Search results for "soliton"
showing 10 items of 534 documents
Vibrations and oscillations of tri-soliton molecules in a mode-locked fiber laser
2018
We present numerical simulations highlighting internal oscillations and vibrations within tri-soliton molecules generated by a mode-locked fiber laser. We highlight major qualitative differences as compared to two-soliton molecules.
Resonance phenomena in a nonlinear neuronal circuit
2015
International audience; We characterizes a nonlinear circuit driven by a bichromatic excitation,that is the sum of two sinusoidal waves with different frequencies f1 and f2 suchthat f2 > f1. Our experiments are confirmed by a numerical analysis of the systemresponse obtained by solving numerically the differential equations which rule thecircuit voltages. Especially, we highlight that the response of the system at the lowfrequency can be optimized by the amplitude of the high frequency. By revisiting thiswell known vibrational resonance effect in the whole amplitude frequency parametricplane, we show experimentally and numerically that a much better resonance can beachieved when the two fre…
Numerical study of blow-up in solutions to generalized Kadomtsev-Petviashvili equations
2013
We present a numerical study of solutions to the generalized Kadomtsev-Petviashvili equations with critical and supercritical nonlinearity for localized initial data with a single minimum and single maximum. In the cases with blow-up, we use a dynamic rescaling to identify the type of the singularity. We present a discussion of the observed blow-up scenarios.
Temporal incoherent solitons supported by a defocusing nonlinearity with anomalous dispersion
2012
http://pra.aps.org/; International audience; We study temporal incoherent solitons in noninstantaneous response nonlinear media. Contrarily to the usual temporal soliton, which is known to require a focusing nonlinearity with anomalous dispersion, we show that a highly noninstantaneous nonlinear response leads to incoherent soliton structures which require the inverted situation: In the focusing regime (and anomalous dispersion) the incoherent wave packet experiences an unlimited spreading, whereas in the defocusing regime (still with anomalous dispersion) the incoherent wave packet exhibits a self-trapping. These counterintuitive results are explained in detail by a long-range Vlasov formu…
Propagation failure in discrete bistable reaction-diffusion systems: Theory and experiments
2001
International audience; Wave front propagation failure is investigated in discrete bistable reaction-diffusion systems. We present a theoretical approach including dissipative effects and leading to an analytical expression of the critical coupling beyond which front propagation can occur as a function of the nonlinearity threshold parameter. Our theoretical predictions are confirmed by numerical simulations and experimental results on an equivalent electrical diffusive lattice.
Pseudodifferential operators of Beurling type and the wave front set
2008
AbstractWe investigate the action of pseudodifferential operators of Beurling type on the wave front sets. More precisely, we show that these operators are microlocal, that is, preserve or reduce wave front sets. Some consequences on micro-hypoellipticity are derived.
Cross-Diffusion Driven Instability in a Predator-Prey System with Cross-Diffusion
2013
In this work we investigate the process of pattern formation induced by nonlinear diffusion in a reaction-diffusion system with Lotka-Volterra predator-prey kinetics. We show that the cross-diffusion term is responsible of the destabilizing mechanism that leads to the emergence of spatial patterns. Near marginal stability we perform a weakly nonlinear analysis to predict the amplitude and the form of the pattern, deriving the Stuart-Landau amplitude equations. Moreover, in a large portion of the subcritical zone, numerical simulations show the emergence of oscillating patterns, which cannot be predicted by the weakly nonlinear analysis. Finally when the pattern invades the domain as a trave…
Broadband telecom to mid-infrared supercontinuum generation in a dispersion-engineered silicon germanium waveguide.
2015
We demonstrate broadband supercontinuum generation (SCG) in a dispersion-engineered silicon-germanium waveguide. The 3 cm long waveguide is pumped by femtosecond pulses at 2.4 μm, and the generated supercontinuum extends from 1.45 to 2.79 μm (at the −30 dB point). The broadening is mainly driven by the generation of a dispersive wave in the 1.5–1.8 μm region and soliton fission. The SCG was modeled numerically, and excellent agreement with the experimental results was obtained.
Two relaxation times and thermal nonlinear waves along wires with lateral heat exchange
2021
Abstract We propose a model for studying several nonlinear waves for heat transport along a cylindrical system with lateral non-linear heat transfer to the environment. We consider relaxational equations, each with its own relaxation time, for longitudinal heat transfer and for lateral heat transfer across the wall. We consider two kinds of nonlinear lateral heat transport: radiative heat transport, and flux-limited heat transport. This work generalizes our previous studies in which the relaxation time for the lateral heat transfer was considered equal to that of the longitudinal heat flux. We explore the influence of both relaxation times on the propagation speed of linear and nonlinear wa…
Wronskian representation of solutions of NLS equation, and seventh order rogue wave.
2012
This work is a continuation of a recent paper in which we have constructed a multi-parametric family of the nonlinear Schrodinger equation in terms of wronskians. When we perform a special passage to the limit, we get a family of quasi-rational solutions expressed as a ratio of two determinants. We have already construct Peregrine breathers of orders N=4, 5, 6 in preceding works; we give here the Peregrine breather of order seven.