2019/01/08 by Giacomo Roberti, Gennady El, Stephane Randoux +1 · 2 citations
Physics and Astronomy · #nlin.PS #nlin.SI
paper · pdf · doi:10.1103/physreve.100.032212
published as Phys. Rev. E 100, 032212 (2019) · 10 pages
arxiv created 2019/01/08 · arxiv updated 2019/09/25
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 semi-classical 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 (resp. low) tails of the statistical distribution emerging in the focusing (resp. defocusing) regime of 1D-NLSE.