Spatiotemporal Complexity Mediated by Higher-Order Peregrine-Like Extreme Events

Frontiers in Physics

Marcel G. Clerc¹  Camus G. L. Tiofack²  Saliya Coulibaly³ 

[1] Departamento de Física and Millennium Institute for Research in Optics, FCFM, Universidad de Chile, Santiago, Chile;Faculty of Sciences, University of Maroua, Maroua, Cameroon;Université de Lille, CNRS, UMR 8523–PhLAM–Physique des Lasers Atomes et Molécules, Lille, France;

关键词: Peregrine soliton;    spatiotemporal chaos;    fiber ring cavity;    Lugiato-Lefever equation;    Kerr frequency comb;   

DOI  :  10.3389/fphy.2021.644584

来源: Frontiers

【 摘 要 】

The Peregrine soliton is the famous coherent solution of the non-linear Schrödinger equation, which presents many of the characteristics of rogue waves. Usually studied in conservative systems, when dissipative effects of injection and loss of energy are included, these intrigued waves can disappear. If they are preserved, their role in the dynamics is unknown. Here, we consider this solution in the framework of dissipative systems. Using the paradigmatic model of the driven and damped non-linear Schrödinger equation, the profile of a stationary Peregrine-type solution has been found. Hence, the Peregrine soliton waves are persistent in systems outside of the equilibrium. In the weak dissipative limit, analytical description has a good agreement with the numerical simulations. The stability has been studied numerically. The large bursts that emerge from the instability are analyzed by means of the local largest Lyapunov exponent. The observed spatiotemporal complexity is ruled by the unstable second-order Peregrine-type soliton.

【 授权许可】

CC BY