  We explore extreme event occurrence in the integrable turbulence with
self-similar asymptotics. We posit that rogue waves in such systems manifest
themselves as giant fluctuations away from average self-similar dynamics of the
system. We support our proposition with numerical simulations of rogue wave
excitation in the self-similar regime of stimulated Raman scattering. We show
that our results hold irrespective of a specific source correlation model,
suggesting the universality of the proposed scenario.
