Effect of modulational instability on rogue wave statistics
In plain words
Rogue waves are ocean or optical waves far taller than their neighbors. It is disputed whether they come mostly from random addition of ordinary waves or from a nonlinear focusing instability, and how much the instability raises their probability.
Precise statement
For directional random surface gravity waves in deep water described by the Zakharov equation or the 2D nonlinear Schrodinger equation, determine how the exceedance probability of crest-to-trough height $H > 2 H_s$ depends on the Benjamin-Feir index BFI (steepness divided by spectral bandwidth) and on directional spreading, and whether it exceeds second-order (bound-wave) statistics in realistic directional seas. An answer is a quantitative law tested against field and tank data.
What would settle it
Large tank experiments and field records with measured spectra showing whether exceedance probabilities rise with BFI beyond second-order theory at realistic directional spreading.