Search results for "solitons"
showing 10 items of 401 documents
Spatial localization and pattern formation in discrete optomechanical cavities and arrays
2020
We investigate theoretically the generation of nonlinear dissipative structures in optomechanical (OM) systems containing discrete arrays of mechanical resonators. We consider both hybrid models in which the optical system is a continuous multimode field, as it would happen in an OM cavity containing an array of micro-mirrors, and also fully discrete models in which each mechanical resonator interacts with a single optical mode, making contact with Ludwig & Marquardt [Phys. Rev. Lett. 101, 073603 (2013)]. Also, we study the connections between both types of models and continuous OM models. While all three types of models merge naturally in the limit of a large number of densely distribu…
Génération expérimentale de solitons de cut-off dans une ligne électrique non linéaire
2015
National audience; Nous étudions le phénomène de supratransmission dans un milieu non linéaire discret, soumis, à une excitation périodique dont la fréquence appartient à la bande interdite. Nous montrons l’existence d’un seuil de tension au dessus duquel l’instabilité modulationnelle (IM) va se développer dans la ligne, valeur de seuil dépendant de la fréquence d’excitation. Si elle n’empêche pas l’apparition de l’IM par supratransmission, la dissipation présente dans la ligne est un obstacle à la génération des solitons de cut-off, obstacle que nous sommes parvenus à contourner par un choix approprié de l’amplitude de l’excitation.
Digital information receiver based on stochastic resonance
2003
International audience; An electronic receiver based on stochastic resonance is presented to rescue subthreshold modulated digital data. In real experiment, it is shown that a complete data restoration is achieved for both uniform and Gaussian white noise.
Structures optiques dissipatives en cavité laser à fibre
2011
This thesis presents a study of the nonlinear dissipative dynamics of localized of self organized structures in passively mode-locked fiber laser through nonlinear polarization evolution. We reveal the existence of a gradual transition from the quasi-cw to mode locked dynamics in the multi-pulsing regime. We emphasize on the intermediate state, where various new dynamics are observed. We study collective behaviors of dissipative solitons in the presence of a continuous background. One of the complex and attractive dynamics presented is the "soliton rain", which composed of three field components : continuous modes of background, drifting of solitons and condensed phase solitons. This dynami…
Arresting soliton collapse in two-dimensional nonlinear Schrödinger systems via spatiotemporal modulation of the external potential
2007
We predict stable, collapse-free solitonslike structures in two-dimensional nonlinear Schr\"odinger systems in subdiffractive regimes, accomplished by a spatiotemporal modulation of the external potential. We investigate the scaling laws, the stability, and the dynamical properties of these subdiffractive solitons.
Effet du couplage non linéaire dans un système de sine-Gordon modifié
2016
National audience; Cette Communication porte sur une étude numérique visant à montrer les conditions d'existence du phénomène de supratransmission dans un milieu gouverné par l'équation de sine-gordon à couplage mixte: le couplage linéaire pur étant associé à un couplage non linéaire. Nous montrons également l'effet de la variation du coefficient du couplage non linéaire sur l'amplitude de seuil du signal excitateur nécessaire pour déclencher le phénomène de supratransmission dans le milieu, en maintenant constant le coefficient du couplage linéaire pur.
Solutions to the NLS equation : differential relations and their different representations
2020
Solutions to the focusing nonlinear Schrödinger equation (NLS) of order N depending on 2N − 2 real parameters in terms of wronskians and Fredholm determinants are given. These solutions give families of quasirational solutions to the NLS equation denoted by vN and have been explicitly constructed until order N = 13. These solutions appear as deformations of the Peregrine breather PN as they can be obtained when all parameters are equal to 0. These quasi rational solutions can be expressed as a quotient of two polynomials of degree N (N + 1) in the variables x and t and the maximum of the modulus of the Peregrine breather of order N is equal to 2N + 1. Here we give some relations between sol…
Non-existence of dark solitons in a nonlinear Schrödinger-Maxwell-Bloch fibre system
2000
We consider the coupled system of nonlinear Schrodinger and Maxwell-Bloch (NLS-MB) equations, which govern the nonlinear pulse propagation in erbium doped optical fibres. With the help of the Painleve singularity structure analysis, we prove the non-existence of optical solitons in the NLS-MB fibre system in the normal dispersion regime.
Photonic Nambu-Goldstone bosons
2017
We study numerically the spatial dynamics of light in periodic square lattices in the presence of a Kerr term, emphasizing the peculiarities stemming from the nonlinearity. We find that, under rather general circumstances, the phase pattern of the stable ground state depends on the character of the nonlinearity: the phase is spatially uniform if it is defocusing whereas in the focusing case, it presents a chess board pattern, with a difference of $\pi$ between neighboring sites. We show that the lowest lying perturbative excitations can be described as perturbations of the phase and that finite-sized structures can act as tunable metawaveguides for them. The tuning is made by varying the in…
From deterministic cellular automata to coupled map lattices
2016
A general mathematical method is presented for the systematic construction of coupled map lattices (CMLs) out of deterministic cellular automata (CAs). The entire CA rule space is addressed by means of a universal map for CAs that we have recently derived and that is not dependent on any freely adjustable parameters. The CMLs thus constructed are termed real-valued deterministic cellular automata (RDCA) and encompass all deterministic CAs in rule space in the asymptotic limit $\kappa \to 0$ of a continuous parameter $\kappa$. Thus, RDCAs generalize CAs in such a way that they constitute CMLs when $\kappa$ is finite and nonvanishing. In the limit $\kappa \to \infty$ all RDCAs are shown to ex…