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Article Dans Une Revue Physical Review A : Atomic, molecular, and optical physics [1990-2015] Année : 2015

Baseband modulation instability as the origin of rogue waves

Résumé

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 Schrödinger equation, and the long-wave-shortwave 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.
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hal-02389169 , version 1 (02-12-2019)

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Fabio Baronio, Shihua Chen, Philippe Grelu, Stefan Wabnitz, Matteo Conforti. Baseband modulation instability as the origin of rogue waves. Physical Review A : Atomic, molecular, and optical physics [1990-2015], 2015, 91 (3), ⟨10.1103/PhysRevA.91.033804⟩. ⟨hal-02389169⟩
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