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We study an inverse random obstacle scattering problems in $\mathbb{R}^2$ where the scatterer is formulated by a Gaussian process defined on the angular parameter domain. Equipped with a modified covariance function which is mathematically…
A review of some of the author's results in the area of inverse scattering is given. The following topics are discussed: 1) Property $C$ and applications, 2) Stable inversion of fixed-energy 3D scattering data and its error estimate, 3)…
We consider the fixed angle inverse scattering problem and show that a compactly supported potential is uniquely determined by its scattering amplitude for two opposite fixed angles. We also show that almost symmetric or horizontally…
We develop the analytical method of field momenta for analyzing the dynamics of optical vector solitons in photorefractive nonlinear media. First, we derive the effective evolution equations for the parameters of multi-component solitons…
The $J$-matrix inverse scattering approach can be used as an alternative to a conventional $R$-matrix in analyzing scattering phase shifts and extracting resonance energies and widths from experimental data. A great advantage of the…
The challenge of solving the initial value problem for the coupled Lakshmanan Porsezian Daniel equation, while considering nonzero boundary conditions at infinity, is addressed through the development of a suitable inverse scattering…
This paper is concerned with the inverse electromagnetic scattering problem for anisotropic media. We use the interior resonant modes to develop an inverse scattering scheme for imaging the scatterer. The whole procedure consists of three…
A static scission configuration in cold ternary fission has been considered in the framework of mean field approach. The inverse scattering method is applied to solve single-particle Schroedinger equation, instead of constrained…
Inverse scattering and spectral one-dimensional problems are discussed systematically in a self-contained way. Many novel results, due to the author are presented. The classical results are often presented in a new way. Several highlights…
We propose a tomographic method to reconstruct the optical properties of a highly-scattering medium from incoherent acousto-optic measurements. The method is based on the solution to an inverse problem for the diffusion equation and makes…
We develop three inverse elastic scattering schemes for locating multiple small, extended and multiscale rigid bodies, respectively. There are some salient and promising features of the proposed methods. The cores of those schemes are…
We present a framework to solve the open problem of formulating the inverse scattering method (ISM) for an integrable PDE on a star-graph. The idea is to map the problem on the graph to a matrix initial-boundary value (IBV) problem and then…
The initial-value problem for cylindrical gravitational waves is studied through the development of the inverse scattering method scheme. The inverse scattering transform in this case can be viewed as a transformation of the Cauchy data to…
Various versions of the Bethe ansatz are suggested for evaluation of scattering two-magnon states in 2D and 3D Heisenberg-Ising ferromagnets. It is shown that for 2D square (3D qubic) finite-periodic or infinite lattices about a half (3/4)…
The numerical algorithm of the inverse quantum scattering is developed. This algorithm is based on the Marchenko theory, and includes three steps. The first one is the algebraic Pade approximation of the unitary S-matrix, what is realized…
In this work, we are interested in the determination of the shape of the scatterer for the two dimensional time harmonic inverse medium scattering problems in acoustics. The scatterer is assumed to be a piecewise constant function with a…
In this paper we present a theory of vessels and its application to the classical inverse scattering of the Sturm-Liouville differential equation. The classical inverse scattering theory, including all its ingredients: Jost solutions, the…
Inverse scattering problem for the operator representing sum of the operator of the third derivative on semi-axis and of the operator of multiplication by a real function is studied in this paper. Properties of Jost solutions of such an…
The inverse problem for electromagnetic field produced by arbitrary altered charge distribution in dipole approximation is solved. The charge distribution is represented by its dipole moment. It is assumed that the spectral properties of…
On a fixed Riemann surface $(M_0,g_0)$ with $N$ Euclidean ends and genus $g$, we show that, under a topological condition, the scattering matrix $S_V(\la)$ at frequency $\la > 0$ for the operator $\Delta+V$ determines the potential $V$ if…