Dynamical criteria for rogue waves in nonlinear Schrodinger models

    Authors

    A. Calini;C. M. Schober

    Comments

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    Abbreviated Journal Title

    Nonlinearity

    Keywords

    DEEP-WATER WAVES; MODULATIONAL INSTABILITY; FREAK-WAVES; EQUATION; Mathematics, Applied; Physics, Mathematical

    Abstract

    We investigate rogue waves in deep water in the framework of the nonlinear Schrodinger (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.

    Journal Title

    Nonlinearity

    Volume

    25

    Issue/Number

    12

    Publication Date

    1-1-2012

    Document Type

    Article

    Language

    English

    First Page

    R99

    Last Page

    R116

    WOS Identifier

    WOS:000310906600001

    ISSN

    0951-7715

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