Emergent rogue wave structures and statistics in spontaneous modulation instability

Shanti Toenger, Thomas Godin, Cyril Billet, Frédéric Dias, Miro Erkintalo, Goëry Genty, John M. Dudley

    Research output: Contribution to journalArticleScientificpeer-review

    78 Citations (Scopus)


    The nonlinear Schrödinger equation (NLSE) is a seminal equation of nonlinear physics describing wave packet evolution in weakly-nonlinear dispersive media. The NLSE is especially important in understanding how high amplitude "rogue waves" emerge from noise through the process of modulation instability (MI) whereby a perturbation on an initial plane wave can evolve into strongly-localised "breather" or "soliton on finite background (SFB)" structures. Although there has been much study of such structures excited under controlled conditions, there remains the open question of how closely the analytic solutions of the NLSE actually model localised structures emerging in noise-seeded MI. We address this question here using numerical simulations to compare the properties of a large ensemble of emergent peaks in noise-seeded MI with the known analytic solutions of the NLSE. Our results show that both elementary breather and higher-order SFB structures are observed in chaotic MI, with the characteristics of the noise-induced peaks clustering closely around analytic NLSE predictions. A significant conclusion of our work is to suggest that the widely-held view that the Peregrine soliton forms a rogue wave prototype must be revisited. Rather, we confirm earlier suggestions that NLSE rogue waves are most appropriately identified as collisions between elementary SFB solutions.

    Original languageEnglish
    Article number10380
    JournalScientific Reports
    Publication statusPublished - 20 May 2015
    Publication typeA1 Journal article-refereed

    Publication forum classification

    • Publication forum level 2

    ASJC Scopus subject areas

    • General


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