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A method of solving Maxwell equations in a vicinity of a multipole particle (moving along an arbitrary trajectory) is proposed. The method is based on a geometric construction of a trajectory-adapted coordinate system, which simplifies…
In this paper, we seek to construct nontrivial global solutions to some quasilinear wave equations in three space dimensions. We first present a conditional result on the construction of nontrivial global solutions to a general system of…
We lift the constraint of a diagonal representation of the Hamiltonian by searching for square integrable bases that support a tridiagonal matrix representation of the wave operator. Doing so results in exactly solvable problems with a…
The solution of the Helmholtz equation in optical semiclassic approximation is associated with the calculation of ray paths and matrices of variations. The transformation rules for elements of matrices on the boundaries of the waveguide are…
A numerical technique is described that can efficiently compute solutions in interface problems. These are problems with data, such as the coefficients of differential equations, discontinuous or even singular across one or more interfaces.…
We prove that every solution of the Helmholtz equation within an equilateral triangle, which obeys the Dirichlet conditions on the boundary, is a member of one of four symmetry classes. We then show how solutions with different symmetries,…
Transformation optics constructions have allowed the design of cloaking devices that steer electromagnetic, acoustic and quantum waves around a region without penetrating it, so that this region is hidden from external observations. The…
Two new approaches to solving first-order quasilinear elliptic systems of PDEs in many dimensions are proposed. The first method is based on an analysis of multimode solutions expressible in terms of Riemann invariants, based on links…
A boundary integral equation formulation is presented for the electromagnetic transmission problem where an incident electromagnetic wave is scattered from a bounded dielectric object. The formulation provides unique solutions for all…
In many time-harmonic electromagnetic wave problems, the considered geometry exhibits an axial symmetry. In this case, by exploiting a Fourier expansion along the azimuthal direction, fully three-dimensional (3D) calculations can be carried…
The concept of gauge invariance in classical electrodynamics assumes tacitly that Maxwell's equations have unique solutions. By calculating the electromagnetic field of a moving particle both in Lorenz and in Coulomb gauge and directly from…
This paper aims at developing new shape functions adapted to smooth vanishing coefficients for scalar wave equation. It proposes the numerical analysis of their interpolation properties. The interpolation is local but high order convergence…
Exact solutions describing trapped modes in a plane quantum waveguide with a small rigid obstacle are constructed in the form of convergent series in powers of the small parameter characterizing the smallness of the obstacle. The terms of…
By a bifurcation argument we prove that the capillary-gravity Whitham equation features asymmetrical periodic travelling wave solution of arbitrarily small amplitude. Such waves exist only in the weak surface tension regime…
We look for travelling wave fields $$ E(x,y,z,t)= U(x,y) \cos(kz+\omega t)+ \widetilde U(x,y)\sin(kz+\omega t),\quad (x,y,z)\in\mathbb{R}^3,\, t\in\mathbb{R} $$ satisfying Maxwell's equations in a nonlinear medium which is not necessarily…
In this paper we consider the direct scattering problem of obliquely incident time-harmonic electromagnetic plane waves by an infinitely long dielectric cylinder. We assume that the cylinder and the outer medium are homogeneous and…
We describe traveling waves in a basic model for three-dimensional water-wave dynamics in the weakly nonlinear long-wave regime. Small solutions that are periodic in the direction of translation (or orthogonal to it) form an…
On the quest towards full control over wave propagation, the development of compact devices that allow asymmetric response is a challenge. In this Letter, we introduce a new paradigm for the engineering of asymmetry in planar structures,…
This article aims to present a general study of the Helmholtz problem in slowly varying waveguides. This work is of particular interest at locally resonant frequencies, where a phenomenon close to the tunnel effect for Schr\"odinger…
This paper is concerned with the invisibility cloaking in electromagnetic wave scattering from a new perspective. We are especially interested in achieving the invisibility cloaking by completely regular and isotropic mediums. Our study is…