Spatiotemporal Complexity Mediated by Higher-Order Peregrine-Like Extreme Events - Coulibaly, Saliya; Tiofack, Camus G. L.; Clerc, Marcel G. (Frontiers in Physics, 2021)
Peregrine soliton is the famous coherent solution of the nonlinear 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 preserve, 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 nonlinear Schrödinger equation, the profile of a stationary Peregrine-type solution has been found. Hence, the Peregrine soliton waves are persistent in systems out of 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-orderPeregrine-type soliton.