Short-wave instabilities in the Benjamin-Bona-Mahoney-Peregrine equation: theory and numerics

In this paper we discuss the nonlinear propagation of waves of short wavelength in dispersive systems. We propose a family of equations that is likely to describe the asymptotic behaviour of a large class of systems. We then restrict our attention to the analysis of the simplest nonlinear short-wave dynamics given by U-0 xi tau, = U-0 - 3(U-0)(2). We integrate numerically this equation for periodic and non-periodic boundary conditions, and we find that short waves may exist only if the amplitude of the initial profile is not too large.

Multioctave infrared supercontinuum generation in large-core As2S3 fibers

We report on infrared supercontinuum (SC) generation through laser filamentation and subsequent nonlinear propagation in a step-index As2S3 fiber. The 100 μm core and high-purity As2S3 fiber used exhibit zero-dispersion wavelength around 4.5 μm, a mid-infrared background loss of 0.2dB/m, and a maximum loss of only 0.55dB/m at the S-H absorption peak around 4.05 μm. When pumping with ultrashort laser pulses slightly above the S-H absorption band, broadband infrared supercontinua were generated with a 20 dB spectral flatness spanning from 1.5 up to 7 μm. The efficiency and spectral shape of the SC produced by ultrashort pulses in large-core As2S3 fiber are mainly determined by its dispersion, the S-H contaminant absorption, and the mid-infrared nonlinear absorption.

Fresnel analysis of wave propagation in nonlinear electrodynamics

We study wave propagation in local nonlinear electrodynamical models. Particular attention is paid to the derivation and the analysis of the Fresnel equation for the wave covectors. For the class of local nonlinear Lagrangian nondispersive models, we demonstrate how the originally quartic Fresnel equation factorizes, yielding the generic birefringence effect. We show that the closure of the effective constitutive (or jump) tensor is necessary and sufficient for the absence of birefringence, i.e., for the existence of a unique light cone structure. As another application of the Fresnel approach, we analyze the light propagation in a moving isotropic nonlinear medium. The corresponding effective constitutive tensor contains nontrivial skewon and axion pieces. For nonmagnetic matter, we find that birefringence is induced by the nonlinearity, and derive the corresponding optical metrics.

Nonlinear short-wave propagation in ferrites

In this paper we discuss the propagation of nonlinear electromagnetic short waves in ferromagnetic insulators. We show that such propagation is perpendicular to an externally applied field. In the nonlinear regime we determine various possible propagation patterns: an isolated pulse, a modulated sinusoidal wave, and an asymptotic two-peak wave. The mathematical structure underlying the existence of these solutions is that of the integrable sine-Gordon equation.

A mathematical model for wave propagation in elastic tubes with inhomogeneities: Application to blood waves propagation

We study the propagation of waves in an elastic tube filled with an inviscid fluid. We consider the case of inhomogeneity whose mechanical and geometrical properties vary in space. We deduce a system of equations of the Boussinesq type as describing the wave propagation in the tube. Numerical simulations of these equations show that inhomogeneities prevent separation of right-going from left-going waves. Then reflected and transmitted coefficients are obtained in the case of localized constriction and localized rigidity. Next we focus on wavetrains incident on various types of anomalous regions. We show that the existence of anomalous regions modifies the wavetrain patterns. (c) 2007 Elsevier B.V. All rights reserved.

Periodic waves and solitons in a nonlinear fibre with resonant impurities

We shall consider a coupled nonlinear Schrodinger equation- Bloch system of equations describing the propagation of a single pulse through a nonlinear dispersive waveguide in the presence of resonances; this could be, for example, a doped optical fibre. By making use of the integrability of the dynamic equations, we shall apply the finite-gap integration method to obtain periodic solutions for this system. Next, we consider the problem of the formation of solitons at a sharp front pulse and, by means of the Whitham modulational theory, we derive the amplitude and velocity of the largest soliton.

Nonlinear Gravitational Waves: Their Form and Effects

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Soliton dynamics at an interface between a uniform medium and a nonlinear optical lattice

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Soliton propagation in a medium with Kerr nonlinearity and resonant impurities: A variational approach

The soliton propagation in a medium with Kerr nonlinearity and resonant impurities was studied by a variational approach. The existence of a solitary wave was shown within the framework of a combined nonintegrable system composed of one nonlinear Schrödinger and a pair of Bloch equations. The analytical solution which was obtained, was tested through numerical simulations confirming its solitary wave nature.

Harmonic propagation analysis in electric energy distribution systems

An important alteration of the equivalent loads profile has been observed in the electrical energy distribution systems, for the last years. Such fact is due to the significant increment of the electronic processors of electric energy that, in general, behave as nonlinear loads, generating harmonic distortions in the currents and voltages along the electric network. The effects of these nonlinear loads, even if they are concentrated in specific sections of the network, are present along the branch circuits, affecting the behavior of the entire electric network. For the evaluation of this phenomenon it is necessary the analysis of the harmonic currents flow and the understanding of the causes and effects of the consequent voltage harmonic distortions. The usual tools for calculation the harmonic flow consider one-line equivalent networks, balanced and symmetrical systems. Therefore, they are not tools appropriate for analysis of the operation and the influence/interaction of mitigation elements. In this context, this work proposes the development of a computational tool for the analysis of the three-phase harmonic propagation using Norton modified models and considering the real nature of unbalanced electric systems operation. © 2011 IEEE.

Causal structure and birefringence in nonlinear electrodynamics

We investigate the causal structure of general nonlinear electrodynamics and determine which Lagrangians generate an effective metric conformal to Minkowski. We also prove that there is only one analytic nonlinear electrodynamics not presenting birefringence.

Wide localized solutions of the parity-time-symmetric nonautonomous nonlinear Schrodinger equation

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)