The nonlinear dynamics of rogue waves and holes in deep-water gravity wavetrains

Roguewaves are rare “giant”, “freak”, “monster” or “steep wave” events in nonlineardeepwatergravitywaves which occasionally rise up to surprising heights above the background wave field. Holes are deep troughs which occur before and/or after the largest rogue crests. The dynamical behavior of these giant waves is here addressed as solutions of the nonlinear Schrödinger equation in both 1+1 and 2+1 dimensions. We discuss analytical results for 1+1 dimensions and demonstrate numerically, for certain sets of initial conditions, the ubiquitous occurrence of roguewaves and holes in 2+1 spatial dimensions. A typical wave field evidently consists of a background of stable wave modes punctuated by the intermittent upthrusting of unstable roguewaves.