Quantitative Relation between Modulational Instability and Several Well-known Nonlinear Excitations

Abstract

We study on the relations between modulational instability and several well-known nonlinear excitations in a nonlinear fiber, such as bright soliton, nonlinear continuous wave, Akhmediev breather, Peregrine rogue wave, and Kuznetsov-Ma breather. We present a quantitative correspondence between them based on the dominant frequency and propagation constant of each perturbation on a continuous wave background. Especially, we find rogue wave comes from modulational instability under the "resonance" perturbation with continuous wave background. These results will deepen our understanding on rogue wave excitation and could be helpful for controllable nonlinear wave excitations in nonlinear fiber and other nonlinear systems.

5 pages, 1 figure

References in corpus (10)

• Vector Rogue Waves and Baseband Modulation Instability in the Defocusing Regime
• Baseband Modulation Instability as the Origin of Rogue Waves
• High-order Rogue Waves in Vector Nonlinear Schrödinger Equations
• Rogue-wave solutions of a three-component coupled nonlinear Schrodinger equation
• Localized nonlinear waves in a two-mode nonlinear fiber
• State Transition Induced by Higher-order Effects and Background Frequency
• Rational W-shaped Optical Soliton on Continuous Wave in Presence of Kerr Dispersion and Stimulated Raman Scattering
• The Rogue Waves with Quintic Nonlinearity and Nonlinear Dispersion effects in Nonlinear Optical Fibers
• Optimal frequency conversion in the nonlinear stage of modulation instability
• Novel Localized Waves in a Two-mode Nonlinear Fiber with High-order Effects

Cited by in corpus (14)

• Symmetric and asymmetric optical multi-peak solitons on a continuous wave background in the femtosecond regime
• Experimental realization of the Peregrine soliton in repulsive two-component Bose-Einstein condensates
• Stable Soliton Excitations in Modulational Instability Regime with the Fourth-order Effects
• The Mechanism of Kuznetsov-Ma Breather
• Darboux transformation and solitonic solution to the coupled complex short pulse equation
• Growth rate of modulation instability driven by superregular breathers
• Modulation instability, rogue waves and spectral analysis for the sixth-order nonlinear Schrodinger equation
• High-order rogue waves of a long wave-short wave model
• Non-degenerate multi-rogue waves and easy ways of their excitation
• Auto-modulation versus breathers in the nonlinear stage of modulational instability
• Several Localized Waves Induced by Linear Interference between a Nonlinear Plane Wave and Bright Solitons
• Controllable generations of several nonlinear waves in optical fibers with third-order dispersion
• Measuring the rogue wave pattern triggered from Gaussian perturbations by deep learning
• Rogue waves collision under incident momentum modulation in two-component Bose-Einstein condensates