Search results for "Nonlinear"

Nonlinear excitations in a compressible quantum Heisenberg chain

2000

Abstract We investigate, both analytically and numerically, nonlinearly coupled magnetic and elastic excitations of compressible Heisenberg chains. From a shallow water wave treatment of perturbation terms, one can derive two types of coupled equations which are coupled Boussinesq and nonlinear Schrodinger (NLS) equations and coupled Boussinesq and NLS-like equations. We also simulate collisions between magnetic and elastic solitons in the compressible Heisenberg chain when a nonlinearized approach is performed to deal with the magnetic modes in the presence of harmonic as well as anharmonic interactions. Finally, from a fast Fourier transform (FFT) algorithm, the dynamical structure factor…

Pulse Generation and Shaping Using Fiber Nonlinearities

2017

Nonlinear pulse shaping and polarization dynamics in mode-locked fiber lasers

2014

International audience; We review our recent progress on the study of new nonlinear mechanisms of pulse shaping in passively mode-locked fiber lasers. These include a mode-locking regime featuring pulses with a triangular distribution of the intensity, and spectral compression arising from nonlinear pulse propagation. We also report on our recent experimental studies unveiling new types of vector solitons with processing states of polarization for multi-pulse and tightly bound-state soliton (soliton molecule) operations in a carbon nanotube (CNT) mode-locked fiber laser with anomalous dispersion cavity.

Self-similarity in ultrafast nonlinear optics

2007

International audience; Recent developments in nonlinear optics have led to the discovery of a new class of ultrashort pulse, the `optical similariton'. Optical similaritons arise when the interaction of nonlinearity, dispersion and gain in a high-power fibre amplifier causes the shape of an arbitrary input pulse to converge asymptotically to a pulse whose shape is self-similar. In comparison with optical solitons, which rely on a delicate balance of nonlinearity and anomalous dispersion and which can become unstable with increasing intensity, similaritons are more robust at high pulse powers. The simplicity and widespread availability of the components needed to build a self-similar amplif…

Thermal Transport and Wiedemann-Franz Law in the Disordered Fermi Liquid

2014

We study thermal transport in the disordered Fermi liquid at low temperatures. Gravitational potentials are used as sources for finding the heat density and its correlation function. For a comprehensive study, we extend the renormalization group (RG) analysis developed for electric transport by including the gravitational potentials into the RG scheme. Our analysis reveals that the Wiedemann-Franz law remains valid even in the presence of quantum corrections caused by the interplay of diffusion modes and the electron electron interaction. In the present scheme this fundamental relation is closely connected with a fixed point in the multi-parametric RG-flow of the gravitational potentials.

Renormalization group approach to chaotic strings

2012

Coupled map lattices of weakly coupled Chebychev maps, so-called chaotic strings, may have a profound physical meaning in terms of dynamical models of vacuum fluctuations in stochastically quantized field theories. Here we present analytic results for the invariant density of chaotic strings, as well as for the coupling parameter dependence of given observables of the chaotic string such as the vacuum expectation value. A highly nontrivial and selfsimilar parameter dependence is found, produced by perturbative and nonperturbative effects, for which we develop a mathematical description in terms of suitable scaling functions. Our analytic results are in good agreement with numerical simulati…

Vorticity cutoff in nonlinear photonic crystals

2005

Using group theory arguments, we demonstrate that, unlike in homogeneous media, no symmetric vortices of arbitrary order can be generated in two-dimensional (2D) nonlinear systems possessing a discrete-point symmetry. The only condition needed is that the non-linearity term exclusively depends on the modulus of the field. In the particular case of 2D periodic systems, such as nonlinear photonic crystals or Bose-Einstein condensates in periodic potentials, it is shown that the realization of discrete symmetry forbids the existence of symmetric vortex solutions with vorticity higher than two.

Radial conformal motions in Minkowski space–time

1999

A study of radial conformal Killing fields (RCKF) in Minkowski space-time is carried out, which leads to their classification into three disjointed classes. Their integral curves are straight or hyperbolic lines admitting orthogonal surfaces of constant curvature, whose sign is related to the causal character of the field. Otherwise, the kinematic properties of the timelike RCKF are given and their applications in kinematic cosmology is discussed.

Nonlinear energy dissipation in a cellular automaton magnetotail field model

1999

A magnetic field model of the magnetotail current sheet based on cellular automaton (CA) is presented. The present isotropic model is a continuously driven, two-dimensional running CA. The model has a physical interpretation in terms of magnetohydrodynamic (MHD) equations, and features self-organized critical (SOC) behavior with power-law scalings both in durations and sizes of instabilities (avalanches). The model has nonlinear energy dissipation, and shows avalanches with and without an external trigger. Thus the model reproduces some of the statistical features recently observed in the magnetotail.

Spatial Solitons in Nonlinear Photonic Crystal Fibers

2017

This chapter aims to review the most relevant results on solitons in nonlinear solid-core photonic crystal fibers since their introduction about fifteen years ago. These include fundamental solitons and vortices, as well as vector systems of two fundamental, vortex or mixed components. Also other related systems as solitons in double-core photonic crystal fibers will be reviewed. The presentation will describe the mode families as well as their stability properties. The work is intended to be a comprehensive document on the field and provide a fast update to the reader as well as the necessary sources for a further detailed documentation.