Related papers: Sub-luminal wave bullets: Exact Localized sublumin…
In this paper we present and analyse a high accuracy method for computing wave directions defined in the geometrical optics ansatz of Helmholtz equation with variable wave number. Then we define an "adaptive" plane wave space with small…
We survey functional analytic methods for studying subwavelength resonator systems. In particular, rigorous discrete approximations of Helmholtz scattering problems are derived in an asymptotic subwavelength regime. This is achieved by…
The existence of localized electromagnetic structures is discussed in the framework of the 1-dimensional relativistic Maxwell-fluid model for a cold plasma with immobile ions. New partially localized solutions are found with a…
The classical solution to the Helmholtz wave equation in spherical coordinates is well known and has found many important applications in wave propagation, scattering, and imaging in optics and acoustics. The separable solution is comprised…
We derive an asymptotically accurate formula for the beam waist of ultrashort, tightly-focused fundamental linearly-polarized, radially-polarized, and azimuthally-polarized modes in free space. We compute the exact beam waist via numerical…
We study the propagation and scattering of electromagnetic waves by random arrays of dipolar cylinders in a uniform medium. A set of self-consistent equations, incorporating all orders of multiple scattering of the electromagnetic waves, is…
Many advances in reflective metasurfaces have been made during the last few years, implementing efficient manipulations of wavefronts, especially for plane waves. Despite numerous solutions that have been developed throughout the years, a…
We consider three novel PDEs associated with the integrable generalizations of the short pulse equation classified recently by Hone {\it et al} (2018 {\it Lett. Math. Phys.} {\bf 108} 927-947). In particular, we obtain a variety of exact…
The dynamics of short intense electromagnetic pulses propagating in a relativistic pair plasma with small temperature asymmetry is of current interest. Such pulses were shown to be governed by a nonlinear Schrodinger equation with a new…
Spatially localized structures are key components of turbulence and other spatio-temporally chaotic systems. From a dynamical systems viewpoint, it is desirable to obtain corresponding exact solutions, though their existence is not…
The numerical analysis of elastic wave propagation in unbounded media may be difficult due to spurious waves reflected at the model artificial boundaries. This point is critical for the analysis of wave propagation in heterogeneous or…
I describe a new algorithm for solving nonlinear wave equations. In this approach, evolution takes place on characteristic hypersurfaces. The algorithm is directly applicable to electromagnetic, Yang-Mills and gravitational fields and other…
Recently, two different proofs for large and intermediate-size solitary waves of the nonlocally dispersive Whitham equation have been presented, using either global bifurcation theory or the limit of waves of large period. We give here a…
It is well-known that reliable and efficient domain truncation is crucial to accurate numerical solution of most wave propagation problems. The perfectly matched layer (PML) is a method which, when stable, can provide a domain truncation…
A new simplified formula is derived for the absorption cross section of small dielectric ellipsoidal particles embedded in lossy media. The new expression leads directly to a closed form solution for the optimal conjugate match with respect…
We introduce a new wave formulation for the relativistic Euler equations with vacuum boundary conditions that consists of a system of non-linear wave equations in divergence form with a combination of acoustic and Dirichlet boundary…
The paper is devoted to the study of circularly coiled optical slab waveguides, which is also applicable to acoustical waveguides. We use a change of variables and the classical Frobenius method to compute Bessel functions of complex order…
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…
We address the existence and properties of discrete embedded solitons (ESs), i.e., localized waves existing inside the phonon band in a nonlinear dynamical-lattice model. The model describes a one-dimensional array of optical waveguides…
In this overview paper, we show existence of smooth solitary-wave solutions to the nonlinear, dispersive evolution equations of the form \begin{equation*} \partial_t u + \partial_x(\Lambda^s u + u\Lambda^r u^2) = 0, \end{equation*} where…