Related papers: Causality in Propagation of a Pulse in a Nonlinear…
We prove the existence of fast traveling pulse solutions in excitable media with non-local coupling. Existence results had been known, until now, in the case of local, diffusive coupling and in the case of a discrete medium, with…
Particles moving along curved trajectories will diffuse if the curvature fluctuates sufficiently in either magnitude or orientation. We consider particles moving at a constant speed with either a fixed or with a Gaussian distributed…
We investigate the spatio-temporal evolution of a Gaussian probe pulse propagating through a four-level $N$-type atomic medium. At two-photon resonance of probe-and control fields, weaker probe pulses may propagate through the medium with…
We investigate propagation of a pulse pair in a three-level medium under the adiabatic following condition for the general case of unequal oscillator strengths. Exact analytical solutions to the propagation equations have been obtained. It…
This paper examines some of the recent experiments on superluminal propagation. It is well known that Sommerfeld and Brillouin analyzed a rectangular sinusoidal signal propagating through a dispersive medium and derived expressions to…
We study the problem of a temporal discontinuity in the permittivity of an unbounded medium with Lorentzian dispersion. More specifically, we tackle the situation in which a monochromatic plane wave forward-travelling in a (generally lossy)…
Over the past 15 years, several groups have engineered media that are both strongly dispersive and roughly transparent for some finite bandwidth. Relationships and intuitive models that are satisfactory when it is reasonable to neglect…
Propagation of extremely short electromagnetic pulses in a homogeneous doubly-resonant medium is considered in the framework of the total Maxwell-Duffing-Lorentz model, where the Duffing oscillators (anharmonic oscillators with cubic…
The features of propagation of intense waves are of great interest for theory and experiment in electrodynamics and acoustics. The behavior of nonlinear waves in a bounded volume is of especial importance and, at the same time, is an…
Evolution of the main signal in a Lorentz dispersive medium is considered. The signal propagating in the medium is excited by a sine-modulated pulse signal, with its envelope described by a hyperbolic tangent function. Both uniform and…
Starting from the wave equation for a medium with material properties that vary periodically, we study a system of recurrence relations that describe propagation of wave packets that oscillate on the microscale (i.e. on lengths of the order…
In this paper we study the invasion fronts of spatially periodic monotone reaction-diffusion systems in a multi-dimensional setting. We study the pulsating traveling waves that connect the trivial equilibrium, for which all components of…
We address the question about the velocity of signals carried by Bessel beams wave packets propagating in vacuum and having well defined wavefronts in time. We find that this problem is analogous to that of propagation of usual plane wave…
The interaction between a light pulse, traveling in air, and a generic linear, non-absorbing and dispersive structure is analyzed. It is shown that energy conservation imposes a constraint between the group velocities of the transmitted and…
This paper is concerned with pulsating waves for multi-dimensional reaction-diffusion equations in spatially periodic media. First, assuming the existence of pulsating waves connecting two linearly stable steady states, we study the…
We develop a general method allowing one to construct the consistent theory of light pulse propagation through an atomic medium in arbitrary nonlinear regime with respect to the field strength, taking into account the light polarization,…
Researchers claim to have observed superluminal (faster than light) propagation of a laser pulse in a gain medium by a new mechanism in which there is no distortion of the pulse [Nature, 406, 277 (2000)]. Our analysis shows that the…
We present a model describing the transmission of light through atomic media with a vanishing index of refraction. Zero index materials are of particular interest as the infinite phase velocity of light within the material offers the…
Motivated by the growing importance of the fidelity and fidelity susceptibility (FS) in quantum critical phenomena, we use these concepts to describe the pulse propagation inside the dispersive media. It is found that there is a dramatic…
We present a phenomenological approach to dispersion in nonlinear elasticity. A simple, thermomechanically sound, constitutive model is proposed to describe the (non-dissipative) properties of a hyperelastic dispersive solid, without…