Quantitative relations between modulational instability and several well-known nonlinear excitations

Abstract

We study 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. We especially demonstrate that rogue wave comes from modulational instability with the resonance perturbation on continuous-wave background. The numerical simulations are performed to test these theoretical results. These results will deepen our understanding of rogue wave excitation and be helpful for controllable nonlinear wave excitations in nonlinear fiber and other nonlinear systems.