Abstract

The question of statistical properties of ensembles of nonlinear waves is a subject of an intense research activity in the context of turbulence or rogue wave (RW) formation [1,2]. Most of the works that have been reported so far in the field of nonlinear optics are related to nonintegrable wave systems (light supercontinuum [3], Raman fiber lasers [4]... ). However it is interesting to notice that coherent structures (Peregrine soliton, Akmediev breather...) that are now considered as prototypes of RW [5] are analytical solutions of the integrable one-dimensional nonlinear Schrödinger equation (1D-NLSE). Up to now, these coherent structures have been only observed in experiments in which a coherent initial condition is carefully designed [6]. Surprisingly, no experiment has shown that these coherent structures can emerge from an incoherent initial condition and influence the wave statistics.

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