Related papers: Predictability of subluminal and superluminal wave…
The Tolman paradox is well known as a base for demonstrating the causality violation by faster-than-light signals within special relativity. It is constructed using a two-way exchange of faster-than-light signals between two inertial…
We study hyperbolic systems of one-dimensional partial differential equations under general, possibly non-local boundary conditions. A large class of evolution equations, either on individual 1-dimensional intervals or on general networks,…
Changing the spheroidal wave equations into new Schro$dinger's form, the super-potential expanded in the series form of the parameter $\alpha$are obtained in the paper. This general form of the super-potential makes it easy to get the…
Astrophysical models developed to explain superluminal motion in beaming phenomena are shown to be incomplete and the correct kinematical expression in any case to predict projected velocities slower than the speed of light. The observed…
We study the ``hyperboloidal Cauchy problem'' for linear and semi-linear wave equations on Minkowski space-time, with initial data in weighted Sobolev spaces allowing singular behaviour at the boundary, or with polyhomogeneous initial data.…
In the first part of our paper we analyze bisolutions and inverses of (non-autonomous) evolution equations. We are mostly interested in pseudo-unitary evolutions on Krein spaces, which naturally arise in linear Quantum Field Theory. We…
We study time evolutions of charged scalar perturbations on the background of a charged hairy black hole, in which the perturbations can be governed by a double-peak effective potential. By extracting quasinormal modes from the waveform of…
Starting from a generic generally covariant classical theory we introduce the logarithmic correction to the quantum wave equation. We demonstrate the emergence of the evolution time from the group of automorphisms of the von Neumann algebra…
In this note we propose a new set of coordinates to study the hyperbolic or non-elliptic cubic nonlinear Schrodinger equation in two dimensions. Based on these coordinates, we study the existence of bounded and continuous hyperbolically…
We give a brief account of supersymmetric Born-Infeld theories with extended supersymmetry, including those with partially broken supersymmetry. Some latest developments in this area are presented. One of them is N=3 supersymmetric…
I present a review of the recent advancements in scattering theory, which provides a unified approach to studying dispersive and hyperbolic equations with general interaction terms and data. These equations encompass time-dependent…
This article addresses linear hyperbolic partial differential equations with non-smooth coefficients and distributional data. Solutions are studied in the framework of Colombeau algebras of generalized functions. Its aim is to prove upper…
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…
A method for studying the causal structure of space-time evolution systems is presented. This method, based on a generalization of the well known Riemann problem, provides intrinsic results which can be interpreted from the geometrical…
In classical continuum physics, a wave is a mechanical disturbance. Whether the disturbance is stationary or traveling and whether it is caused by the motion of atoms and molecules or the vibration of a lattice structure, a wave can be…
Theoretical and numerical wave propagation analysis of an oscillating electric dipole is presented. The results show that upon creation at the source, both the longitudinal electric and transverse magnetic fields propagate superluminally…
Unstable systems such as media with inverted atomic population have been shown to allow the propagation of analytic wavepackets with group velocity faster than that of light, without violating causality. We illuminate the important role…
It is well known that in manifestly Lorentz invariant theories with nontrivial kinetic terms, perturbations around some classical backgrounds can travel faster than light. These exotic "supersonic" models may have interesting consequences…
In this paper, we investigate the problem of electromagnetic wave propagation in hyperbolic nonlinear media. To address this problem, we consider the scalar hyperbolic nonlinear Schr\"odinger system and its coupled version, namely…
We provide a significant extension of the Hyperboloidal Foliation Method introduced by the authors in 2014 in order to establish global existence results for systems of quasilinear wave equations posed on a curved space, when wave equations…