Search results for "Pattern formation"

Shallow water rogue wavetrains in nonlinear optical fibers

2013

International audience; In addition to deep-water rogue waves which develop from the modulation instability of an optical CW, wave propagation in optical fibers may also produce shallow water rogue waves. These extreme wave events are generated in the modulationally stable normal dispersion regime. A suitable phase or frequency modulation of a CW laser leads to chirp-free and flat-top pulses or flaticons which exhibit a stable self-similar evolution. Upon collision, flaticons at different carrier frequencies, which may also occur in wavelength division multiplexed transmission systems, merge into a single, high-intensity, temporally and spatially localized rogue pulse.

Polarization modulation instability in a Manakov fiber system

2015

International audience; The Manakov model is the simplest multicomponent model of nonlinear wave theory: It describes elementary stable soliton propagation and multisoliton solutions, and it applies to nonlinear optics, hydrodynamics, and Bose-Einstein condensates. It is also of fundamental interest as an asymptotic model in the context of the widely used wavelength-division-multiplexed optical fiber transmission systems. However, although its physical relevance was confirmed by the experimental observation of Manakov (vector) solitons in a planar waveguide in 1996, there have in fact been no quantitative experiments confirming its validity for nonlinear dynamics other than soliton formatio…

Peregrine soliton generation and breakup in standard telecommunications fiber

2011

International audience; We present experimental and numerical results showing the generation and breakup of the Peregrine soliton in standard telecommunications fiber. The impact of non-ideal initial conditions is studied through direct cut back measurements of the longitudinal evolution of the emerging soliton dynamics, and is shown to be associated with the splitting of the Peregrine soliton into two subpulses, with each subpulse itself exhibiting Peregrine soliton characteristics. Experimental results are in good agreement with simulations.

Fiber Bragg gratings with various chirp profiles made in etched tapers

1996

We have studied, both theoretically and experimentally, fibre Bragg gratings with a number of different chirp profiles. These chirp profiles can be easily achieved with a recently demonstrated technique involving a taper of desired profile being etched into the cladding of a fibre. Performances of gratings with linear, quadratic, periodically modulated and step chirp profiles are numerically analysed. The versatility of the technique is demonstrated when linearly and quadratically chirped gratings were made as examples of continuous chirp and gratings with step chirps were made as examples of discontinuously chirped structure.

Condensation of classical optical waves beyond the cubic nonlinear Schrodinger equation

2012

International audience; A completely classical nonlinear wave is known to exhibit a process of condensation whose thermodynamic properties are analogous to those of the genuine Bose-Einstein condensation. So far this phenomenon of wave condensation has been studied essentially in the framework of the nonlinear Schrodinger (NLS) equation with a pure cubic Kerr nonlinearity. We study wave condensation by considering two representative generalizations of the NLS equation that are relevant to the context of nonlinear optics, the nonlocal nonlinearity and the saturable nonlinearity. For both cases we derive analytical expressions of the condensate fraction in the weakly and the strongly nonlinea…

Parametric Solitons in Two-Dimensional Lattices of Purely Nonlinear Origin

2008

We demonstrate spatial solitons via twin-beam second-harmonic generation in hexagonal lattices realized by poling lithium niobate planar waveguides. These simultons can be steered by acting on power, direction, and wavelength of the fundamental frequency input.

Stationary, Oscillatory, Spatio-Temporal Patterns and Existence of Global Solutions in Reaction-Diffusion Models of Three Species

2023

The goal of my Ph.D. research is to analyze three species models in order to describe the behavior of an ecological community. In particular, two reaction-diffusion systems describing different local interactions between three species have been considered to obtain species coexistence, diversity, and distribution patterns. The first analyzed model describes intraguild predation: there are an IG-predator species, an IG-prey species, and a common resource species, which is shared by both of them. The IGP interaction is of Lotka-Volterra type, coupled with nonlinear diffusion, since we assume that the IG-prey moves towards lower density areas of the IG-predator. In this model, the extinction o…

Pattern formation and bifurcation analysis for some chemotaxis-reaction-diffusion systems

Pattern formation driven by cross–diffusion in a 2D domain

2012

Abstract In this work we investigate the process of pattern formation in a two dimensional domain for a reaction–diffusion system with nonlinear diffusion terms and the competitive Lotka–Volterra kinetics. The linear stability analysis shows that cross-diffusion, through Turing bifurcation, is the key mechanism for the formation of spatial patterns. We show that the bifurcation can be regular, degenerate non-resonant and resonant. We use multiple scales expansions to derive the amplitude equations appropriate for each case and show that the system supports patterns like rolls, squares, mixed-mode patterns, supersquares, and hexagonal patterns.

A SUBCRITICAL BIFURCATION FOR A NONLINEAR REACTION–DIFFUSION SYSTEM

2010

In this paper the mechanism of pattern formation for a reaction-diffusion system with nonlinear diffusion terms is investigated. Through a linear stability analysis we show that the cross-diffusion term allows the pattern formation. To predict the form and the amplitude of the pattern we perform a weakly nonlinear analysis. In the supercritical case the Stuart-Landau equation is found, which rules the evolution of the amplitude of the most unstable mode. With the increasing distance from the bifurcation value of the cross-diffusion parameter, the weakly nonlinear analysis fails and a Fourier–Galerkin approach is adopted. In the subcritical case the weakly nonlinear analysis must be pushed u…