TY - JOUR
TI - Floquet analysis of Kuznetsov-Ma breathers: A path towards spectral stability of rogue waves
AU - Cuevas-Maraver, J.
AU - Kevrekidis, P.G.
AU - Frantzeskakis, D.J.
AU - Karachalios, N.I.
AU - Haragus, M.
AU - James, G.
JO - Physical Review E
PY - 2017
VL - 96
TODO - 1
SP - null
PB - American Physical Society
SN - 2470-0045, 2470-0053
TODO - 10.1103/PhysRevE.96.012202
TODO - Solitons;  Stability, Eigen modes;  Extreme wave events;  Floquet analysis;  Floquet multiplier;  Non-trivial tasks;  Spectral stability;  Unstable modes;  Wave structures, Periodic structures
TODO - 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 nontrivial 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. © 2017 American Physical Society.
ER -