Inverse scattering for impedance Schrödinger operators. I: Step-like impedance lattice
type: Item
instance of: scholarly article
title: Inverse scattering for impedance Schrödinger operators. I: Step-like impedance lattice
zbMATH Open document ID: 1382.34094
published in: Journal of Mathematical Analysis and Applications
publication date: 2017-11-02T00:00:00Z
review text: The main aim of this paper is to study the inverse scattering problem for the Schrödinger equation on the line in impedance form \[ ({1\over p^{2}(x)} {d\over dx} p^{2}(x) {d\over dx}+\omega^{2})u(x,\omega)=0, \] where the impedance function \(p\) is uniformly positive, uniformly bounded on the whole line and has jumps located at the vertices of a periodic lattice. A direct method -- that can be considered as discrete analogous of the classical Marchenko approach for the full line potential scattering -- for reconstructing piece-wise constant impedance functions \(p\) is developed.
reviewed by: Mihai Pascu
Mathematics Subject Classification ID: 34L25
Mathematics Subject Classification ID: 81U40
Mathematics Subject Classification ID: 34L40
zbMATH DE Number: 6802303
zbMATH Keywords: inverse scattering problem
zbMATH Keywords: one dimensional Schrödinger operator
zbMATH Keywords: piece-wise constant impedance
author: S. Albeverio
author: R. Hryniv
author: Ya. Mykytyuk
MaRDI profile type: Publication
full work available at URL: j.jmaa.2017.07.068
OpenAlex ID: W2743877454
cites work: Recovery of discontinuities in a non-homogeneous medium
cites work: Inverse scattering for discontinuous impedance Schrödinger operators: a model example
cites work: Q3992922
cites work: Q5522887
cites work: Inverse scattering for Schrödinger operators with Miura potentials: I. Unique Riccati representatives and ZS-AKNS systems
cites work: Inverse problems in scattering. An introduction
cites work: Inverse scattering problem for an elastic layered medium
cites work: Inverse Scattering for Schrödinger Operators with Miura Potentials, II. Different Riccati Representatives
cites work: Q5556050
cites work: Inverse scattering method in electromagnetic sounding theory
cites work: Q3997293
cites work: Sturm-Liouville operators and applications. Transl. from the Russian by A. Iacob
cites work: Q3969279
cites work: Continuous and Discrete Inverse-Scattering Problems in a Stratified Elastic Medium. I. Plane Waves at Normal Incidence
DOI: 10.1016/J.JMAA.2017.07.068
description: scientific article; zbMATH DE number 6802303