Baseband modulation instability as the origin of rogue waves

Year: 2015

Authors: Baronio F., Chen S., Grelu P., Wabnitz S., Conforti M.

Autors Affiliation: Dipartimento di Ingegneria dell’Informazione, Universita di Brescia, Via Branze 38, 25123 Brescia, Italy; Department of Physics, Southeast University, Nanjing 211189,China; Laboratoire Interdisciplinaire Carnot de Bourgogne, UMR 6303 CNRS-Universite de Bourgogne, Boıte Postale 47870 Dijon Cedex 21078, France; PhLAM/IRCICA UMR 8523/USR 3380, CNRS-Universite Lille 1, F-59655 Villeneuve d’Ascq, France

Abstract: We study the existence and properties of rogue-wave solutions in different nonlinear wave evolution models that are commonly used in optics and hydrodynamics. In particular, we consider the Fokas-Lenells equation, the defocusing vector nonlinear Schrodinger equation, and the long-wave-short-wave resonance equation. We show that rogue-wave solutions in all of these models exist in the subset of parameters where modulation instability is present if and only if the unstable sideband spectrum also contains cw or zero-frequency perturbations as a limiting case (baseband instability). We numerically confirm that rogue waves may only be excited from a weakly perturbed cw whenever the baseband instability is present. Conversely, modulation instability leads to nonlinear periodic oscillations.


Volume: 91 (3)      Pages from: 033804  to: 033804

More Information: The present research was supported by the Italian Ministry of University and Research (MIUR, Project No. 2012BFNWZ2) and by the Agence Nationale de la Recherche (Projects No. ANR-13-JS04-0004 TOPWAVE, No. ANR-14-ACHN-0014 NoAWE, and No. ANR-12-BS04-0011 OP-TIROC).
KeyWords: Modulation; Stability, Baseband modulation; Dinger equation; Limiting case; Modulation instabilities; Nonlinear periodic oscillation; Nonlinear waves; Sideband spectrum; Zero frequency, Nonlinear equations
DOI: 10.1103/PhysRevA.91.033804

Citations: 113
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