Related papers: On the Localized superluminal Solutions to the Max…
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 address the issue of potential superluminal propagation of gravitational waves in backgrounds neighboring the previously suggested bounce [arXiv:1807.08361] in beyond Horndeski theory. We find that the bouncing solution lies right at the…
Spatially dispersive (also known as non-local) electromagnetic media are considered where the parameters defining the permittivity relation vary periodically. Maxwell's equations give rise to a difference equation corresponding to the…
Localization phenomena in light scattering from random fluctuations of matter fields and spacetime metric near a black hole horizon were predicted to produce a pronounced peak in the angular distribution of second harmonic light in the…
We study the stochastic viscous nonlinear wave equations (SvNLW) on $\mathbb T^2$, forced by a fractional derivative of the space-time white noise $\xi$. In particular, we consider SvNLW with the singular additive forcing $D^\frac{1}{2}\xi$…
It is known that in quantum field theory, localized operations, e.g.\ given by unitary operators in local observable algebras, may lead to non-causal, or superluminal, state changes within their localization region. In this article, it is…
We propose and discuss a new approach to the analysis of the correlation functions which contain light-like Wilson lines or loops, the latter being cusped in addition. The objects of interest are therefore the light-like Wilson…
Recent theoretical results show the existence of arbitrary speeds (0 <= v < \infty) solutions of all relativistic wave equations. Some recent experiments confirm the results for sound waves. The question arises naturally: What is the…
Encyclopedic article covering shallow water wave models used in oceanography and atmospheric science. Sections: Definition of the Subject; Introduction and Historical Perspective; Completely Integrable Shallow Water Wave Equations; Shallow…
An asymptotic investigation of monochromatic electromagnetic fields in a layered periodic medium is carried out under the assumption that the wave frequency is close to the frequency of a stationary point of the dispersion surface. We find…
It is shown in linear approximation that in the case of one-dimensional problem of transverse electron waves in a half-infinite slab of homogeneous Maxwellian collisionless plasma with the given boundary field frequency two wave branches of…
Based on nonlocal symmetry method, localized excitations and interactional solutions are investigated for the reduced Maxwell-Bloch equations. The nonlocal symmetries of the reduced Maxwell-Bloch equations are obtained by the truncated…
The existence of resonant enhanced transmission and collimation of light waves by subwavelength slits in metal films [for example, see T.W. Ebbesen et al., Nature (London) 391, 667 (1998) and H.J. Lezec et al., Science, 297, 820 (2002)]…
A new method for numerical solving of boundary problem for ordinary differential equations with slowly varying coefficients which is aimed at better representation of solutions in the regions of their rapid oscillations or exponential…
The existence of twisted light may be inferred from modern quantum concepts and experimental data. These waves possess energy, impulse and angular momentum. However, the Maxwell's four-dimensional theory of electromagnetism does not imply…
A method for solving a quasilinear nonelliptical equation of the second order is developed and we give classification and parametrization of simple elements of the equation.We find exact solutions of an equation for potential stationary…
Assuming that a formal approximation of multiple waves has been obtained by matched asymptotic methods, we derive a {\em Spatial Shadowing lemma} to construct exact solutions near the formal approximation. In Part I, we consider a general…
We consider wave equations on Lorentzian manifolds in case of low regularity. We first extend the classical solution theory to prove global unique solvability of the Cauchy problem for distributional data and right hand side on smooth…
For semi-linear wave equations with null form non-linearities on $\mathbb{R}^{3+1}$, we exhibit an open set of initial data which are allowed to be large in energy spaces, yet we can still obtain global solutions in the future. We also…
For the short pulse initial data with a first order outgoing constraint condition and optimal orders of smallness, we establish the global existence of smooth solutions to 2D quasilinear wave equations with higher order null conditions.…