Related papers: Diagonalization of pp-waves
Superposition of explicit (analytic) monotone non-increasing shock waves for the KdV-Burgers equation is studied, modelled numerically and graphically presented. Initial profile chosen as a sum of two such shock waves gradually transforms…
We address shock waves generated upon the interaction of tilted plane waves with negative refractive index defect in defocusing media with linear gain and two-photon absorption. We found that in contrast to conservative media where…
Some classes of the so called "travelling wave" solutions of Einstein and Einstein - Maxwell equations in General Relativity and of dynamical equations for massless bosonic fields in string gravity in four and higher dimensions are…
We consider generalised pp-waves with purely axial torsion, which we previously showed to be new vacuum solutions of quadratic metric-affine gravity. Our analysis shows that classical pp-waves of parallel Ricci curvature should not be…
Two methods are explained to exactly solve Maxwell's equations where permittivity, permeability and conductivity may vary in space. In the constitutive relations, retardation is regarded. If the material properties depend but on one…
Tsunamis are often generated by a moving sea bottom. This paper deals with the case where the tsunami source is an earthquake. The linearized water-wave equations are solved analytically for various sea bottom motions. Numerical results…
The theory for large amplitude circularly polarized waves propagating along an external magnetic field is extended in order to include also vacuum polarization effects. A general dispersion relation, which unites previous results, is…
We often observe that waves on the surface of shallow water form complex web-like patterns. They are examples of nonlinear waves, and these patterns are generated by nonlinear interactions among several obliquely propagating waves. In this…
This paper is concerned with the study of the wave equation on compact surfaces and locally distributed damping. We study the case where the damping is effective in a well-chosen subset of arbitrarily small measure.
A formalism is introduced to describe a number of physical processes that may break down the coherence of a matter wave over a characteristic length scale l. In a second-quantized description, an appropriate master equation for a set of…
We present some new derivations of the effect of a plane gravitational wave on a light ray. A simple interpretation of the results is that a gravitational wave causes a phase modulation of electromagnetic waves. We arrive at this picture…
We investigated the modulation in the polarization-dependent optical behaviour of the waveguiding plasmonic crystal by varying the illumination and detection geometry. We employed the finite element method-based COMSOL simulation and…
Matter wave interferometry is becoming an increasingly important technique in quantum metrology. However, unlike its photonic counterpart, this technique relies on the interference of particles possessing a non-zero rest mass and an…
We generalize the pointwise decay estimates for large data solutions of the defocusing semilinear wave equations which we obtained earlier under restriction to spherical symmetry. Without the symmetry the conformal transformation we use…
We extend the transformation-optics paradigm to a complex spatial coordinate domain, in order to deal with electromagnetic metamaterials characterized by balanced loss and gain, giving special emphasis to parity-time (PT) symmetric…
In this article, spatially-structured gravitational waves are investigated. Drawing upon analogies between electrodynamics and general relativity, a new gauge is found. We investigate the polarization and degrees of freedom of the resulting…
The hypothesis of an alternative way of obtaining gravitational waves is the physical motivation of this article. Using the linear field approximation and a symmetry transformation of the affine connection, new field equations and new gauge…
Based on the known implicit solution for nonlinear plasma waves, an explicit solution was obtained in the form of decomposition into harmonics. The solution obtained exhibits a mechanism for steepening of nonlinear plasma wave as a result…
To date, the influence of non-linear stratifications and two layer stratifications on internal wave propagation has been studied for two-dimensional wave fields in a cartesian geometry. Here, we use a novel wave generator configuration to…
Impulsive pp-waves are commonly described either by a distributional spacetime metric or, alternatively, by a continuous one. The transformation $T$ relating these forms clearly has to be discontinuous, which causes two basic problems:…