The inverse problem we consider in this tutorial is to determine the shape of an obstacle from the knowledge of the far field pattern for scattering of time-harmonic plane waves. In the first part we will concentrate on the issue of uniqueness, i.e., we will investigate under what conditions an obstacle and its boundary condition can be identified from a knowledge of its far field pattern for i...

A regularized recursive linearization method is developed for a two-dimensional inverse medium scattering problem that arises in near-field optics, which reconstructs the scatterer of an inhomogeneous medium deposited on a homogeneous substrate from data accessible through photon scanning tunneling microscopy experiments. In addition to the ill-posedness of the inverse scattering problems, two ...

The inverse scattering transform for the vector defocusing nonlinear Schrödinger NLS equation with nonvanishing boundary values at infinity is constructed. The direct scattering problem is formulated on a two-sheeted covering of the complex plane. Two out of the six Jost eigenfunctions, however, do not admit an analytic extension on either sheet of the Riemann surface. Therefore, a suitable mod...

this paper is devoted to the proof of the unique solvability ofthe inverse problems for second-order differential operators withregular singularities. it is shown that the potential functioncan be determined from spectral data, also we prove a uniquenesstheorem in the inverse problem.

We consider the scattering of an electromagnetic time harmonic plane wave by very thin obstacles. In this lecture we will restrict ourselves to the scattering of an Epolarized electromagnetic field by a perfectly conducting infinite cylinder having an open arc in R as cross section. We further allow the possibility that one side of the cylinder is coated with a dielectric material. This leads t...