title: Emergent rogue wave structures and statistics in spontaneous modulation instability.
abstract: 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.
authors.affiliation: Institut FEMTO-ST, UMR 6174 CNRS-Université de Franche-Comté, Besançon, France.
authors.forename: Shanti
authors.initials: S
authors.lastname: Toenger
authors.affiliation: Institut FEMTO-ST, UMR 6174 CNRS-Université de Franche-Comté, Besançon, France.
authors.forename: Thomas
authors.initials: T
authors.lastname: Godin
authors.affiliation: Institut FEMTO-ST, UMR 6174 CNRS-Université de Franche-Comté, Besançon, France.
authors.forename: Cyril
authors.initials: C
authors.lastname: Billet
authors.affiliation: School of Mathematical Sciences, University College Dublin, Belfield, Dublin 4, Ireland.
authors.forename: Frédéric
authors.initials: F
authors.lastname: Dias
authors.affiliation: Department of Physics, University of Auckland, Auckland, New Zealand.
authors.forename: Miro
authors.initials: M
authors.lastname: Erkintalo
authors.affiliation: Department of Physics, Tampere University of Technology, Tampere, Finland.
authors.forename: Goëry
authors.initials: G
authors.lastname: Genty
authors.affiliation: Institut FEMTO-ST, UMR 6174 CNRS-Université de Franche-Comté, Besançon, France.
authors.forename: John M
authors.initials: JM
authors.lastname: Dudley