__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.