Floquet Analysis of Kuznetsov--Ma breathers: A Path Towards Spectral Stability of Rogue Waves
arXiv:1701.06212 · doi:10.1103/PhysRevE.96.012202
Abstract
In the present work, we aim at taking a step towards the spectral stability analysis of Peregrine solitons, i.e., wave structures that are used to emulate extreme wave events. Given the space-time localized nature of Peregrine solitons, this is a priori a non-trivial task. Our main tool in this effort will be the study of the spectral stability of the periodic generalization of the Peregrine soliton in the evolution variable, namely the Kuznetsov--Ma breather. Given the periodic structure of the latter, we compute the corresponding Floquet multipliers, and examine them in the limit where the period of the orbit tends to infinity. This way, we extrapolate towards the stability of the limiting structure, namely the Peregrine soliton. We find that multiple unstable modes of the background are enhanced, yet no additional unstable eigenmodes arise as the Peregrine limit is approached. We explore the instability evolution also in direct numerical simulations.
References in corpus (3)
Cited by in corpus (10)
- The Mechanism of Kuznetsov-Ma Breather
- Transverse Instability of Rogue Waves
- Stabilization of the Peregrine soliton and Kuznetsov-Ma breathers by means of nonlinearity and dispersion management
- Rogue Waves and Periodic Solutions of a Nonlocal Nonlinear Schrödinger Model
- Excitation of Peregrine-type waveforms from vanishing initial conditions in the presence of periodic forcing
- Exciting extreme events in the damped and AC-driven NLS equation through plane wave initial conditions
- Stability of compact breathers in translationally-invariant nonlinear chains with flat dispersion bands
- Rogue waves in extended Gross-Pitaevskii Models with a Lee-Huang-Yang correction
- Extreme wave events for a nonlinear Schrödinger equation with linear damping and Gaussian driving
- Floquet stability of periodically stationary pulses in a short-pulse fiber laser