The purpose of this chapter is to provide a survey of our book by placing what we have to
say in a historical context. We obviously cannot give a complete account of inverse …

Looking Back on Inverse Scattering Theory Page 1 Copyright © by SIAM. Unauthorized
reproduction of this article is prohibited. SIAM REVIEW c 2018 Society for Industrial and Applied …

The present Special Issue on Inverse Problems consists of five invited papers, which
basically refer to the solution of nonlinear inverse wave scattering problems. So far, the …

FOR MORE THAN A CENTURY the problem of solving Helmholtz equation, or the reduced
wave equation, in exterior domains has occupied a central position in the fields of acoustics …

In 1967 a new method of mathematical physics was discovered by Gardner, Greene,
Kruskal, and Miura. Their significant results have received much attention, and numerous …

Using the single-scattering approximation we invert for the material parameters of an
acoustic two-parameter medium and then for a three-parameter isotropic elastic medium …

The field of inverse scattering theory has been a particularly active field in applied
mathematics for the past 25 years. The aim of research in this field has been to not only …

The inverse scattering problem consists of determining the functional form of a scattering
potential given the scattering matrix A (kos. koso) for all scattering directions s and one or …

The inverse problem the authors consider is to determine the shape of a sound-soft two-
dimensional time-harmonic acoustic scatterer from the knowledge of the scattered far-field …

We survey some of the highlights of inverse scattering theory as it has developed over the
last 15 years, with emphasis on uniqueness theorems and reconstruction algorithms for time …