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Floquet analysis of Kuznetsov-Ma breathers: A path towards spectral stability of rogue waves

 

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Opened Access Floquet analysis of Kuznetsov-Ma breathers: A path towards spectral stability of rogue waves
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Author: Cuevas-Maraver, Jesús
Kevrekidis, Panayotis G.
Frantzeskakis, Dimitri J.
Karachalios, Nikolaos I.
Haragus, Mariana
James, Guillaume
Coordinator/Director: Archilla, Juan F. R.
Department: Universidad de Sevilla. Departamento de Física Aplicada I
Date: 2017
Published in: Physical Review E, 1, 012202-1-012202-8.
Document type: Article
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 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.
Cite: Cuevas-Maraver, J., Kevrekidis, P.G., Frantzeskakis, D.J., Karachalios, N.I., Haragus, M. y James, G. (2017). Floquet analysis of Kuznetsov-Ma breathers: A path towards spectral stability of rogue waves. Physical Review E, 1, 012202-1-012202-8.
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URI: http://hdl.handle.net/11441/62397

DOI: 10.1103/PhysRevE.96.012202

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