Topic
Inverse scattering problem
About: Inverse scattering problem is a research topic. Over the lifetime, 10328 publications have been published within this topic receiving 246234 citations. The topic is also known as: direct scattering problem.
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TL;DR: In this article, a systematic method is developed which allows one to identify certain important classes of evolution equations which can be solved by the method of inverse scattering, where the form of each evolution equation is characterized by the dispersion relation of its associated linearized version and an integro-differential operator.
Abstract: A systematic method is developed which allows one to identify certain important classes of evolution equations which can be solved by the method of inverse scattering The form of each evolution equation is characterized by the dispersion relation of its associated linearized version and an integro-differential operator A comprehensive presentation of the inverse scattering method is given and general features of the solution are discussed The relationship of the scattering theory and Backlund transformations is brought out In view of the role of the dispersion relation, the comparatively simple asymptotic states, and the similarity of the method itself to Fourier transforms, this theory can be considered a natural extension of Fourier analysis to nonlinear problems
2,746 citations
Book•
01 Jan 1983
TL;DR: In this article, the Riesz-Fredholm theory for compact operators is applied to boundary-value problems for the scalar Helmholtz equation and the time-harmonic Maxwell equations.
Abstract: Preface to the Classics Edition Preface Symbols 1. The Riesz-Fredholm theory for compact operators 2. Regularity properties of surface potentials 3. Boundary-value problems for the scalar Helmholtz equation 4. Boundary-value problems for the time-harmonic Maxwell equations and the vector Helmholtz equation 5. Low frequency behavior of solutions to boundary-value problems in scattering theory 6. The inverse scattering problem: exact data 7. Improperly posed problems and compact families 8. The determination of the shape of an obstacle from inexact far-field data 9. Optimal control problems in radiation and scattering theory References Index.
2,135 citations
Book•
26 Sep 1996
TL;DR: Inverse Eigenvalue Problems and Inverse Problem in Electrical Impedance Tomography Inverse Scattering Problem as mentioned in this paper is a regularization theory for Equations of the First Kind.
Abstract: Introduction and Basic Concepts.- Regularization Theory for Equations of the First Kind.- Regularization by Discretization.- Inverse Eigenvalue Problems.- An Inverse Problem in Electrical Impedance Tomography.- An Inverse Scattering Problem.- References.- Index
1,880 citations
Book•
01 Dec 2004
TL;DR: Inverse Problems and Interpretation of Measurements: Inverse problems and interpretation of measurements as mentioned in this paper, classical regularization methods, Statistical Inversion Theory, Nonstationary Inverse Problems, Classical Methods Revisited, Model Problems.
Abstract: Inverse Problems and Interpretation of Measurements.- Classical Regularization Methods.- Statistical Inversion Theory.- Nonstationary Inverse Problems.- Classical Methods Revisited.- Model Problems.- Case Studies.
1,825 citations