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We develop the Riemann-Hilbert problem approach to inverse scattering for the two-dimensional Schrodinger equation at fixed energy. We obtain global or generic versions of the key results of this approach for the case of positive energy and…

Mathematical Physics · Physics 2016-12-19 Evgeny L. Lakshtanov , Roman G. Novikov , Boris R. Vainberg

Light-matter interactions inside turbid medium can be controlled by tailoring the spatial distribution of energy density throughout the system. Wavefront shaping allows selective coupling of incident light to different transmission…

Optics · Physics 2017-09-06 M. Koirala , R. Sarma , H. Cao , A. Yamilov

We consider the third-order linear differential equation $$\displaystyle\frac{d^3\psi}{dx^3}+Q(x)\,\displaystyle\frac{d\psi}{dx}+P(x)\,\psi=k^3\,\psi,\qquad x\in\mathbb R,$$ where the complex-valued potentials $Q$ and $P$ are assumed to…

Mathematical Physics · Physics 2025-06-12 Tuncay Aktosun , Ivan Toledo , Mehmet Unlu

We consider the inverse problem of reconstructing an effective model for a prototypical diffusion process in strongly heterogeneous media based on coarse measurements. The approach is motivated by quasi-local numerical effective forward…

Numerical Analysis · Mathematics 2020-05-05 Alfonso Caiazzo , Roland Maier , Daniel Peterseim

We present a solution method for the inverse scattering problem for integrable two-dimensional relativistic quantum field theories, specified in terms of a given massive single particle spectrum and a factorizing S-matrix. An arbitrary…

Mathematical Physics · Physics 2016-08-09 Sabina Alazzawi , Gandalf Lechner

We consider inverse obstacle and transmission scattering problems where the source of the incident waves is located on a smooth closed surface that is a boundary of a domain located outside of the obstacle/inhomogeneity of the media. The…

Mathematical Physics · Physics 2017-10-12 Evgeny Lakshtanov , Boris Vainberg

This paper aims to solve numerically the two-dimensional inverse medium scattering problem with far-field data. This is a challenging task due to the severe ill-posedness and strong nonlinearity of the inverse problem. As already known, it…

Numerical Analysis · Mathematics 2025-09-25 Kai Li , Bo Zhang , Haiwen Zhang

This paper is concerned with the problem of scattering of time-harmonic electromagnetic waves from an impenetrable obstacle in a piecewise homogeneous medium. The well-posedness of the direct problem is established, employing the integral…

Analysis of PDEs · Mathematics 2015-05-18 Xiaodong Liu , Bo Zhang , Jiaqing Yang

An Inverse Scattering Method is developed for the Camassa-Holm equation. As an illustration of our approach the solutions corresponding to the reflectionless potentials are explicitly constructed in terms of the scattering data. The main…

Exactly Solvable and Integrable Systems · Physics 2007-05-23 Adrian Constantin , Vladimir S. Gerdjikov , Rossen I. Ivanov

In this work we propose a theoretical and computational framework for solving the three dimensional inverse medium scattering problem, based on a set of data-driven basis arising from the linearized problem. This set of data-driven basis…

Numerical Analysis · Mathematics 2026-01-27 Yuyuan Zhou , Lorenzo Audibert , Shixu Meng , Bo Zhang

In this paper, an efficient iterative method is proposed for solving multiple scattering problem in locally inhomogeneous media. The key idea is to enclose the inhomogeneity of the media by well separated artificial boundaries and then…

Numerical Analysis · Mathematics 2019-10-23 Ziqing Xie , Rui Zhang , Bo Wang , Li-lian Wang

We discuss a time-harmonic inverse scattering problem for a nonlinear Helmholtz equation with compactly supported inhomogeneous scattering objects that are described by a nonlinear refractive index in unbounded free space. Assuming the…

Analysis of PDEs · Mathematics 2022-02-14 Roland Griesmaier , Marvin Knöller , Rainer Mandel

We consider the inverse problem of recovering the optical properties of a highly-scattering medium from acousto-optic measurements. Using such measurements, we show that the scattering and absorption coefficients of the radiative transport…

Analysis of PDEs · Mathematics 2016-09-27 Francis J Chung , John C Schotland

In this paper we introduce a reproducing kernel Hilbert space defined on $\mathbb{R}^{d+1}$ as the tensor product of a reproducing kernel defined on the unit sphere $\mathbb{S}^{d}$ in $\mathbb{R}^{d+1}$ and a reproducing kernel defined on…

Numerical Analysis · Mathematics 2015-12-24 Johann S. Brauchart , Josef Dick , Lou Fang

In this paper, a reconstruction method for the spatially distributed dielectric constant of a medium from the back scattering wave field in the frequency domain is considered. Our approach is to propose a globally convergent algorithm,…

Analysis of PDEs · Mathematics 2016-03-01 Michael V. Klibanov , Loc H. Nguyen , Anders Sullivan , Lam Nguyen

This paper is concerned with time domain forward scattering and inverse scattering problems with a single moving point source as the emitter. Approximate solutions are provided for the forward scattering problem with a moving emitter.…

Numerical Analysis · Mathematics 2025-10-13 Yu Sun , Bo Chen , Peng Gao , Qiuyi Li , Yao Sun

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

Consider the scattering of the two- or three-dimensional Helmholtz equation where the source of the electric current density is assumed to be compactly supported in a ball. This paper concerns the stability analysis of the inverse source…

Analysis of PDEs · Mathematics 2016-07-26 Peijun Li , Ganghua Yuan

Mean-field control problems have received continuous interest over the last decade. Despite being more intricate than in classical optimal control, the linear-quadratic setting can still be tackled through Riccati equations. Remarkably, we…

Optimization and Control · Mathematics 2023-08-23 Pierre-Cyril Aubin-Frankowski , Alain Bensoussan

We study a reproducing kernel Hilbert space of functions defined on the positive integers and associated to the binomial coefficients. We introduce two transforms, which allow us to develop a related harmonic analysis in this Hilbert space.…

Complex Variables · Mathematics 2014-12-19 Daniel Alpay , Palle Jorgensen