Related papers: On the Localized superluminal Solutions to the Max…
An alternate set of equations to describe the electrodynamics of superconductors at a macroscopic level is proposed. These equations resemble equations originally proposed by the London brothers but later discarded by them. Unlike the…
We study the propagation properties of the solutions of the finite-difference space semi-discrete wave equation on an uniform grid of the whole Euclidean space. We provide a construction of high frequency wave packets that propagate along…
The representation of solutions of Maxwell's equations as superpositions of scalar wavelets with vector coefficients developed earlier is generalized to wavelets with polarization, which are matrix-valued. The construction proceeds in four…
We introduce an exact analytical solution of the homogeneous space-fractional Helmholtz equation in cylindrical coordinates. This solution, called vector Space-Fractional Bessel Beam (SFBB), has been established from the Lorenz' gauge…
We analyse the superluminal propagation of narrow-band pulses at resonances in dissipative media. The output waveform is an attenuated, undistorted, time-advanced version of the input which can be interpreted as the result of the…
Our aim in this paper is to recall some essential points of "Extended special Relativity", now more correctly called "Non-Restricted special Relativity" theory (NRR), and in particular of the extended Maxwell Equations; as well as to set…
We present an analytical description of the nonlocal optical response of plasmonic nanowire metamaterials that enable negative refraction, subwavelength light manipulation, and emission lifetime engineering. We show that dispersion of…
The detection of a stochastic background of low-frequency gravitational waves by pulsar-timing and astrometric surveys will enable tests of gravitational theories beyond general relativity. These theories generally permit gravitational…
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…
Two-dimensional periodic surface waves propagating under the combined influence of gravity and surface tension on water of finite depth are considered. Within the framework of small-amplitude waves, we find the exact solutions of the…
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…
The article first studies the propagation of well prepared high frequency waves with small amplitude $\eps$ near constant solutions for entropy solutions of multidimensional nonlinear scalar conservation laws. Second, such oscillating…
The so-called Localized Waves (LW), and the "Frozen Waves" (FW), have arisen significant attention in the areas of Optics and Ultrasound, because of their surprising energy localization properties. The LWs resist the effects of diffraction…
Propagation, transmission and reflection properties of linearly polarized plane waves and arbitrarily short electromagnetic pulses in one-dimensional dispersionless dielectric media possessing an arbitrary space-time dependence of the…
We identify a large class of systems of semilinear wave equations, on fixed accelerated expanding FLRW spacetimes, with nearly at spatial slices, for which we prove small data future global well-posedness. The family of systems we consider…
We study the existence of polychromatic solutions of cubically nonlinear Maxwell equations in the whole space and with dispersive media, i.e., with a time delayed polarization. Due to the complex nature of the dielectric function, the…
In this article we present a systematic derivation of the Maxwell-Bloch equations describing amplification and laser action in a ring cavity. We derive the Maxwell-Bloch equations for a two-level medium and discuss their applicability to…
We develop a general theory for the existence, uniqueness, and higher regularity of solutions to wave-type equations on Lorentzian manifolds with timelike curves of cone-type singularities. These singularities may be of geometric type (cone…
We discuss the possible relation between certain geometrical properties of the loop space and energy evolution of the cusped Wilson exponentials defined on the light-cone. Analysis of the area differential equations for this special class…
The behavior of wave signals in the far zone is not only of theoretical interest but also of paramount practical importance in communications and other fields of applications of optical, electromagnetic or acoustic waves. Long time ago T.…