Rogue Waves In Multiphase Solutions Of The Focusing Nonlinear Schrödinger Equation

Keywords

Fnite-band potentials; Focusing nonlinear Schrödinger equation; Rogue waves

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 generalized rogue wave notion then naturally enters as a largeamplitude localized 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 finiteband potentials of the fNLS equation that exhibit generalized rogue waves.

Publication Date

10-1-2016

Publication Title

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

Volume

472

Issue

2194

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1098/rspa.2016.0340

Socpus ID

85020247607 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/85020247607

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