We numerically investigate dispersive perturbations of the nonlinear Schrödinger (NLS)
equation, which model waves in deep water. We observe that a chaotic regime greatly
increases the likelihood of rogue wave formation. These large amplitude waves are well
modeled by higher order homoclinic solutions of the NLS equation for which the spatial
excitations have coalesced to produce a wave of maximal amplitude. Remarkably, a
Melnikov analysis of the conditions for the onset of chaos identifies the observed maximal …