Related papers: Limited-Diffraction Solutions to Maxwell and to Sc…
The classical free-space solutions of Maxwell's equations for light propagation in one dimension include wave packets of any shape that travel at the speed of light. This includes highly-localised wave packets that remain localised at all…
Traditionally, the diffraction of a scalar wave satisfying Helmholtz equation through an aperture on an otherwise black screen can be solved approximately by Kirchhoff's integral over the aperture. Rubinowicz, on the other hand, was able to…
We analyze the spectral properties and peculiar behavior of solutions of a damped wave equation on a finite interval with a singular damping of the form $\alpha/x$, $\alpha>0$. We establish the exponential stability of the semigroup for all…
We show that 1-D rarefaction wave solutions are unique in the class of bounded entropy solutions to the multidimensional compressible Euler system. Such a result may be viewed as a counterpart of the recent examples of non-uniqueness of the…
Maxwell's equations are cast in the form of the Schr\"{o}dinger equation. The Lanczos propagation method is used in combination with the fast Fourier pseudospectral method to solve the initial value problem. As a result, a time-domain,…
We continue the study of scattering theory for the system consisting of a Schr"odinger equation and a wave equation with a Yukawa type coupling in space dimension 3. In a previous paper we proved the existence of modified wave operators for…
A qubit lattice algorithm (QLA) is developed for Maxwell equations in a two-dimensional Cartesian geometry. In particular, the initial value problem of electromagnetic pulse scattering off a localized 2D dielectric object is considered. A…
The problem of diffraction of an electromagnetic plane wave by a perfectly conducting circular disk and its complementary problem, diffraction by a circular hole in an infinite conducting plate, are rigorously solved using the method of the…
Chirped Bessel waves are introduced as stable (non-diffracting) solutions of the paraxial wave equation in optical antiguides with a power-law radial variation in their index of refraction. Through numerical simulations, we investigate the…
In recent years the topic of localized wave solutions of the homogeneous scalar wave equation, i.e., the wave fields that propagate without any appreciable spread or drop in intensity, has been discussed in many aspects in numerous…
In this paper, we determine the C-infinity type wave front sets of the solutions to the Schrodinger equations with time-dependent variable coefficients and potentials by using the wave packet transform. We introduce the infinite sum and…
In our study we consider nonlinear, power-law field-dependent electrical permitivity and magnetic permeability and investigate the time-dependent Maxwell equations with the self-similar Ansatz. This is a first-order hyperbolic PDE system…
Using the very basic physics principles, we have studied the implications of quantum corrections to classical electrodynamics and the propagation of electromagnetic waves and pulses. The initial nonlinear wave equation for the…
Presented is an overview of electromagnetic versions of the so-called X-type waves intensively studied since their invention in early 1990.-ies in ultrasonics. These waves may be extremely localized both laterally and longitudinally and -…
In recent times, we experimentally realized a quite efficient modeling of the shape of diffraction-resistant optical beams; thus generating for the first time the so-called Frozen Waves (FW), whose longitudinal intensity pattern can be…
Manipulating elastic waves using a transformation approach is challenging due to the complex constitutive relationship. However, for flexural waves, approximated as scalar waves, two straightforward approaches emerge based on geometric…
This paper provides a theoretical analysis of diffraction-limited superresolution, demonstrating that arbitrarily close point sources can be resolved in ideal situations. Precisely, we assume that the incoming signal is a linear combination…
We consider the Maxwell's equations with perfect electric conductor boundary conditions in three-dimensional unbounded domains which are the union of a bounded resonator and one or several semi-infinite waveguides. We are interested in the…
New boundary conditions are imposed on the familiar cylindrical gravitational wave vacuum spacetimes. The new spacetime family represents cylindrical waves in a flat expanding (Kasner) universe. Space sections are flat and nonconical where…
We investigate the diffraction of singularities of solutions to the linear elastic equation on manifolds with edge singularities. Such manifolds are modeled on the product of a smooth manifold and a cone over a compact fiber. For the…