Titre :

Incoherent shock waves in long-range optical turbulence

Auteur(s) :

Xu, Gang [Auteur]
Laboratoire de Physique des Lasers, Atomes et Molécules - UMR 8523 [PhLAM]
Garnier, Josselin [Auteur]
Laboratoire de Probabilités et Modèles Aléatoires [LPMA]
Laboratoire Jacques-Louis Lions [LJLL]
Faccio, Daniele [Auteur]
Heriot-Watt University [Edinburgh] [HWU]
Trillo, Stefano [Auteur]
Engineering Department [Ferrara]
Picozzi, Antonio [Auteur]
Laboratoire Interdisciplinaire Carnot de Bourgogne [ICB]

Titre de la revue :

Physica D: Nonlinear Phenomena

Pagination :

310–322

Éditeur :

Elsevier

Date de publication :

2016

ISSN :

0167-2789

Mot(s)-clé(s) en anglais :

Dispersive shock waves
Optical turbulence
Random nonlinear waves

Discipline(s) HAL :

Mathématiques [math]/Probabilités [math.PR]
Mathématiques [math]/Equations aux dérivées partielles [math.AP]
Mathématiques [math]/Statistiques [math.ST]

Résumé en anglais : [en]

Considering the nonlinear Schrödinger (NLS) equation as a representative model, we report a unified presentation of different forms of incoherent shock waves that emerge in the long-range interaction regime of a turbulent ...
Lire la suite >Considering the nonlinear Schrödinger (NLS) equation as a representative model, we report a unified presentation of different forms of incoherent shock waves that emerge in the long-range interaction regime of a turbulent optical wave system. These incoherent singularities can develop either in the temporal domain through a highly noninstantaneous nonlinear response, or in the spatial domain through a highly nonlocal nonlinearity. In the temporal domain, genuine dispersive shock waves (DSW) develop in the spectral dynamics of the random waves, despite the fact that the causality condition inherent to the response function breaks the Hamiltonian structure of the NLS equation. Such spectral incoherent DSWs are described in detail by a family of singular integro-differential kinetic equations, e.g. Benjamin–Ono equation, which are derived from a nonequilibrium kinetic formulation based on the weak Langmuir turbulence equation. In the spatial domain, the system is shown to exhibit a large scale global collective behavior, so that it is the fluctuating field as a whole that develops a singularity, which is inherently an incoherent object made of random waves. Despite the Hamiltonian structure of the NLS equation, the regularization of such a collective incoherent shock does not require the formation of a DSW — the regularization is shown to occur by means of a different process of coherence degradation at the shock point. We show that the collective incoherent shock is responsible for an original mechanism of spontaneous nucleation of a phase-space hole in the spectrogram dynamics. The robustness of such a phase-space hole is interpreted in the light of incoherent dark soliton states, whose different exact solutions are derived in the framework of the long-range Vlasov formalism.Lire moins >

Langue :

Anglais

Comité de lecture :

Oui

Audience :

Internationale

Vulgarisation :

Non

Collections :

• Laboratoire de Physique des Lasers, Atomes et Molécules (PhLAM) - UMR 8523

Source :

Harvested from HAL