Rogue waves, rational solitons and wave turbulence theory

Considering a simple one-dimensional nonlinear Schrödinger optical model, we study the existence of rogue wave events in the highly incoherent state of the system and compare them with the recently identified hierarchy of rational soliton solutions. We show that rogue waves can emerge in the genuine turbulent regime and that their coherent deterministic description provided by the rational soliton solutions is compatible with an accurate statistical description of the random wave provided by the wave turbulence theory. Furthermore, the simulations reveal that even in the weakly nonlinear regime, the nonlinearity can play a key role in the emergence of an individual rogue wave event in a turbulent environment.

► Rogue wave events are studied in the highly incoherent regime of interaction.
► We show that rogue waves can emerge in the genuine turbulent regime.
► Their coherent deterministic description is provided by the rational solutions.
► It coexists with a statistical description provided of the random wave.
► The nonlinearity plays a key role even in a turbulent environment.