Inverse scattering problem in anisotropic media
type: Item
instance of: scholarly article
title: Inverse scattering problem in anisotropic media
zbMATH Open document ID: 0952.35085
author: Gregory Eskin
published in: Communications in Mathematical Physics
publication date: 2001-01-04T00:00:00Z
review text: Second-order elliptic equations in \(\mathbb{R}^n\) which carry no smallness assumptions on the coefficients are considered (and rewritten as an Laplace-Beltrami equation). From the scattering amplitudes the integrals are recovered. So it is possible to obtain a class of scattering invariants (constructed from the amplitude) by using results of geometric optics. These invariants are used to recover the metric tensor from the hodographic function (solving the hodographic problem). It is shown that for different operators from the considered class with the same scattering amplitude the metrics in semigeodesic coordinates can be reconstructed. If these metrics are close in terms of the Sobolev norm in semigeodesic coordinates, they are unique up to a diffeomorphism so one can pulling back the metrics into each other.
reviewed by: Thoralf Chrobok
Mathematics Subject Classification ID: 35P25
Mathematics Subject Classification ID: 35J05
Mathematics Subject Classification ID: 47A40
Mathematics Subject Classification ID: 81U40
zbMATH DE Number: 1330572
zbMATH Keywords: inverse scattering
zbMATH Keywords: scattering invariants
zbMATH Keywords: Laplace-Beltrami equation
zbMATH Keywords: hodograph problem
MaRDI profile type: Publication
full work available at URL: s002200050509
OpenAlex ID: W2084541898
DOI: 10.1007/S002200050509
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description: scientific article; zbMATH DE number 1330572