Orbital Instability of the Peregrine Soliton

    Authors

    R. A. Van Gorder

    Comments

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    Abbreviated Journal Title

    J. Phys. Soc. Jpn.

    Keywords

    ROGUE WAVES; SUPERCONTINUUM GENERATION; MODULATION INSTABILITY; SCHRODINGER-EQUATIONS; FREAK WAVE; DEEP-WATER; DYNAMICS; FIBER; MECHANISMS; STABILITY; Physics, Multidisciplinary

    Abstract

    The Peregrine soliton is one possible model of a rogue wave. Importantly, this type of soliton corresponds nicely to rogue waves recently observed experimentally in a water tank [A. Chabchoub, N. P. Hoffmann, and N. Akhmediev, Phys. Rev. Lett. 106, 204502 (2011)] and in optical fiber [B. Kibler, J. Fatome, C. Finot, G. Millot, F. Dias, G. Genty, N. Akhmediev, and J. M. Dudley, Nat. Phys. 6, 790 (2010)]. Starting with a family of Peregrine solitons indexed by their spectral parameter, we analytically demonstrate a type of instability in the Peregrine soliton through a concise orbital stability analysis. This analysis is completely analytical, and to verify the approach we also discuss a numerical linear instability analysis. We give the growth/decay rate for these solitons as a function of the initial amplitude, which for each soliton shall depend on the spectral parameter.

    Journal Title

    Journal of the Physical Society of Japan

    Volume

    83

    Issue/Number

    5

    Publication Date

    1-1-2014

    Document Type

    Article

    Language

    English

    First Page

    3

    WOS Identifier

    WOS:000334596100012

    ISSN

    0031-9015

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