Inverse scattering in one-dimensional nonconservative media
type: Item
instance of: scholarly article
title: Inverse scattering in one-dimensional nonconservative media
zbMATH Open document ID: 0916.34070
DOI: 10.1007/BF01195585
author: Martin Klaus
author: Tuncay Aktosun
author: C. van der Mee
published in: Integral Equations and Operator Theory
publication date: 1999-05-05T00:00:00Z
review text: The authors give a careful analysis of the direct and inverse scattering problem for the (generalized) Schrödinger equation \[ \psi''+k^2 \psi = (\pm i k P +Q) \psi \] on the real line. Here, as usual, the prime denotes the derivative with respect to the spatial variable \(x\), \(k\) is the wavenumber, and the real-valued functions \(P(x)\) and \(Q(x)\) denote the energy absorption/generation and the restoring force density, respectively. The scattering data of the above equation with the \(+\) sign are suitably defined and are complemented with those of the \(-\) sign equation in order to recover \(P(x)\) and \(Q(x)\). The inverse scattering procedure developed by the authors makes use of a pair of uncoupled Marchenko integral equations. Conditions for the uniqueness of solutions to such equations are presented. The paper concludes with some illustrative examples.
Mathematics Subject Classification ID: 34L25
Mathematics Subject Classification ID: 81U40
Mathematics Subject Classification ID: 74J25
Mathematics Subject Classification ID: 34A55
zbMATH DE Number: 1140087
zbMATH Keywords: inverse scattering
zbMATH Keywords: Marchenko equations
zbMATH Keywords: Riemann-Hilbert problems
reviewed by: J. P. Zubelli
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1140087