Title :

Early stage of integrable turbulence in the one-dimensional nonlinear Schrodinger equation: A semiclassical approach to statistics

Author(s) :

Roberti, Giacomo [Auteur]
Department of Mathematics, Physics and Electrical Engineering [Newcastle]
El, Gennady [Auteur]
Northumbria University [Newcastle]
Randoux, Stephane [Auteur]
Laboratoire de Physique des Lasers, Atomes et Molécules - UMR 8523 [PhLAM]
Suret, Pierre [Auteur]
Laboratoire de Physique des Lasers, Atomes et Molécules - UMR 8523 [PhLAM]

Journal title :

Physical Review E

Publication date :

2019

HAL domain(s) :

Science non linéaire [physics]

English abstract : [en]

We examine statistical properties of integrable turbulence in the defocusing and focusing regimes of one-dimensional small-dispersion nonlinear Schrodinger equation (1D-NLSE). Specifically, we study the 1D-NLSE evolution ...
Show more >We examine statistical properties of integrable turbulence in the defocusing and focusing regimes of one-dimensional small-dispersion nonlinear Schrodinger equation (1D-NLSE). Specifically, we study the 1D-NLSE evolution of partially coherent waves having Gaussian statistics at time t = 0. Using short time asymptotic expansions and taking advantage of the scale separation in the semiclassical regime we obtain a simple explicit formula describing an early stage of the evolution of the fourth moment of the random wave field amplitude, a quantitative measure of the ``tailedness'' of the probability density function. Our results show excellent agreement with numerical simulations of the full 1D-NLSE random field dynamics and provide insight into the emergence of the well-known phenomenon of heavy (respectively, low) tails of the statistical distribution occurring in the focusing (respectively, defocusing) regime of 1D-NLSE.Show less >

Language :

Anglais

ANR Project :

Centre Européen pour les Mathématiques, la Physique et leurs Interactions

Collections :

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

Source :

Harvested from HAL