Propagation of exremely short pulses in non-resonant media: the total Maxwell-Duffing model

Many intriguing properties of driven nonlinear resonators, including the appearance of chaos, are very important for understanding the universal features of nonlinear dynamical systems and can have great practical significance. We consider a cylindrical cavity resonator driven by an alternating voltage and filled with a nonlinear nondispersive medium. It is assumed that the medium lacks a center of inversion and the dependence of the electric displacement on the electric fiel...

In an attempt to solve Maxwell's first order system of equations, starting from a given initial state, it is found that a consistent solution depending on the temporal evolution of the sources cannot be calculated. The well known retarded solutions of the second order equations, which are based on the introduction of potentials, turn out to be in disagreement with a direct solution of the first order system.

We consider the evolution of ultra-short optical pulses in linear and nonlinear media. For the linear case, we first show that the initial-boundary value problem for Maxwell's equations in which a pulse is injected into a quiescent medium at the left endpoint can be approximated by a linear wave equation which can then be further reduced to the linear short-pulse equation. A rigorous proof is given that the solution of the short pulse equation stays close to the solutions of ...

In a previous paper [Phys. Rev. E64 (2001) 066603; e-print physics/0001039], we showed that localized Superluminal solutions to the Maxwell equations exist, which propagate down (non-evanescence) regions of a metallic cylindrical waveguide. In this paper we construct analogous non-dispersive waves propagating along coaxial cables. Such new solutions, in general, consist in trains of (undistorted) Superluminal "X-shaped" pulses. Particular attention is paid to the construction...

We consider the full set of Maxwell equations in a slab or cylindrical waveguide with a cubically nonlinear material law for the polarization of the electric field. The nonlinear polarization may be instantaneous or retarded, and we assume it to be confined inside the core of the waveguide. We prove existence of infinitely many spatially localized, real-valued and time-periodic solutions (breathers) propagating inside the waveguide by applying a variational minimization metho...

We will provide detailed arguments showing that the set of Maxwell equations, and the corresponding wave equations, do not properly describe the evolution of electromagnetic wave-fronts. We propose a nonlinear corrected version that is proven to be far more appropriate for the modellization of electromagnetic phenomena. The suitability of this approach will soon be evident to the reader, through a sequence of astonishing congruences, making the model as elegant as Maxwell's, ...

We derive a model for the propagation of short pulses in nonlinear media. The model is a higher order regularization of the short pulse equation (SPE). The regularization term arises as the next term in the expansion of the susceptibility in derivation of the SPE. Without the regularization term there do not exist traveling pulses in the class of piecewise smooth functions with one discontinuity. However, when the regularization term is added we show, for a particular paramet...

The paper has been temporarily withdrawn by the authors.

In this paper we investigate the existence of ground states and dual ground states for Maxwell's Equations in $\mathbb{R}^3$ in nonlocal nonlinear metamaterials. We prove that several nonlocal models admit ground states in contrast to their local analogues.

If the interior of a conducting cavity (such as a capacitor or a coaxial cable) is supplied with a very high-frequency electric signal, the information between the walls propagates with an appreciable delay, due to the finiteness of the speed of light. The configuration is typical of cavities having size larger than the wavelength of the injected signal. Such a non rare situation, in practice, may cause a break down of the performances of the device. We show that the classica...