Intermittent-Type Chaos in Nonsinusoidal Driven Oscillators

The intermittent-type chaos occurring in rf- and dc- nonsinusoidal driven oscillators is investigated analytically and numerically. The attention is focused on a general class of oscillators in which the total potential VRP(,r) is the Remoissenet-Peyrard potential which has constant amplitude and is 2π-periodic in , and whose shape can be varied as a function of parameter r ( |r| < 1). A simple physical model for calculating analytically the Melnikov function is proposed. The onset of chaos is studied through an analysis of the phase space, a construction of the bifurcation diagram and a computation of the Lyapunov exponent. The parameter regions of chaotic behaviour predicted by the theore…

Chaotic behaviour in deformable models: the asymmetric doubly periodic oscillators

Abstract The motion of a particle in a one-dimensional perturbed asymmetric doubly periodic (ASDP) potential is investigated analytically and numerically. A simple physical model for calculating analytically the Melnikov function is proposed. The onset of chaos is studied through an analysis of the phase space, a construction of the bifurcation diagram and a computation of the Lyapunov exponent. Theory predicts the regions of chaotic behaviour of orbits in a good agreement with computer calculations.

Chaotic behavior in deformable models: the double-well doubly periodic oscillators

Abstract The motion of a particle in a one-dimensional perturbed double-well doubly periodic potential is investigated analytically and numerically. A simple physical model for calculating analytically the Melnikov function is proposed. The onset of chaos is studied through an analysis of the phase space, a construction of the bifurcation diagram and a computation of the Lyapunov exponent. The parameter regions of chaotic behavior predicted by the theoretical analysis agree very well with numerical simulations.

FIBER AND GUIDED WAVE OPTICS | Nonlinear Effects (Basics)

Generation of High-Repetition-Rate Dark Soliton Trains and Frequency Conversion in Optical Fibers

Induced modurational polarization instability in birefringent fibers leads to trains of dark soliton-like pulses. Optimal large-signal cw and soliton frequency conversion is also analysed.

SOLITONS | Optical Fiber Solitons, Physical Origin and Properties

Cutoff solitons and bistability of the discrete inductance-capacitance electrical line: Theory and experiments

A discrete nonlinear system driven at one end by a periodic excitation of frequency above the upper band edge (the discreteness induced cutoff) is shown to be a means to (1) generate propagating breather excitations in a long chain and (2) reveal the bistable property of a short chain. After detailed numerical verifications, the bistability prediction is demonstrated experimentally on an electrical transmission line made of 18 inductance-capacitance $(LC)$ cells. The numerical simulations of the $LC$-line model allow us also to verify the breather generation prediction with a striking accuracy.

Pulsating Dissipative Light Bullets

Finding domains of existence for (3+1)D spatio-temporal dissipative solitons, also called “dissipative light bullets”, by direct numerical solving of a cubic-quintic Ginzburg-Landau equation (CGLE) is a lengthy procedure [1,2]. Variational approaches pave the way for quicker soliton solution mapping, as long as tractable trial functions remain suitable approximations for exact solutions [3,4].

Modulational instability processes in optical isotropic fibers under dual-frequency pumping

Experiments are presented showing that under dual-frequency, circular polarization pumping, a host modulational instability processes can be generated in a single isotropic fiber, by carefully tuning the frequency spacing between the pumps.

SCATTERING | Scattering Phenomena in Optical Fibers

Comparison of conventional and dense dispersion managed systems for 160 Gb/s transmissions

International audience; In this paper, we carry out, by numerical simulations and experiments on recirculating loop.. a comparative analysis of the performances of two types of dispersion management techniques for 160 Gb/s transmission systems, which correspond to short-period dispersion maps (dense dispersion management) and long-period dispersion maps (conventional dispersion management), respectively. We show that the dense dispersion management system suffers performance degradation by the effects of polarization mode dispersion (PMD) and fiber splicing losses, in a more dramatic manner than in the system with long-period map. We experimentally find that, at constant PMD, dense dispersi…

Stationary and pulsating dissipative light bullets from a collective variable approach

A collective variable approach is used to map domains of existence for (3+1) -dimensional spatiotemporal soliton solutions of a complex cubic-quintic Ginzburg-Landau equation. A rich variety of evolution behaviors, which include stationary and pulsating dissipative soliton dynamics, is revealed. Comparisons between the results obtained by the semianalytical approach of collective variables, and those obtained by a purely numerical approach show good agreement for a wide range of equation parameters. This also demonstrates the relevance of the semianalytical method for a systematic search of stability domains for spatiotemporal solitons, leading to a dramatic reduction of the computation tim…