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This paper is concerned with inverse scattering of plane waves by a locally perturbed infinite plane (which is called a locally rough surface) with the modulus of the total-field data (also called the phaseless near-field data) at a fixed…

Numerical Analysis · Mathematics 2018-08-28 Xiaoxu Xu , Bo Zhang , Haiwen Zhang

We consider a class of self-adjoint Sturm-Liouville problems with rational functions of the spectral parameter in the boundary conditions. The uniform stability for direct and inverse spectral problems is proved for the first time for…

Spectral Theory · Mathematics 2025-09-03 Natalia P. Bondarenko

We develop a model for the reflection and transmission of plane waves by an isotropic layer sandwiched between two uniaxial crystals of arbitrary orientation. In the laboratory frame, reflection and transmission coefficients corresponding…

Materials Science · Physics 2009-04-29 Erik S. Thomson , Larry A. Wilen , John S. Wettlaufer

The inverse problem of spectral analysis for the non-self-adjoint matrix Sturm-Liouville operator on a finite interval is investigated. We study properties of the spectral characteristics for the considered operator, and provide necessary…

Spectral Theory · Mathematics 2014-07-15 Natalia Bondarenko

We examine an inverse backscattering property of wave motion imposed by an obstacle. We show that if the wave propagator decays super-exponentially along the back-scattered geodesics, then the involved scatterer must be trivial. In…

Functional Analysis · Mathematics 2011-01-21 Lung-Hui Chen

We consider a fixed angle inverse scattering problem in the presence of a known Riemannian metric. First, assuming a no caustics condition, we study the direct problem by utilizing the progressing wave expansion. Under a symmetry assumption…

Analysis of PDEs · Mathematics 2021-07-21 Shiqi Ma , Mikko Salo

In this paper, we develop an inverse scattering transform for the integrable focusing nonlinear Schr\"odinger (NLS) equation on the half-line subject to a class of boundary conditions. The method is based on the notions of integrable…

Exactly Solvable and Integrable Systems · Physics 2021-06-22 Cheng Zhang

This paper concerns the inverse scattering problem of a topologically non-trivial waveguide separating two-dimensional topological insulators. We consider the specific model of a Dirac system. We show that a short-range perturbation can be…

Mathematical Physics · Physics 2026-05-20 Guillaume Bal , Xixian Wang , Zhongjian Wang

We provide a general scheme, in the combined frameworks of Mathematical Scattering Theory and Factorization Method, for inverse scattering for the couple of self-adjoint operators $(\widetilde\Delta,\Delta)$, where $\Delta$ is the free…

Analysis of PDEs · Mathematics 2020-01-08 Andrea Mantile , Andrea Posilicano

We study the scattering of a massless scalar field in a generic Kerr background. Using a particular gauge choice based on the current conservation of the radial equation, we give a generic formula for the scattering coefficient in terms of…

High Energy Physics - Theory · Physics 2015-11-09 Bruno Carneiro da Cunha , Fábio Novaes

In the present paper we discuss stationary scattering theory for repulsive Hamiltonians. We show the existence and completeness of stationary wave operators and unitarity of the scattering matrix. Moreover we completely characterize…

Mathematical Physics · Physics 2021-06-30 Kyohei Itakura

In this paper, we address the existence of global solutions to the Cauchy problem for the integrable nonlocal modified Korteweg-de vries (nonlocal mKdV) equation with the initial data $u_0 \in H^{3}(\mathbb{R}) \cap H^{1,1}(\mathbb{R}) $…

Analysis of PDEs · Mathematics 2023-05-29 Anran Liu , Engui Fan

In a recent article the authors showed that the radiative Transfer equations with multiple frequencies and scattering can be formulated as a nonlinear integral system. In the present article, the formulation is extended to handle reflective…

Numerical Analysis · Mathematics 2023-06-12 Olivier Pironneau , Pierre-Henri Tournier

Wave fields obeying the 2D Helmholtz equation on branched surfaces (Sommerfeld surfaces) are studied. Such surfaces appear naturally as a result of applying the reflection method to diffraction problems with straight scatterers bearing…

Mathematical Physics · Physics 2021-02-09 Raphael C. Assier , Andrey V. Shanin

This paper presents a fast high-order method for the solution of two-dimensional problems of scattering by penetrable inhomogeneous media, with application to high-frequency configurations containing (possibly) discontinuous refractivities.…

Numerical Analysis · Mathematics 2023-07-31 Oscar P. Bruno , Ambuj Pandey

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

Inverse scattering focuses on recovering unknown scatterers from wave measurements. A fundamental challenge is determining whether an inverse obstacle problem can be resolved from a single far-field measurement, a task particularly…

Analysis of PDEs · Mathematics 2026-04-15 Huaian Diao , Hongyu Liu , Longyue Tao

In this work we consider the method of non-linear boundary integral equation for solving numerically the inverse scattering problem of obliquely incident electromagnetic waves by a penetrable homogeneous cylinder in three dimensions. We…

Numerical Analysis · Mathematics 2024-02-23 Drossos Gintides , Leonidas Mindrinos

We present an inverse method to compute freeform optical surfaces that transform a light distribution, parameterized by two source planes, into two separate target distributions. The surfaces can be reflectors or lenses, and control both…

In this paper we consider the inverse scattering problem at a fixed energy for the Schr\"odinger equation with a long-range potential in $\ere^d, d\geq 3$. We prove that the long-range part can be uniquely reconstructed from the leading…

Mathematical Physics · Physics 2020-05-22 Ricardo Weder , Dimitri Yafaev