Related papers: Numerical results of solving 3D inverse scattering…
The inverse scattering problem for the relativistic three-dimensional equation $\Bigl(2E_{\bf p'}-2E_{\bf p}\Bigr)<{\bf p'}|\Psi_{\bf p}>= -\int V(t)d^3{\bf p''}<{\bf p''}|\Psi_{\bf p}>$ with $E_{\bf p}=\sqrt{m^2+{\bf p}^2}$ and…
In this paper we review the results of the author on the theory of scalar and vector wave scattering by small bodies of an arbitrary shape with the emphasis on practical applicability of the formulas obtained and on the mathematical rigor…
A numerical solution to the problem of wave scattering by many small particles is studied under the assumption k<<1, d>>a, where a is the size of the particles and d is the distance between the neighboring particles. Impedance boundary…
This paper is about perfectly electrically conducting structures designed to produce negligible scattered power when exposed to a time-harmonic plane electromagnetic wave. The structures feature cavities capable of concealing objects.…
We will consider the resolution of the 3D non linear wave equation under the assumption of spherical symmetry on the euclidian space. For this purpose, we will build a non trivial measure on distributions such that there exists a set of…
We introduce two data completion algorithms for the limited-aperture problems in inverse acoustic scattering. Both completion algorithms are independent of the topological and physical properties of the unknown scatterers. The main idea is…
Let $f\in L^2(S^2)$ be an arbitrary fixed function with small norm on the unit sphere $S^2$, and $D\subset \R^3$ be an arbitrary fixed bounded domain. Let $k>0$ and $\alpha\in S^2$ be fixed. It is proved that there exists a potential $q\in…
We prove that the singularities of a potential in the two and three dimensional Schr\"odinger equation are the same as the singularities of the Born approximation (Diffraction Tomography), obtained from backscattering inverse data, with an…
In three dimensional scattering, the energy continuum wavefunction is obtained by utilizing two independent solutions of the reference wave equation. One of them is typically singular (usually, near the origin of configuration space). Both…
We study quantum scattering theory off $n$ point inhomogeneities ($n\in\bbN$) in three dimensions. The inhomogeneities (or generalized point interactions) positioned at $\{\xi_1,...,\xi_n\}\subset\bbR^3$ are modeled in terms of the $n^2$…
We develop direct and inverse scattering theory for one-dimensional Schroedinger operators with steplike potentials which are asymptotically close to different finite-gap periodic potentials on different half-axes. We give a complete…
This work is concerned with various aspects of the formulation of the quantum inverse scattering method for the one-dimensional Hubbard model. We first establish the essential tools to solve the eigenvalue problem for the transfer matrix of…
We study the nonlinear Schr\"odinger equation with an inverse-square potential in dimensions $3\leq d \leq 6$. We consider both focusing and defocusing nonlinearities in the mass-supercritical and energy-subcritical regime. In the focusing…
We transform an inverse scattering problem to be an interior transmission problem. We find an inverse uniqueness on the scatterer with a knowledge of a fixed interior transmission eigenvalue. By examining the solution in a series of…
An approximate method is proposed for the recovery of a compactly supported spherically-symmetric potential from the set of fixed-energy phase-shifts known for all angular momenta. The method reduces the inverse scattering problem to a…
This paper is concerned with the inverse spectral problem for the third-order differential equation with distribution coefficient. The inverse problem consists in the recovery of the differential expression coefficients from the spectral…
In this paper, we develop a high order numerical method for the numerical solutions of scattering problems with slightly perturbed periodic surfaces in two dimensional spaces. Based on the regularity property introduced in Part I, the…
We consider a linearized inverse scattering problem for elastic waves. We prove that a fully anisotropic perturbation of the elastic parameters around an isotropic and homogeneous reference can be uniquely determined by (single-)scattered…
We apply the Marchenko method of quantum inverse scattering to study nucleon scattering problems. Assuming a $\beta/r^2$ type repulsive core and comparing our results to the Reid93 phenomenological potential we estimate the constant…
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…