Onset times of long-lived rogue waves in an optical waveguide array

We study the effects of increasing modulation instability and disorder on the onset times of rogue waves in waveguide arrays as described by the discrete unstable nonlinear Schrödinger equation (UNLSE). We analytically determine regions of instability, where rogue waves are likely to occur in the UNLSE, and then use numerical techniques to study the time evolution of these systems. Only for small modulation instability is the effect of fluctuations prominent on the onset times; otherwise, we find that large modulation instability dominates the onset time behavior.