Related papers: Can N-th Order Born Approximation Be Exact?
A simple closed form expression is obtained for the scattering phase shift perturbatively to any given order in effective one-dimensional problems. The result is a hierarchical scheme, expressible in quadratures, requiring only knowledge of…
The main aim of this paper is twofold. (1) Exact solutions of a scalar field in the Schwarzschild spacetime are presented. The exact wave functions of scattering states and bound-states are presented. Besides the exact solution, we also…
Spectral analysis is performed on the Born equation, a strongly singular integral equation modeling the interactions between electromagnetic waves and arbitrarily shaped dielectric scatterers. Compact and Hilbert--Schmidt operator…
We present a new class of exact self-similar solutions possessing cylindrical or spherical symmetry in Born-Infeld theory. A cylindrically symmetric solution describes the propagation of a cylindrical electromagnetic disturbance in a…
This article studies the rational solutions of the Half-Wave Maps equation (HWM) in the non-singular spectrum case. We first provide characterizations to what we call \emph{scattering behavior}, and show that they imply scattering in…
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.…
We propose a numerical method to approximate the scattering amplitudes for the elasticity system with a non-constant matrix potential in dimensions $d=2$ and $3$. This requires to approximate first the scattering field, for some incident…
A rigorous theory of electromagnetic (EM) wave scattering by small perfectly conducting particles is developed. The limiting case when the number of particles tends to infinity is discussed.
We propose a first order equation from which the Schrodinger equation can be derived. Matrices that obey certain properties are introduced for this purpose. We start by constructing the solutions of this equation in 1D and solve the problem…
In the formulation of the problem of scattering of monochromatic waves and the numerical simulation of the solution to the Helmholtz equation, there is a computational inconvenience: the calculation is performed on a finite grid of…
In one dimension one can dissect a scattering potential $ v(x) $ into pieces $ v_i(x) $ and use the notion of the transfer matrix to determine the scattering content of $ v(x) $ from that of $ v_i(x) $. This observation has numerous…
We prove global existence and scattering for small localized solutions of the Cauchy problem for the Zakharov system in 3 space dimensions. The wave component is shown to decay pointwise at the optimal rate of t^{-1}, whereas the…
We formulate a problem that can be viewed as a natural variation of the so-called Pompeiu or Schiffer problem in the context of scattering of plane waves for the Linear Helmholtz equation. For the two dimensional version of this variation,…
We consider the classical self-dual Yang-Mills equation in 3+1-dimensional Minkowski space. We have found an exact solution, which describes scattering of $n$ plane waves. In order to write the solution in a compact form, it is convenient…
A scattering resonance is one of the most striking quantum effects in low-temperature molecular collisions. Predicted decades ago theoretically, they have only been resolved experimentally for systems involving at most four atoms. Extension…
The soliton dressing matrices for the higher-order zeros of the Riemann-Hilbert problem for the $N$-wave system are considered. For the elementary higher-order zero, i.e. whose algebraic multiplicity is arbitrary but the geometric…
A direct three dimensional EIT reconstruction algorithm based on complex geometrical optics solutions and a nonlinear scattering transform is presented and implemented for spherically symmetric conductivity distributions. The scattering…
Shape derivative is an important analytical tool for studying scattering problems involving perturbations in scatterers. Many applications, including inverse scattering, optimal design, and uncertainty quantification, are based on shape…
A self-contained discussion of nonrelativistic quantum scattering is presented in the case of central potentials in one space dimension, which will facilitate the understanding of the more complex scattering theory in two and three…
The numerically stable evaluation of scattering matrix elements near the infrared limit of gauge theories is of great importance for the success of collider physics experiments. We present a novel algorithm that utilizes double precision…