Related papers: Inverse scattering problem for the Maxwell's equat…
In this paper, we study the inverse electromagnetic medium scattering problem of estimating the support and shape of medium scatterers from scattered electric or magnetic near-field data. We shall develop a novel direct sampling method…
Solution of the Cox-Thompson inverse scattering problem at fixed energy [1,2,3] is reformulated resulting in semi-analytic equations. The new set of equations for the normalization constants and the nonphysical (shifted) angular momenta are…
A 3D singular integral equation is derived for electromagnetic wave scattering by bodies of arbitrary shape. Its numerical solution by a projection method is outlined.
We study the inverse scattering problem for the three dimensional nonlinear Schroedinger equation with the Yukawa potential. The nonlinearity of the equation is nonlocal. We reconstruct the potential and the nonlinearity by the knowledge of…
A simple method for some class of inverse obstacle scattering problems is introduced. The observation data are given by a wave field measured on a known surface surrounding unknown obstacles over a finite time interval. The wave is…
This paper discusses a fast direct solver using boundary integral equations for Helmholtz transmission problems involving multiple inclusions in two dimensions. Efficiently addressing scattering problems in the presence of numerous…
The purpose of this paper is to solve the inverse scattering problem of nonlinear Alfv\'en waves governed by the three dimensional ideal incompressible MHD system. Bridging together geometric methods and weighted energy estimates, we…
In this paper we present a hybrid approach to numerically solve two-dimensional electromagnetic inverse scattering problems, whereby the unknown scatterer is hosted by a possibly inhomogeneous background. The approach is `hybrid' in that it…
The inverse scattering problem of the three-dimensional Schroedinger equation is considered at fixed scattering energy with spherically symmetric potentials. The phase shifts determine the potential therefore a constructive scheme for…
We present a new formulation for the problem of electromagnetic scattering from perfect electric conductors. While our representation for the electric and magnetic fields is based on the standard vector and scalar potentials ${\bf A},\phi$…
This paper gives a note on an application of the enclosure method to an inverse obstacle scattering problem governed by the Helmholtz equation in two dimensions. It is shown that one can uniquely determine the convex hull of an unknown…
A simple algorithm for the inverse scattering approach to the Camassa-Holm equation is presented.
It is known that the Jost-function formulation of quantum scattering theory can be applied to classical problems concerned with the scattering of a plane scalar wave by a medium with a spherically symmetric inhomogeneity of finite extent.…
New solvable one-dimensional quantum mechanical scattering problems are presented. They are obtained from known solvable potentials by multiple Darboux transformations in terms of virtual and pseudo virtual wavefunctions. The same method…
The direct and inverse scattering problems on the full line are analyzed for a first-order system of ordinary linear differential equations associated with the derivative nonlinear Schr\"odinger equation and related equations. The system…
A new proof is given of the existence of the solution to electromagnetic (EM) wave scattering problem for an impedance body of an arbitrary shape. The proof is based on the elliptic systems theory and elliptic estimates for the solutions of…
A deep learning scheme is proposed to solve the electromagnetic (EM) scattering problems where the profile of the dielectric scatterer of interest is incomplete. As a compensation, a limited amount of scattering data is provided, which is…
We study an inverse scattering problem for the discrete Schr\"{o}dinger operator on the multi-dimensional square lattice, with compactly supported potential. We show that the potential is uniquely reconstructed from a scattering matrix for…
A rigorous mathematical model and an efficient computational method are proposed to solving the inverse elastic surface scattering problem which arises from the near-field imaging of periodic structures. We demonstrate how an enhanced…
We consider the direct electromagnetic scattering problem of time-harmonic obliquely incident waves by a infinitely long, homogeneous and doubly-connected cylinder in three dimensions. We apply a hybrid integral equation method (combination…