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Title: Rogue waves in multiphase solutions of the focusing nonlinear Schrödinger equation
Authors: Bertola, Marco
El, G.A.
Tovbis, Alexander
Issue Date: 2016
Publisher: © The Authors. Published by The Royal Society
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.
Abstract: 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.
Description: This paper is in closed access until October 2017.
Version: Accepted for publication
DOI: 10.1098/rspa.2016.0340
URI: https://dspace.lboro.ac.uk/2134/22790
Publisher Link: http://dx.doi.org/10.1098/rspa.2016.0340
ISSN: 1364-5021
Appears in Collections:Closed Access (Maths)

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