Stabilizing Rogue Waves in a Driven-Dissipative Nonlinear System

The study of rogue waves (RWs) is currently an active multidisciplinary research area, encompassing oceanography, hydrodynamics, optics, plasma physics, Bose-Einstein condensation, and others. RWs are often modeled using Peregrine solitons or Kuznetsov–Ma breathers, which, however, have recently been shown to be dynamically unstable. Investigating the stability of RWs has now become an intriguing and important topic, not only for fundamental scientific interest but also for practical applications. Here, we propose a scheme for stabilizing RWs by utilizing external driving and dissipation in a nonlinear system governed by the Lugiato-Lefever equation. We find that RW instability can be completely suppressed through multistability, together with a dual balance between dispersion and nonlinearity and between driving and dissipation. We also elucidate the stability diagram of RWs in the parameter space of detuning and driving intensity, and demonstrate that RWs may exhibit different propagation dynamics in different regions of this parameter space. The scheme presented here can be extended to stabilize other nonlinearly localized structures with nonzero backgrounds in various driven-dissipative nonlinear systems.