Related papers: On Localized "X-shaped" Superluminal Solutions to …
The wave propagation of edge modes in a superlattice of 2D electron Gases in quantum Hall regime is investigated. After introducing surfaces charge and current densities at the edge, the Maxwell equations are solved for waves running along…
For monochromatic solutions of D'Alembert's wave equation and Maxwell's equations, we obtain sharp bounds on the sup norm as a function of the far field energy. The extremizer in the scalar case is radial. In the case of Maxwell's equation,…
We present the exact solution to the linearized Maxwell equations in space-time slightly curved by a gravitational wave. We show that in general, even dealing with a first-order theory in the strength of the gravitational field, the…
We study propagation of high-frequency electromagnetic waves in a curved spacetime. We demonstrate how a modification of the standard geometric optics allows one to include the helicity dependent corrections into the equations of motion of…
The Riemann -- Silberstein -- Majorana -- Oppenheimer approach to the Maxwell electrodynamics in vacuum is investigated within the matrix formalism. The matrix form of electrodynamics includes three real 4 \times 4 matrices. Within the…
We construct two classes of exact solutions to six and higher dimensional Einstein-Maxwell theory in which the metric functions can be written as convolution-like integrals of two special functions. The solutions are regular everywhere and…
We will provide detailed arguments showing that the set of Maxwell equations, and the corresponding wave equations, do not properly describe the evolution of electromagnetic wave-fronts. We propose a nonlinear corrected version that is…
The scattering of electromagnetic waves by an obstacle is analyzed through a set of partial differential equations combining the Maxwell's model with the mechanics of fluids. Solitary type EM waves, having compact support, may easily be…
We find new solutions to the Einstein-Maxwell equations in the presence of mimetic field in $ D $ dimensions, all of which are asymptotically Antide Sitter. We derive the solutions in five-dimensional spacetime, in detail. By extending the…
We consider Maxwell's equations in a 3-dimensional material, in which both, the electric permittivity, as well as the magnetic permeability, fluctuate in space. Differently from all previous treatments of the disordered electromagnetic…
We prove propagation of weighted Sobolev regularity for solutions of the hyperboloidal Cauchy problem for a class of quasi-linear symmetric hyperbolic systems, under structure conditions compatible with the Einstein-Maxwell equations in…
The general method to obtain solutions of the Maxwellian equations from scalar representatives is developed and applied to the diffraction of electromagnetic waves. Kirchhoff's integral is modified to provide explicit expressions for these…
A new formulation of the Maxwell equations based on two vector and two scalar potentials is proposed. The use of these potentials allows the electromagnetic field equations to be written in the form of a hyperbolic system. In contrast to…
We present the application of the variational-wavelet analysis to the quasiclassical calculations of the solutions of Wigner/von Neumann/Moyal and related equations corresponding to the nonlinear (polynomial) dynamical problems. (Naive)…
This paper studies highly oscillatory solutions to a class of systems of semilinear hyperbolic equations with a small parameter, in a setting that includes Klein--Gordon equations and the Maxwell--Lorentz system. The interest here is in…
We outline a regular way for solving Maxwell's equations. We take, as the starting point, the notion of vector potentials. The rationale for introducing this notion in electrodynamics is that the set of Maxwell's equations is seemingly…
We consider a linearized Euler--Maxwell model for the propagation and absorption of electromagnetic waves in a magnetized plasma. We present the derivation of the model, and we show its well-posedeness, its strong and polynomial stability…
We extend the duality symmetry between the electric and the magnetic fields to the case in which an additional axion-like term is present, and we derive the set of Maxwell's equations that preserves this symmetry. This new set of equations…
The existence and the properties of isolated solutions to the relativistic Vlasov-Maxwell system with initial data on the backward hyperboloid $t=-\sqrt{1+|x|^2}$ are investigated. Isolated solutions of Vlasov-Maxwell can be defined by the…
Superluminal behavior has been extensively studied in recent years, especially with regard to the topic of superluminality in the propagation of a signal. Particular interest has been devoted to Bessel-X waves propagation, since some…