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We develop a dynamical formulation of one-dimensional scattering theory where the reflection and transmission amplitudes for a general, possibly complex and energy-dependent, scattering potential are given as solutions of a set of dynamical…

Quantum Physics · Physics 2015-06-17 Ali Mostafazadeh

In this paper, we study the Strichartz-type estimates of the solution for the linear wave equation with inverse square potential. Assuming the initial data possesses additional angular regularity, especially the radial initial data, the…

Analysis of PDEs · Mathematics 2013-12-09 Changxing Miao , Junyong Zhang , Jiqiang Zheng

In what follows we first set the context for inverse scattering in nuclear physics with a brief account of inverse problems in general. We then turn to inverse scattering which involves the S-matrix, which connects the interaction potential…

Nuclear Theory · Physics 2012-05-03 Raymond S. Mackintosh

Formulas are derived for solutions of many-body wave scattering problems by small particles in the case of acoustically soft, hard, and impedance particles embedded in an inhomogeneous medium. The limiting case is considered, when the size…

Mathematical Physics · Physics 2011-05-10 Alexander G. Ramm

In this paper we generalise our previous results [1] concerning scattering on the exterior of collapsing dust clouds to the charged case, including in particular the extremal case. We analyse the energy boundedness of solutions $\phi$ to…

General Relativity and Quantum Cosmology · Physics 2023-09-07 Frederick Alford

We introduce a model to design reflectors that take into account the inverse square law for radiation. We prove existence of solutions, both in the near and far field cases, when the input and output energies are prescribed.

Analysis of PDEs · Mathematics 2013-05-31 Cristian E. Gutierrez , Ahmad Sabra

Electromagnetic (EM) wave scattering by many parallel infinite cylinders is studied asymptotically as a tends to 0, where a is the radius of the cylinders. It is assumed that the centres of the cylinders are distributed so that their…

Computational Physics · Physics 2015-06-05 A. G. Ramm , M. I. Andriychuk

We derive dispersion estimates for solutions of a one-dimensional discrete Dirac equations with a potential. In particular, we improve our previous result, weakening the conditions on the potential. To this end we also provide new results…

Spectral Theory · Mathematics 2022-04-11 Elena Kopylova , Gerald Teschl

We study the direct and inverse scattering problem for the one-dimensional Schr\"odinger equation with steplike potentials. We give necessary and sufficient conditions for the scattering data to correspond to a potential with prescribed…

Spectral Theory · Mathematics 2017-08-04 Iryna Egorova , Zoya Gladka , Till Luc Lange , Gerald Teschl

This paper is concerned with the direct and inverse random source scattering problems for elastic waves where the source is assumed to be driven by an additive white noise. Given the source, the direct problem is to determine the…

Analysis of PDEs · Mathematics 2016-08-10 Gang Bao , Chuchu Chen , Peijun Li

Seismic data are commonly modeled by a high-frequency single scattering approximation. This amounts to a linearization in the medium coefficient about a smooth background. The discontinuities are contained in the medium perturbation. The…

Analysis of PDEs · Mathematics 2009-09-25 Christiaan C. Stolk , Maarten V. de Hoop

In this article, we study the inverse scattering problem for the nonlinear fractional Helmholtz equation with cubic nonlinearity in three dimensions, where we recover a compactly supported potential from scattering amplitude.

Analysis of PDEs · Mathematics 2026-03-30 Saumyajit Das , Susovan Pramanik

We present a new method for the control of waves based on inverse multiple scattering theory. Conceived as a generalization of the concept of metagrating, we call metaclusters to a finite set of scatterers whose position and properties are…

Applied Physics · Physics 2021-02-03 Pawel Packo , Andrew Norris , Dani Torrent

In this paper we consider the inverse electromagnetic scattering for a cavity surrounded by an inhomogeneous medium in three dimensions. The measurements are scattered wave fields measured on some surface inside the cavity, where such…

Analysis of PDEs · Mathematics 2020-12-10 Fang Zeng , Shixu Meng

We study one of multidimensional inverse scattering problems for quantum systems in a constant electric field, by utilization of the Enss-Weder time-dependent method. The main purpose of this paper is to propose some methods of sharpening…

Mathematical Physics · Physics 2023-07-31 Tadayoshi Adachi , Yuta Tsujii

We consider the inverse problem of reconstructing the scattering coefficient of a simple radiative transport equation (RTE) used to model light propagation inside a scattering medium. To do so, we extract information from the second term in…

Analysis of PDEs · Mathematics 2025-08-07 Francis Chung , Faith Hensley

We prove the small energy scattering for the three-dimensional generalized Zakharov system with radial symmetry based on the idea by Guo and Nakanishi (2014), which treats the usual Zakharov system. For the proof, we use the…

Analysis of PDEs · Mathematics 2024-02-12 Jun Kato , Osamu Tojo

We show how the scattering-into-cones and flux-across-surfaces theorems in Quantum Mechanics have very intuitive pathwise probabilistic versions based on some results by Carlen about large time behaviour of paths of Nelson diffusions. The…

Mathematical Physics · Physics 2009-11-07 Andrea Posilicano , Stefania Ugolini

Scattering of electromagnetic waves lies at the heart of most experimental techniques over nearly the entire electromagnetic spectrum, ranging from radio waves to optics and X-rays. Hence, deep insight into the basics of scattering theory…

We develop the scattering theory of general conformally compact metrics. For low frequencies, the domain of the scattering matrix is shown to be frequency dependent. In particular, generalized eigenfunctions exhibit L^2 decay in directions…

Spectral Theory · Mathematics 2007-05-23 David Borthwick