Intermittency in integrable turbulence.

We examine the statistical properties of nonlinear random waves that are ruled by the one-dimensional defocusing and integrable nonlinear Schrödinger equation. Using fast detection techniques in an optical fiber experiment, we observe that the probability density function of light fluctuations is characterized by tails that are lower than those predicted by a Gaussian distribution. Moreover, by applying a bandpass frequency optical filter, we reveal the phenomenon of intermittency; i.e., small scales are characterized by large heavy-tailed deviations from Gaussian statistics, while the large ones are almost Gaussian. These phenomena are very well described by numerical simulations of the one-dimensional nonlinear Schrödinger equation.