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We use Maxwell's equations in a sourceless, inhomogeneous medium with continuous permeability $\mu (\mathbf{r}) $ and permittivity $% \epsilon (\mathbf{r}) $ to study the wave propagation. The general form of the wave equation is derived…
The Trefftz Discontinuous Galerkin (TDG) method is a technique for approximating the Helmholtz equation (or other linear wave equations) using piecewise defined local solutions of the equation to approximate the global solution. When…
The computation of light scattering by the superposition T-matrix scheme has been so far restricted to systems made of particles that are either sparsely distributed or of near-spherical shape. In this work, we extend the range of…
Exact solutions for nonexpanding impulsive waves in a background with nonzero cosmological constant are constructed using a `cut and paste' method. These solutions are presented using a unified approach which covers the cases of de Sitter,…
In this paper, we prove even symmetry of monotone traveling wave solutions to the balanced Allen-Cahn equation in the entire plane. Related results for the unbalanced Allen-Cahn equation are also discussed.
A quantum theory of dispersion for an inhomogeneous solid is obtained, from a starting point of multipolar coupled atoms interacting with an electromagnetic field. The dispersion relations obtained are equivalent to the standard classical…
Particle physics has for some time made extensive use of extended field configuations such as solitons, instantons, and sphalerons. However, no direct use has yet been made of the quite extensive literature on ``localized wave''…
We study {\it analytically} the physical and mathematical properties of spatially regular massless scalar field configurations which are non-minimally coupled to the electromagnetic field of a spherically symmetric charged reflecting shell.…
We derive the Hamiltonian describing Pauli-Fierz massive gravitons on a flat Friedmann-Robertson-Walker (FRW) cosmology in a particular, non-generic effective field theory. The cosmological evolution is driven by a scalar field Phi with an…
Massless vector and scalar Green's functions are obtained in closed form for a plane gravitational wave spacetime using three independent methods: direct solution of the Green-function equation and construction via the DeWitt and Hadamard…
The Maxwell equations for the electromagnetic potential, supplemented by the Lorenz gauge condition, are decoupled and solved exactly in de Sitter space-time studied in static spherical coordinates. There is no source besides the…
We show that radiation from complex and inherently random but correlated wave sources can be modelled efficiently by using an approach based on the Wigner distribution function. Our method exploits the connection between correlation…
We give exact results for the emission spectra of both nonlinear Breit-Wheeler pair production and nonlinear Compton scattering in ultra-intense, ultra-short duration plane wave backgrounds, modelled as delta-function pulses. This includes…
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…
We study radial waves in (2+1)-dimensional noncommutative scalar field theory, using operatorial methods. The waves propagate along a discrete radial coordinate and are described by finite series deformations of Bessel-type functions. At…
We consider space-times with two isometries which represent gravitational waves with distinct wavefronts which propagate into exact Friedmann-Robertson-Walker (FRW) universes. The geometry of possible wavefronts is analysed in detail in all…
We consider Einstein's equations coupled to the Euler equations in plane symmetry, with compact spatial slices and constant mean curvature time. We show that for a wide variety of equations of state and a large class of initial data,…
The B\"{a}cklund transformation for the three-level Maxwell-Bloch equation is presented in the matrix potential formalism. By applying the B\"{a}cklund transformation to a constant electric field background, we obtain a general solution for…
We explicitly demonstrate that the known solutions for expanding impulsive spherical gravitational waves that have been obtained by a "cut and paste" method may be considered to be impulsive limits of the Robinson-Trautman vacuum type N…
A formalism is introduced which may describe both standard linearized waves and gravitational waves in Isaacson's high-frequency limit. After emphasizing main differences between the two approximation techniques we generalize the Isaacson…