Title

Dynamical Criteria For Rogue Waves In Nonlinear Schrödinger Models

Abstract

We investigate rogue waves in deep water in the framework of the nonlinear Schrödinger (NLS) and Dysthe equations. Amongst the homoclinic orbits of unstable NLS Stokes waves, we seek good candidates to model actual rogue waves. In this paper we propose two selection criteria: stability under perturbations of initial data, and persistence under perturbations of the NLS model. We find that 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 that rogue wave events in random oceanic sea states are well predicted by proximity to homoclinic data of the NLS equation. © 2012 IOP Publishing Ltd & London Mathematical Society.

Publication Date

12-1-2012

Publication Title

Nonlinearity

Volume

25

Issue

12

Number of Pages

-

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1088/0951-7715/25/12/R99

Socpus ID

84869133777 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/84869133777

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