In this talk we investigate  rogue waves in deep water in the framework of the nonlinear Schr\"{o}dinger (NLS) and  Dysthe  equations.

Amongst the homoclinic orbits of unstable NLS Stokes waves, we seek good candidates to model actual rogue waves.

We propose two selection criteria: stability under perturbations of initial data, and persistence under perturbations of the NLS model. We find requiring stability selects  homoclinic orbits of maximal dimension. Persistence under (a particular) perturbation selects a homoclinic orbit of maximal dimension  all of whose  spatial modes are coalesced.

These  results suggest that more realistic sea states, described by JONSWAP  power spectra, may be analyzed in terms of proximity to NLS homoclinic data. In fact,  using the NLS spectral theory, we find rogue wave events in random oceanic sea states are well predicted by  proximity to homoclinic data of the NLS equation.