Related papers: Multi-Channel Inverse Scattering Problem on the Li…
A solution of the scattering problem is obtained for the Schr\"odinger equation with the potential of induced dipole interaction, which decreases as the inverse square of the distance. Such a potential arises in the collision of an incident…
A recently formulated version of the eigenchannel method [R. Szmytkowski, Ann. Phys. (N.Y.) {\bf 311}, 503 (2004)] is applied to quantum scattering of Schr\"odinger particles from non-local separable potentials. Eigenchannel vectors and…
We formulate scattering in one dimension due to the coupled Schr\"{o}dinger equation in terms of the $S$ matrix, the unitarity of which leads to constraints on the scattering amplitudes. Levinson's theorem is seen to have the form $\eta(0)…
A multi-channel algebraic scattering theory, to find solutions of coupled-channel scattering problems with interactions determined by collective models, has been structured to ensure that the Pauli principle is not violated. Positive…
We consider the Schr\"odinger equation with a multipoint potential of Bethe-Peierls-Thomas-Fermi type. For this singular potential, we develop scattering and inverse scattering at high energies. In particular, in this framework, our results…
The inverse source problem for the radiative transfer equation is considered, with partial data. Here it is shown that under certain smoothness conditions on the scattering and absorption coefficients, one can recover sources supported in a…
We consider a Sturm-Liouville operator on a finite interval as well as a scattering problem on the real line both with transfer conditions at the origin. On a finite interval we show that the the Titchmarsh-Weyl $m$-function can be uniquely…
We aim to monitor and characterize signals in the subsurface by combining these passive signals with recorded reflection data at the surface of the Earth. To achieve this, we propose a method to create virtual receivers from reflection data…
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 inverse scattering problem of retrieving the structural parameters of a stratified medium consisting of dispersive materials, given knowledge of the complex reflection coefficient in a finite frequency range. It is shown…
Inverse scattering problem for an operator, which is a sum of the operator of the third derivative and of an operator of multiplication by a real function, is solved. The main closed system of equations of inverse problem is obtained. This…
This paper addresses the inverse obstacle scattering problem of simultaneously reconstructing the obstacle geometry and boundary conditions from multi-frequency near-field backscattering data. We first establish rigorous high-frequency…
We give a new proof of well posedness of the inverse modified scattering problem for the Vlasov--Poisson system: for every suitable scattering profile there exists a solution of Vlasov--Poisson which disperses and scatters, in a modified…
In this paper, we study the inverse acoustic medium scattering problem to reconstruct the unknown inhomogeneous medium from far field patterns of scattered waves. We propose the reconstruction scheme based on the Kalman filter, which…
A striking prediction from the random matrix theory in mesoscopic physics is the existence of "open channels": waves that can use multipath interference to achieve perfect transmission across an opaque disordered medium even in the…
An Andreev molecule is a system of closely spaced superconducting weak links accommodating overlapping Andreev Bound States. Recent theoretical proposals have considered one-dimensional Andreev molecules with a single conduction channel.…
The following electromagnetism (EM) inverse problem is addressed. It consists in estimating local radioelectric properties of materials recovering an object from the global EM scattering measurement, at various incidences and wave…
We present a systematic formulation of scattering theory for nonlinear interactions in one dimension and develop a nonlinear generalization of the transfer matrix that has a composition property similar to its linear analog's. We offer…
The scattering problem can be implemented in a square-integrable basis via the so-called $J$-matrix method. While methods to compute the phase shift in the $J$-matrix approach are known, we introduce a novel formula in square-integrable…
We define scattering data for the Newton equation in a potential $V\in C^2(\R^n,\R)$, $n\ge2$, that decays at infinity like $r^{-\alpha}$ for some $\alpha\in (0,1]$. We provide estimates on the scattering solutions and scattering data and…