Search results for "SOLITONS"
showing 10 items of 401 documents
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.
A nonlinear oscillators network devoted to image processing
2004
A contrast enhancement and image inverting tool using a lattice of uncoupled nonlinear oscillators is proposed. We show theoretically and numerically that the gray scale picture contrast is strongly enhanced even if this one is initially very small. An image inversion can be also obtained in real time with the same Cellular Nonlinear Network (CNN) without reconfiguration of the network. A possible electronic implementation of this CNN is finally discussed.
Noise removal using a nonlinear two-dimensional diffusion network
1998
Un reseau electrique non lineaire bidimensionnel, constitue de N×N cellules identiques, et modelisant l’equation de Nagumo discrete est presente. A l’aide d’une nouvelle description de la fonction non lineaire, on peut predire analytiquement l’evolution temporelle de la partie coherente du signal, ainsi que celle des perturbations de petites amplitudes qui lui sont superposees. Enfin, des applications a l’amelioration du rapport signal sur bruit, ou au traitement d’images sont suggerees.
COLORED NOISE EFFECTS ON GHOST STOCHASTIC RESONANCE
2014
International audience; We analyze the Ghost Stochastic Resonance (GSR) effect in an electronic circuit exactly ruled by the FitzHugh-Nagumo (FHN) equations, both numerically and experimentally. When the circuit is excited with a bichromatic driving with two close frequencies, we show that for an appropriate noise intensity the circuit response exhibits a ghost frequency which is not present in the biharmonic input signal. In this paper, we highlight the e ects of colored noise on GSR.
A comparative study of noise effects in a FitzHugh-Nagumo circuit
2014
International audience; This paper focuses on the behaviour of a nonlinear FitzHugh-Nagumo circuit in the stochastic case that is in presence of noise and without deterministic driving. When the circuit is tuned below the Andronov-Hopf bifurcation, classical coherence res- onance signature is revealed. We compare the stochastic response of the system when the noise acts on two different parameters of the system. It is experimentally shown that an enhancement of the systems response can be achieved when the noise is directly added into the nonlinearity.