016/J.PHYSD.2021.132985
description: scientific article; zbMATH DE number 7477787