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Scattering of a plane electromagnetic wave by an anisotropic impedance right-angled concave wedge at skew incidence is analyzed. A closed-form solution is derived by reducing the problem to a symmetric order-2 vector Riemann-Hilbert problem…

Mathematical Physics · Physics 2014-01-16 Y. A. Antipov

We propose a new approach for proving uniqueness of semi-wavefronts in generally non-monotone monostable reaction-diffusion equations with distributed delay. This allows to solve an open problem concerning the uniqueness of non-monotone…

Classical Analysis and ODEs · Mathematics 2019-02-27 Abraham Solar , Sergei Trofimchuk

In recent time, by working in a plane with the metric associated with wave equation (the Special Relativity non-definite quadratic form), a complete formalization of space-time trigonometry and a Cauchy-like integral formula have been…

Mathematical Physics · Physics 2012-09-17 F. Catoni , P. Zampetti

The molecular theory of Rayleigh light scattering in dense isotropic polar fluids is reconsidered by suitably adapting local field concepts of electrostatics to propagating electromagnetic waves, hence accounting for both the rotational and…

Statistical Mechanics · Physics 2026-05-14 P. M. Déjardin

We consider an inverse boundary value problem for a semilinear wave equation on a time-dependent Lorentzian manifold with time-like boundary. The time-dependent coefficients of the nonlinear terms can be recovered in the interior from the…

Analysis of PDEs · Mathematics 2021-01-27 Peter Hintz , Gunther Uhlmann , Jian Zhai

We give an example of a scalar second order differential operator in the plane with double periodic coefficients and describe its modification, which causes an additional spectral band in the essential spectrum. The modified operator is…

Analysis of PDEs · Mathematics 2017-08-14 F. L. Bakharev , G. Cardone , S. A. Nazarov , J. Taskinen

We investigate, within the framework of linear elasticity theory, edge Rayleigh waves of a two-dimensional elastic solid with broken time-reversal and parity symmetries due to a Berry term. As our prime example, we study the elastic edge…

Mesoscale and Nanoscale Physics · Physics 2021-08-04 Claudio Benzoni , Bhilahari Jeevanesan , Sergej Moroz

The paper continues the analysis, started in [1] (Part I,arXiv:2302.04353), of the model open wave-guide problem defined by 2 semi-infinite, rectangular wave-guides meeting along a common perpendicular line. In Part I we reduce the solution…

Mathematical Physics · Physics 2025-11-11 Charles L. Epstein

We prove short-time existence of smooth solutions for a class of nonlinear, and in general spatially nonlocal, Hamiltonian evolution equations that describe the self-interaction of weakly nonlinear scale-invariant waves. These equations…

Analysis of PDEs · Mathematics 2007-05-23 John K. Hunter

We consider inverse problems for non-linear hyperbolic and elliptic equations and give an introduction to the method based on the multiple linearization, or on the construction of artificial sources, to solve these problems. The method is…

Analysis of PDEs · Mathematics 2025-03-18 Matti Lassas

Many applications require recovering the geometry information of multiple elastic particles based on the scattering information. In this paper, we consider the inverse time-harmonic elastic scattering of multiple rigid particles in three…

Mathematical Physics · Physics 2022-09-21 Jun Lai , Jinrui Zhang

This paper recovers Hermitian connections of semi-linear wave equations with cubic nonlinearity. The main novelty is in the geometric generality: we treat the case of an arbitrary globally hyperbolic Lorentzian manifold. Our approach is…

Analysis of PDEs · Mathematics 2025-10-01 Lauri Oksanen , Ruochong Zhang

This paper focuses on stability estimates of the inverse random source problems for the polyharmonic, electromagnetic, and elastic wave equations. The source is represented as a microlocally isotropic Gaussian random field, which is defined…

Analysis of PDEs · Mathematics 2024-10-11 Peijun Li , Ying Liang , Xu Wang

Let $c$ be a piecewise smooth wave speed on $\mathbb R^n$, unknown inside a domain $\Omega$. We are given the solution operator for the scalar wave equation $(\partial_t^2-c^2\Delta)u=0$, but only outside $\Omega$ and only for initial data…

Analysis of PDEs · Mathematics 2018-01-11 Peter Caday , Maarten V. de Hoop , Vitaly Katsnelson , Gunther Uhlmann

This work is concerned with the propagation of electromagnetic waves in isotropic chiral media and with the effects produced by a plane boundary between two such media. In analogy with the phenomena of reflection and refraction of plane…

Optics · Physics 2007-05-23 Jose F. Nieves , Palash B. Pal

Possibility of asymmetric square convection is investigated numerically using a few mode Lorenz-like model for thermal convection in Boussinesq fluids confined between two stress free and conducting flat boundaries. For relatively large…

Pattern Formation and Solitons · Physics 2009-10-31 Alaka Das , Ujjal Ghosal , Krishna Kumar

We consider nonlinear elastic wave equations generalizing Gol'dberg's five constants model. We analyze the nonlinear interaction of two distorted plane waves and characterize the possible nonlinear responses. Using the boundary measurements…

Analysis of PDEs · Mathematics 2018-05-11 Maarten de Hoop , Gunther Uhlmann , Yiran Wang

In this paper, we consider the numerical approximation of the Steklov eigenvalue problem that arises in inverse acoustic scattering. The underlying scattering problem is for an inhomogeneous isotropic medium. These eigenvalues have been…

Analysis of PDEs · Mathematics 2021-04-21 Isaac Harris

Exact solutions describing the Rayleigh-Bloch waves for the two-dimensional Helmholtz equation are constructed in the case when the refractive index is a sum of a constant and a small amplitude function which is periodic in one direction…

Mathematical Physics · Physics 2018-06-13 A. Merzon , P. Zhevandrov , M. I. Romero Rodríguez , J. E. De la Paz Méndez

We consider the problem of recovering material parameters in a transversely isotropic medium from the qP and qSV waves' travel times, given the axis of isotropy and the material parameters associated to the qSH wave speed. The operators…

Analysis of PDEs · Mathematics 2022-07-28 Yuzhou Zou