Homoclinic chaos increases the likelihood of rogue wave

formation

Constance Schober

University of Central Florida

We numerically investigate symmetry breaking perturbations of the nonlinear Schr\"{o}dinger (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 localized wave of maximal amplitude. Remarkably, a Melnikov analysis of the conditions for the onset of chaos identifies the observed maximal amplitude homoclinic solutions as the persistent hyperbolic structures throughout the perturbed dynamics.