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We study the inverse problem of determining a time-dependent globally hyperbolic Lorentzian metric from the scattering operator for semilinear wave equations.

Analysis of PDEs · Mathematics 2024-11-15 Peter Hintz , Antônio Sá Barreto , Gunther Uhlmann , Yang Zhang

We construct a scattering theory for harmonic one-forms on Riemann surfaces, obtained from boundary value problems involving systems of curves and the jump problem. We obtain an explicit expression for the scattering matrix in terms of…

Differential Geometry · Mathematics 2025-06-11 Eric Schippers , Wolfgang Staubach

High frequency estimates for the Dirichlet-to-Neumann and Neumann-to-Dirichlet operators are obtained for the Helmholtz equation in the exterior of bounded obstacles. These a priori estimates are used to study the scattering of plane waves…

Mathematical Physics · Physics 2013-07-18 Evgeny Lakshtanov , Boris Vainberg

In this paper, scattering of incident plane waves from rough surfaces have been modeled in a fractional space. It is shown how wave scattering from a rough surface, could be a simple reflection problem in a fractional space. In the integer…

Optics · Physics 2013-05-31 H. Safdari , M. Vahabi , G. R. Jafari

We consider the inverse scattering problem to reconstruct a local perturbation of a given inhomogeneous periodic layer in $\mathbb{R}^d$, $d=2,3$, using near field measurements of the scattered wave on an open set of the boundary above the…

Analysis of PDEs · Mathematics 2024-12-20 Alexander Konschin , Armin Lechleiter

The Helmholtz equation in one dimension, which describes the propagation of electromagnetic waves in effectively one-dimensional systems, is equivalent to the time-independent Schr\"odinger equation. The fact that the potential term…

Classical Physics · Physics 2021-09-15 Farhang Loran , Ali Mostafazadeh

This paper is concerned with the cavity scattering problem in an infinite thin plate, where the out-of-plane displacement is governed by the two-dimensional biharmonic wave equation. Based on an operator splitting, the scattering problem is…

Numerical Analysis · Mathematics 2023-01-25 Heping Dong , Peijun Li

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

Analysis of PDEs · Mathematics 2009-12-09 xiaodong Liu , Bo Zhang

A problem of scattering by a Dirichlet right angle on a discrete square lattice is studied. The waves are governed by a discrete Helmholtz equation. The solution is looked for in the form of the Sommerfeld integral. The Sommerfeld…

Mathematical Physics · Physics 2021-12-21 A. V. Shanin , A. I. Korolkov

This paper concerns the stability on the inverse source scattering problem for the one-dimensional Helmholtz equation in a two-layered medium. We show that the increasing stability can be achieved by using multi-frequency wave field at the…

Analysis of PDEs · Mathematics 2017-09-13 Yue Zhao , Peijun Li

We present in this work a numerical model for characterizing the scattering properties of the human lens. After analyzing the scattering properties of two main scattering particles actually described in the literature through Finite Element…

Medical Physics · Physics 2024-01-17 A Cuadrado , LM Sanchez-Brea , FJ Torcal-Milla , JA Quiroga , JA Gomez-Pedrero

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

The Helmholtz wave scattering problem by screens in 2D can be recast into first-kind integral equations which lead to ill-conditioned linear systems after discretization. We introduce two new preconditioners, in the form of square-roots of…

Numerical Analysis · Mathematics 2019-12-03 François Alouges , Martin Averseng

This paper is concerned with the inverse problem of scattering of time-harmonic acoustic waves by an inhomogeneous penetrable obstacle in a piecewise homogeneous medium. The well-posedness of the direct problem is first established by using…

Analysis of PDEs · Mathematics 2009-12-16 Xiaodong Liu , Bo Zhang

In this paper, we use a straightforward numerical method to solve scattering models in one-dimensional lattices based on a tight-binding band structure. We do this by using the wave packet approach to scattering, which presents a more…

Physics Education · Physics 2022-07-06 M. Staelens , F. Marsiglio

Based on the Hamiltonian formalism approach, a generalized L\"uscher's formula for two particle scattering in both the elastic and coupled-channel cases in moving frames is derived from a relativistic Lippmann-Schwinger equation. Some…

High Energy Physics - Lattice · Physics 2013-08-09 Peng Guo , Jozef Dudek , Robert Edwards , Adam P. Szczepaniak

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

We address the direct scattering problem for a penetrable obstacle in an infinite elastic two--dimensional Kirchhoff--Love plate. Under the assumption that the plate's thickness is small relative to the wavelength of the incident wave, the…

Analysis of PDEs · Mathematics 2026-02-20 Rafael Ceja Ayala , Isaac Harris , Tonatiuh Sánchez-Vizuet

The aim of the lecture is to briefly describe the mathematical background of scattering theory for two- and three-particle quantum systems. We discuss basic objects of the theory: wave and scattering operators and the corresponding…

Mathematical Physics · Physics 2022-05-27 Dmitri Yafaev

We start from the remark that in wave turbulence theory, exemplified by the cubic twodimensional Schr{\"o}dinger equation (NLS) on the real plane, the regularity of the resonant manifold is linked with dispersive properties of the equation…

Analysis of PDEs · Mathematics 2023-07-06 Erwan Faou , Antoine Mouzard