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Rogue waves in multiphase solutions of the focusing nonlinear Schrödinger equation

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journal contribution
posted on 2016-10-11, 14:43 authored by Marco Bertola, Gennady El, Alexander Tovbis
Rogue waves appearing on deep water or in optical fibres are often modelled by certain breather solutions of the focusing nonlinear Schrödinger (fNLS) equation which are referred to as solitons on finite background (SFBs). A more general modelling of rogue waves can be achieved via the consideration of multiphase, or finite-band, fNLS solutions of whom the standard SFBs and the structures forming due to their collisions represent particular, degenerate, cases. A generalised rogue wave notion then naturally enters as a large amplitude localised coherent structure occurring within a finite-band fNLS solution. In this paper, we use the winding of real tori to show the mechanism of the appearance of such generalized rogue waves and derive an analytical criterion distinguishing finite band potentials of the fNLS equation that exhibit generalised rogue waves.

History

School

  • Science

Department

  • Mathematical Sciences

Published in

Proceedings of the Royal Society of London: Mathematical, Physical and Engineering Sciences

Citation

BERTOLA, M., EL, G.A. and TOVBIS, A., 2016. Rogue waves in multiphase solutions of the focusing nonlinear Schrödinger equation. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 472 (2194), paper 340.

Publisher

© The Authors. Published by The Royal Society

Version

  • AM (Accepted Manuscript)

Publisher statement

This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/

Acceptance date

2016-09-26

Publication date

2016-10-01

Copyright date

2016

Notes

This paper was accepted for publication in the journal Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences and the definitive published version is available at http://dx.doi.org/10.1098/rspa.2016.0340

ISSN

1364-5021

Language

  • en

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