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

J. Cuevas-Maraver, P. G. Kevrekidis, D. J. Frantzeskakis, N. I. Karachalios, M. Haragus, and G. James
Phys. Rev. E 96, 012202 – Published 5 July 2017

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.

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  • Received 22 January 2017
  • Revised 4 May 2017

DOI:https://doi.org/10.1103/PhysRevE.96.012202

©2017 American Physical Society

Physics Subject Headings (PhySH)

  1. Physical Systems
Nonlinear Dynamics

Authors & Affiliations

J. Cuevas-Maraver

  • Grupo de Física No Lineal, Departamento de Física Aplicada I, Universidad de Sevilla, Escuela Politécnica Superior, C/ Virgen de África, 7, 41011-Sevilla, Spain and Instituto de Matemáticas de la Universidad de Sevilla (IMUS), Edificio Celestino Mutis, Avenida Reina Mercedes s/n, 41012-Sevilla, Spain

P. G. Kevrekidis

  • Department of Mathematics and Statistics, University of Massachusetts Amherst, Amherst, Massachusetts 01003-4515, USA

D. J. Frantzeskakis

  • Department of Physics, National and Kapodistrian University of Athens, Panepistimiopolis, Zografos, Athens 15784, Greece

N. I. Karachalios

  • Department of Mathematics, University of the Aegean, Karlovassi, 83200 Samos, Greece

M. Haragus

  • Institut FEMTO-ST, Département OPTIQUE, Université Bourgogne Franche-Comté, 25030 Besançon Cedex, France

G. James

  • INRIA Grenoble - Rhône-Alpes, Bipop Team-Project, Inovallée, 655 Avenue de l'Europe, 38334 Saint Ismier Cedex, France

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Issue

Vol. 96, Iss. 1 — July 2017

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