Baseband Modulation Instability as the Origin of Rogue Waves

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 Fokas-Lenells equation, the defocusing vector nolinear Schrödinger 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.

References in corpus (4)

• Instabilities, breathers and rogue waves in optics
• Vector Rogue Waves and Baseband Modulation Instability in the Defocusing Regime
• Rogue-wave solutions of a three-component coupled nonlinear Schrodinger equation
• Inelastic Scattering and Interactions of Three-Wave Parametric Solitons

Cited by in corpus (4)

• Doubly periodic solutions of the focusing nonlinear Schrödinger equation: recurrence, period doubling and amplification outside the conventional modulation instability band
• Experimental study of breathers and rogue waves generated by random waves over non-uniform bathymetry
• A new integrable model of long wave-short wave interaction and linear stability spectra
• Vector rogue waves in spin-1 Bose-Einstein condensates with spin-orbit coupling