Obtaining scattering kernels using invariant imbedding
type: Item
instance of: scholarly article
title: Obtaining scattering kernels using invariant imbedding
zbMATH Open document ID: 0542.35058
DOI: 10.1016/0022-247X(83)90115-4
author: James Corones
author: Robert J. Krueger
published in: Journal of Mathematical Analysis and Applications
publication date: 1983-01-01T00:00:00Z
review text: Scattering kernels are the kernels of certain integral operators that transform incident waves into reflected and transmitted waves. For the wave equation \(u_{xx}-u_{tt}+A(x)u_ x+B(x)u_ t=0,\) in which A and B have compact support, the authors use ideas of invariant imbedding to obtain nonlinear equations for the four scattering kernels. Here the methods of invariant imbedding require the determination of the effect of perturbing the supports of A and B. The rather involved analysis is described clearly. The results are illustrated by applying them to an example in which A and B are equal and constant. The relatively simple analysis is contrasted with the more complicated investigation of this example by another method.
Mathematics Subject Classification ID: 35P25
Mathematics Subject Classification ID: 35L10
Mathematics Subject Classification ID: 35R05
Mathematics Subject Classification ID: 35R20
zbMATH DE Number: 3861676
zbMATH Keywords: invariant imbedding
zbMATH Keywords: scattering kernels
MaRDI profile type: Publication
cites work: Q4089129
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description: scientific article; zbMATH DE number 3861676