Floquet Analysis of Kuznetsov-Ma breathers: A Path Towards Spectral Stability of Rogue Waves - Archive ouverte HAL Access content directly
Journal Articles Physical Review E Year : 2017

Floquet Analysis of Kuznetsov-Ma breathers: A Path Towards Spectral Stability of Rogue Waves

(1) , (2, 3) , (4) , (5) , (6) , (7)
1
2
3
4
5
6
7

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 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. Lastly, we speculate on the implications of these conclusions towards the stability of the Peregrine soliton structure.

Dates and versions

hal-01465351 , version 1 (11-02-2017)

Identifiers

Cite

Jesús Cuevas-Maraver, Panayotis Kevrekidis, Dimitri J. Frantzeskakis, Nikolaos Karachalios, Mariana Larger Haragus, et al.. Floquet Analysis of Kuznetsov-Ma breathers: A Path Towards Spectral Stability of Rogue Waves. Physical Review E , 2017, 96 (1), pp.012202. ⟨10.1103/PhysRevE.96.012202⟩. ⟨hal-01465351⟩
471 View
0 Download

Altmetric

Share

Gmail Facebook Twitter LinkedIn More