Rogue waves: rational solitons and wave turbulence theory

International audience; Solitons on finite background (SFB) and particularly rational solitons (RS) are exact analytical solutions of integrable wave equations, and for this reason they may be regarded as a coherent and deterministic approach to the understanding of rogue wave (RW) phenomena. However, RWs events are known to spontaneously emerge from an incoherent turbulent state of the system. It is thus of fundamental importance to study whether RSs can emerge from a turbulent environment (i.e., in more realistic oceanic conditions). To this aim, we first review here our recent experiments based on optical fiber systems to generate the localized nonlinear structures evolving upon a nonzero b…