Discrete scattering theory
type: Item
instance of: scholarly article
title: Discrete scattering theory
zbMATH Open document ID: 0621.34076
DOI: 10.1016/0022-0396(86)90082-3
published in: Journal of Differential Equations
publication date: 1986-01-01T00:00:00Z
review text: The author develops the discrete and inverse scattering theory corresponding to a certain eigenvalue problem of the form \[ \psi (n+1,z)=J(z)\psi (n,z)+J(z)Q_ 0(n)\psi (n,z)+Q_ 1(n)\psi (n+1,z) \] where \(J(z)=diag(z,z^{-1})\) and \(Q_ 0\), \(Q_ 1\) and the unknown \(\psi\) are also \(2\times 2\) matrix-valued functions. This is used to solve the initial value problem for a class of differential-difference equations. The results are similar to those obtained for the continuous case, using different methods, by \textit{R. Beals} and \textit{R. R. Coifman} [Commun. Pure Appl. Math. 37, 39-90 (1984; Zbl 0514.34021)].
Mathematics Subject Classification ID: 34K99
Mathematics Subject Classification ID: 34L99
Mathematics Subject Classification ID: 39A10
Mathematics Subject Classification ID: 34A55
zbMATH DE Number: 4006771
zbMATH Keywords: inverse scattering theory
zbMATH Keywords: matrix-valued functions
zbMATH Keywords: differential- difference equations
author: H. Bhate
reviewed by: Alan L. Andrew
MaRDI profile type: Publication
full work available at URL: 0022-0396(86)90082-3
OpenAlex ID: W2004083290
cites work: The Inverse Scattering Transform‐Fourier Analysis for Nonlinear Problems
cites work: Nonlinear differential−difference equations
cites work: Q3931796
cites work: Scattering and inverse scattering for first order systems
cites work: Inverse scattering on the line
cites work: Q5522887
cites work: Method for Solving the Korteweg-deVries Equation
description: scientific article; zbMATH DE number 4006771