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

TL;DR

This paper establishes a quantitative relationship between modulational instability and various nonlinear excitations in optical fibers, revealing how rogue waves originate from specific instability conditions, aiding in controlled wave manipulation.

Contribution

It provides a novel quantitative framework linking modulational instability to well-known nonlinear wave phenomena, enhancing understanding of rogue wave formation.

Findings

Rogue waves originate from modulational instability under resonance conditions.

A quantitative correspondence is established based on frequency and propagation constants.

Results can inform control of nonlinear wave excitations in fibers.

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.