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We analyze the inverse scattering series for diffuse waves in random media. In previous work the inverse series was used to develop fast, direct image reconstruction algorithms in optical tomography. Here we characterize the convergence,…

Analysis of PDEs · Mathematics 2009-11-13 Shari Moskow , John C. Schotland

Scattering-type scanning near-field optical microscopy is a powerful imaging technique for studying materials beyond the diffraction limit. However, interpreting near-field measurements poses challenges in mapping the response of…

The standard unitarity-cut method is applied to several massive two-dimensional models, including the world-sheet AdS$_5\times S^5$ superstring, to compute $2\to 2$ scattering S-matrices at one loop from tree level amplitudes. Evidence is…

High Energy Physics - Theory · Physics 2014-01-03 Valentina Forini , Lorenzo Bianchi , Ben Hoare

In this paper we demonstrate a computational method to solve the inverse scattering problem for a star-shaped, smooth, penetrable obstacle in 2D. Our method is based on classical ideas from computational geometry. First, we approximate the…

This paper is concerned with the inverse elastic scattering problem for a random potential in three dimensions. Interpreted as a distribution, the potential is assumed to be a microlocally isotropic Gaussian random field whose covariance…

Analysis of PDEs · Mathematics 2021-02-16 Jianliang Li , Peijun Li , Xu Wang

Here we discuss a regularized version of the factorization method for positive operators acting on a Hilbert Space. The factorization method is a qualitative reconstruction method that has been used to solve many inverse shape problems. In…

Analysis of PDEs · Mathematics 2022-04-11 Isaac Harris

Scattering is a ubiquitous phenomenon which is observed in a variety of physical systems which span a wide range of length scales. The scattering matrix is the key quantity which provides a complete description of the scattering process.…

Statistical Mechanics · Physics 2014-01-21 André Nock , Santosh Kumar , Hans-Jürgen Sommers , Thomas Guhr

Scattering problem for a self-adjoint integro-differential operator, which is the sum of the operator of second derivative and of a finite-dimensional self-adjoint operator, is studied. Jost solutions are found and it is shown that the…

Classical Analysis and ODEs · Mathematics 2023-12-25 Vladimir A. Zolotarev

We present a solution method for the integrable system (derivative nonlinear Schr\"odinger II system) or the Chen--Lee--Liu system. This is done by presenting a solution technique for the inverse scattering problem for the corresponding…

Exactly Solvable and Integrable Systems · Physics 2025-07-30 Mehmet Unlu

A simple and efficient variational method is introduced to accelerate the convergence of the eigenenergy computations for a Hamiltonian H with singular potentials. Closed-form analytic expressions in N dimensions are obtained for the matrix…

Mathematical Physics · Physics 2009-11-10 Nasser Saad , Richard L. Hall , Qutaibeh D. Katatbeh

We consider the multi-channel inverse scattering problem in one-dimension in the presence of thresholds and bound states for a potential of finite support. Utilizing the Levin representation, we derive the general Marchenko integral…

Quantum Physics · Physics 2009-11-10 M. Braun , S. A. Sofianos , H. Leeb

We study an inverse source scattering problem for the Schr\"odinger equation with a quadratic nonlinearity. In general, uniqueness of inverse source problems can not be guaranteed at a fixed energy. Therefore, additional information is…

Analysis of PDEs · Mathematics 2023-03-22 Lei Zhang , Yue Zhao

The direct and inverse scattering problems on the full line are analyzed for a first-order system of ordinary linear differential equations associated with the derivative nonlinear Schr\"odinger equation and related equations. The system…

Mathematical Physics · Physics 2019-08-15 Tuncay Aktosun , Ramazan Ercan

We introduce a new iterative method to recover a real compact supported potential of the Schr\"odinger operator from their fixed angle scattering data. The method combines a fixed point argument with a suitable approximation of the…

Analysis of PDEs · Mathematics 2018-07-16 Juan A. Barceló , Carlos Castro , Teresa Luque , Mari Cruz Vilela

The inverse scattering problem of the three-dimensional Schroedinger equation is considered at fixed scattering energy with spherically symmetric potentials. The phase shifts determine the potential therefore a constructive scheme for…

Mathematical Physics · Physics 2011-11-28 Tamas Palmai , Barnabas Apagyi

The use of orthonormal wavelet basis functions for solving singular integral scattering equations is investigated. It is shown that these basis functions lead to sparse matrix equations which can be solved by iterative techniques. The…

Nuclear Theory · Physics 2009-11-10 B. M. Kessler , G. L. Payne , W. N. Polyzou

We describe inverse scattering for the matrix Schroedinger operator with general selfadjoint boundary conditions at the origin using the Marchenko equation. Our approach allows the recovery of the potential as well as the boundary…

Mathematical Physics · Physics 2007-05-23 M. Harmer

We report on the recent construction of a scattering theory for Maxwell potentials on curved spacetimes.

General Relativity and Quantum Cosmology · Physics 2024-05-01 Grigalius Taujanskas

In the present paper we describe a simple black box algorithm for efficiently and accurately solving scattering problems related to the scattering of time-harmonic waves from radially-symmetric potentials in two dimensions. The method uses…

Numerical Analysis · Mathematics 2020-08-03 Jeremy Hoskins , Vladimir Rokhlin

This research focuses on the possibility of the surjective relation between symmetric potential function and its scattering matrix in 1-dimension. The theory bases on the property of wave function symmetry and boundary conditions. This…

Quantum Physics · Physics 2022-12-29 Youngik Lee