By Constance Schober, University of Central Florida
Breather type (homoclinic) solutions of the Nonlinear Schrodinger equation have been widely used as models for rogue waves. In this talk we examine the generation of rogue waves for random sea states characterized by JONSWAP spectra using an approach based on the NLS equation and its inverse spectral theory. We introduce a spectral quantity, the ``splitting distance'' between consecutive simple points in the associated discrete Floquet spectrum. Using the splitting distance we correlate the development of rogue waves for JONSWAP data with the proximity in spectral space to instabilities and homoclinic data of the NLS equation.