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An ill-posed Cauchy problem for the wave equation is considered: the solution is to be determined by the Cauchy data on some part of the time-space boundary. By means of Fourier method we obtain a regularization algorithm for this problem,…
The scattering of polarized light incident from one dielectric medium on its two-dimensional randomly rough interface with a second dielectric medium is studied. A reduced Rayleigh equation for the scattering amplitudes is derived for the…
We present a new extension of the UKRmol electron-molecule scattering code suite, which allows one to compute ab initio photoionization and photorecombination amplitudes for complex molecules, resolved both on the molecular alignment…
The mediated photon-photon interaction due to the resonant Kerr nonlinearity in an inhomogeneously broadened atomic vapor is considered. The time-scale for photon-photon scattering is computed and found to be determined by the inhomogeneous…
We employ the so-called companion matrix method from computational algebraic geometry, tailored for zero-dimensional ideals, to study the scattering equations. The method renders the CHY-integrand of scattering amplitudes computable using…
A rigorous reduction of the many-body wave scattering problem to solving a linear algebraic system is given bypassing solving the usual system of integral equation. The limiting case of infinitely many small particles embedded into a medium…
Adamjan-Arov (Lax--Phillips) model space is considered as a scattering representation space for a CMV matrix in context of an extended Marchenko--Faddeev scattering theory. That is, there exists a basis in which the multiplication by…
The Schr\"{o}dinger equation, in hyperspherical coordinates, is solved in closed form for a system of three particles on a line, interacting via pair delta functions. This is for the case of equal masses and potential strengths. The…
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…
In this paper, we consider acoustic or electromagnetic scattering in two dimensions from an infinite three-layer medium with thousands of wavelength-size dielectric particles embedded in the middle layer. Such geometries are typical of…
This paper presents a new method to model X-ray scattering on random rough surfaces. It combines the approaches we presented in two previous papers -- \zs\cite{zhao03} \& \pz\cite{zhao15}. An actual rough surface is (incompletely) described…
We consider the nonlinear Schrodinger equation with a modified spatial dispersion, given either by an homogeneous Fourier multiplier, or by a bounded Fourier multiplier. Arguments based on ordinary differential equations yield ill-posedness…
A simple stochastic formulation of the multiple scattering representation solution of the classical linear incoherent trapping problem is presented for a broad audience. A clear connection with the alternative Holstein's solution ansatz is…
We solve the inverse scattering problem for multidimensional vector fields and we use this result to construct the formal solution of the Cauchy problem for the second heavenly equation of Plebanski, a scalar nonlinear partial differential…
We here use our non-perturbative, cluster decomposable relativistic scattering formalism to calculate photon-spinor scattering, including the related particle-antiparticle annihilation amplitude. We start from a three-body system in which…
We study the Cauchy problem for the one-dimensional wave equation with an inverse square potential. We derive dispersive estimates, energy estimates, and estimates involving the scaling vector field, where the latter are obtained by…
Formula for calculating the atomic scattering factor for spherical x-ray waves is derived and used to solve the near field effects problem in X-ray Fluorescence Holography theory. A rigorous formalism to calculate the X-ray fluorescence…
We have obtained new solutions and methods for the process of thermal Comptonization. We modify the solution to the kinetic equation of Sunyaev \& Titarchuk to allow its application up to mildly relativistic electron temperatures and…
This work studies the parameter-dependent diffusion equation in a two-dimensional domain consisting of locally mirror symmetric layers. It is assumed that the diffusion coefficient is a constant in each layer. The goal is to find…
We investigate the scattering phenomena in two dimensions produced by a general finite-range nonseparable potential. This situation can appear either in a Cartesian geometry or in a heterostructure with cylindrical symmetry. Increasing the…