srep29238.pdf (1.05 MB)
Download file

Inverse scattering transform analysis of rogue waves using local periodization procedure

Download (1.05 MB)
journal contribution
posted on 30.06.2016, 09:13 authored by Stephane Randoux, Pierre Suret, Gennady El
The nonlinear Schrodinger equation (NLSE) stands out as the dispersive nonlinear partial differential equation that plays a prominent role in the modeling and understanding of the wave phenomena relevant to many fields of nonlinear physics. The question of random input problems in the one-dimensional and integrable NLSE enters within the framework of integrable tur- bulence, and the specific question of the formation of rogue waves (RWs) has been recently extensively studied in this context. The determination of exact analytic solutions of the focusing 1D-NLSE prototyping RW events of statistical relevance is now considered as the problem of central importance. Here we address this question from the perspective of the inverse scattering transform (IST) method that relies on the integrable nature of the wave equation. We develop a conceptually new approach to the RW classification in which appropriate, locally coherent structures are specifically isolated from a globally incoherent wave train to be subsequently analyzed by implementing a numerical IST procedure relying on a spatial periodization of the object under consideration. Using this approach we extend the existing classifications of the prototypes of RWs from standard breathers and their collisions to more general nonlinear modes characterized by their nonlinear spectra.

Funding

This work has been partially supported by Ministry of Higher Education and Research, Nord-Pas de Calais Regional Council and European Regional Development Fund (ERDF) through the Contrat de Projets Etat-R ́ egion (CPER) 2007–2013, as well as by the Agence Nationale de la Recherche through the LABEX CEMPI project (ANR-11-LABX-0007) and the OPTIROC project (ANR-12-BS04-0011 OPTIROC). This work has been also partially supported by the Interuniversity Attraction Poles program of the Belgian Science Policy Office, under grant IAP P7-35.

History

School

  • Science

Department

  • Mathematical Sciences

Published in

Scientific Reports

Citation

RANDOUX, S., SURET, P. and EL, G.A., 2016. Inverse scattering transform analysis of rogue waves using local periodization procedure. Scientific Reports, 6, article 29238.

Publisher

© The Authors. Published by Nature Publishing Group

Version

VoR (Version of Record)

Publisher statement

This work is made available according to the conditions of the Creative Commons Attribution 4.0 International (CC BY 4.0) licence. Full details of this licence are available at: http://creativecommons.org/licenses/ by/4.0/

Acceptance date

13/06/2016

Publication date

2016

Notes

This is an open access article licensed under a Creative Commons Attribution 4.0 International License (CC BY 4.0), http://creativecommons.org/licenses/by/4.0/

ISSN

2045-2322

Language

en

Usage metrics

Keywords

Licence

Exports