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We demonstrate a simple cascade mechanism that drives the formation andemergence of rogue waves in the generalized non-linear Schr\"{o}dinger equationwith third-order dispersion. This conceptually novel generation mechanism isbased on inelastic collisions of quasi-solitons and is well described by aresonant-like scattering behaviour for the energy transfer in pair-wisequasi-soliton collisions. Our results demonstrate a threshold for rogue waveemergence and the existence of a period of reduced amplitudes - a "calm beforethe storm" - preceding the arrival of a rogue wave event. Comparing withultra-long time window simulations of $3.865\times 10^{6}$ps we observe thestatistics of rogue waves in optical fibres with an unprecedented level ofdetail and accuracy, unambiguously establishing the long-ranged character ofthe rogue wave power-distribution function over seven orders of magnitude.

Rogue wave generation by inelastic quasi-soliton collisions in optical fibres