Rogue_Criterion_PRSA_rev.pdf (3.66 MB)
Rogue waves in multiphase solutions of the focusing nonlinear Schrödinger equation
journal contribution
posted on 2016-10-11, 14:43 authored by Marco Bertola, Gennady El, Alexander TovbisRogue 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 SciencesCitation
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 SocietyVersion
- 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
2016-09-26Publication date
2016-10-01Copyright date
2016Notes
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.2016.0340ISSN
1364-5021Publisher version
Language
- en