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Much experimental evidence of superluminal phenomena has been available by electromagnetic wave propagation experiments, with the results showing that the phase time do describe the barrier traversal time. Based on the extrapolated phase…
We consider the one-dimensional Maxwell equations with low contrast periodic linear refractive index and weak Kerr nonlinearity. In this context, wave packet initial conditions with a single carrier frequency excite infinitely many…
Since the early works[1-4] on the so-called nondiffracting waves (called also Localized Waves), a great deal of results has been published on this important subject, from both the theoretical and the experimental point of view. Initially,…
A formulation for stationary axisymmetric electromagnetic fields in general relativity is derived by casting them into the form of an anisotropic fluid. Several simplifications of the formalism are carried out in order to analyze different…
The field of scalar and vector potentials in electrodynamics is shown to represent an informational field capable of superluminally transmitting a signal (information) with no energy and momentum transfer. This conclusion strictly follows…
We express Maxwell's equations as a single equation, first using the divergence of a special type of matrix field to obtain the four current, and then the divergence of a special matrix to obtain the Electromagnetic field. These two…
Using similarity transformations we construct explicit nontrivial solutions of nonlinear Schr\"odinger equations with potentials and nonlinearities depending on time and on the spatial coordinates. We present the general theory and use it…
We obtain a class of rotating charged stationary circularly symmetric solutions of Einstein-Maxwell theory coupled to a topological mass term for the Maxwell field. These solutions are regular, have finite mass and angular momentum, and are…
An axisymmetric space-localized solution of nonlinear electrodynamics is considered as massive charged particle with spin and magnetic moment. The appropriate solution for nonlinear electrodynamics with ring singularity is investigated. In…
We consider the Maxwell field coupled to a single rotating charge. This Hamiltonian system admits soliton-type solutions, where the field is static, while the charge rotates with constant angular velocity. We prove that any solution of…
Recently, no-go theorems for the existence of solitonic solutions in Einstein-Maxwell-scalar (EMS) models have been established in arXiv:1902.07721. Here we discuss how these theorems can be circumvented by a specific class of non-minimal…
We present exact solutions to the Einstein-Maxwell system of equations in spherically symmetric gravitational fields with a specified form of the electric field intensity. The condition of pressure isotropy yields a difference equation with…
The focusing cubic NLS is a canonical model for the propagation of laser beams. In dimensions 2 and 3, it is known that a large class of initial data leads to finite time blow-up. Now, physical experiments suggest that this blow-up does not…
The transformation converting equations invariant under Lorentz into the equations invariant under Galileo is obtained. On this basis: (1) the super-light electromagnetic wave with longitudinal and transversal modes is found out; (2) it is…
Many physically interesting quantities of the electromagnetic field can be computed using the electromagnetic scalar product. However, none of the existing expressions for such scalar product are directly applicable when the fields are only…
We take as starting point the planar model arising from the dimensional reduction of the Maxwell Electrodynamics with the (Lorentz-violating) Carroll-Field-Jackiw term. We then write and study the extended Maxwell equations and the…
We consider the focusing $L^2$-supercritical Schr\"odinger equation in the exterior of a smooth, compact, strictly convex obstacle. We construct a solution behaving asymptotically as a solitary waves on $R^3$, as large time. When the…
The study explores the conformable electromagnetic field theory. The concept of the conformable delta function is introduced. Subsequently, the conformable Maxwell's equations are derived.
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 $D^\frac{1}{2}\xi$…
We construct Einstein-Maxwell-Scalar (EMS) theories that admit regular electric black holes. Such a Maxwell-scalar theory is equivalent to some nonlinear electrodynamics (NLED) at the level of equations of motion, but it has the advantage…