The super rogue wave dynamics in optical fibers are investigated within the framework of a generalized nonlinear Schrödinger equation containing group-velocity dispersion, Kerr and quintic nonlinearity, and self-steepening effect. In terms of the explicit rogue wave solutions up to the third order, we show that, for a rogue wave solution of order n, it can be shaped up as a single super rogue wave state with its peak amplitude 2n + 1 times the background level, which results from the superposition of n(n + 1)/2 Peregrine solitons. Particularly, we demonstrate that these super rogue waves involve a frequency chirp that is also localized in both time and space. The robustness of the super chirped rogue waves against white-noise perturbations as well as the possibility of generating them in a turbulent field is numerically confirmed, which anticipates their accessibility to experimental observation.

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We show that two-color Peregrine solitary waves in quadratic nonlinear media can resonantly radiate dispersive waves even in the absence of higher-order dispersion, owing to a phase-matching mechanism that involves the weaker second-harmonic component. We give very simple criteria for calculating the radiated frequencies in terms of material parameters, finding excellent agreement with numerical simulations.