Riemann-Hilbert problem approach for two-dimensional flow inverse scattering
type: Item
instance of: scholarly article
zbMATH Open document ID: 1305.81133
DOI: 10.1063/1.4896741
published in: Journal of Mathematical Physics
publication date: 2014-11-06T00:00:00Z
Mathematics Subject Classification ID: 81U40
Mathematics Subject Classification ID: 35R30
Mathematics Subject Classification ID: 35P25
Mathematics Subject Classification ID: 35G35
Mathematics Subject Classification ID: 35Q40
Mathematics Subject Classification ID: 35Q15
Mathematics Subject Classification ID: 76Q05
Mathematics Subject Classification ID: 81Q05
zbMATH DE Number: 6366344
zbMATH Keywords: time-harmonic wave equation
zbMATH Keywords: inverse problem
zbMATH Keywords: inverse scattering problem
zbMATH Keywords: reconstruction algorithms
zbMATH Keywords: non-local Riemann-Hilbert problem
author: A. D. Agaltsov
author: R. G. Novikov
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1063/1.4896741
OpenAlex ID: W2046432369
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title: Riemann-Hilbert problem approach for two-dimensional flow inverse scattering
review text: Inverse scattering problem for time-harmonic wave equation with first-order perturbation in two dimensions is considered. Namely, consider the equation NEWLINE\[NEWLINE -\Delta \psi -2i A(x) \nabla \psi + V(x) \psi = E \psi, \;\;x \in R^2, \;\;E>0. NEWLINE\]NEWLINE Here \(A=(A_1, A_2)\) and \(V\) are vector and scalar potentials on \(\mathbb R^2\), respectively, under some additional conditions. The above equation can be considered as a model equation for the time-harmonic acoustic pressure \(\psi\) in a two-dimensional moving fluid. The equation can also be considered as the two-dimensional Schrödinger equation at fixed energy \(E\) with the appropriate magnetic and electric potentials. The inverse problem is, given scattering amplitude at fixed \(E>0\), find potentials \(A\) and \(V\). This problem arises in particular in the acoustic tomography of moving fluid. Linearized and nonlinearized reconstruction algorithms are suggested for the problem of inverse scattering. The nonlinearized reconstruction algorithm under consideration is based on the non-local Riemann-Hilbert problem approach. Comparisons with preceding results are given.
reviewed by: Elena V. Tabarintseva
description: scientific article; zbMATH DE number 6366344