Title

Orbital Instability Of The Peregrine Soliton

Abstract

The Peregrine soliton is one possible model of a rogue wave. Importantly, this type of soliton corresponds nicely to rogue waves recently observed experimentally in a water tank [A. Chabchoub, N. P. Hoffmann, and N. Akhmediev, Phys. Rev. Lett. 106, 204502 (2011)] and in optical fiber [B. Kibler, J. Fatome, C. Finot, G. Millot, F. Dias, G. Genty, N. Akhmediev, and J. M. Dudley, Nat. Phys. 6, 790 (2010)]. Starting with a family of Peregrine solitons indexed by their spectral parameter, we analytically demonstrate a type of instability in the Peregrine soliton through a concise orbital stability analysis. This analysis is completely analytical, and to verify the approach we also discuss a numerical linear instability analysis. We give the growth/decay rate for these solitons as a function of the initial amplitude, which for each soliton shall depend on the spectral parameter.

Publication Date

5-15-2014

Publication Title

Journal of the Physical Society of Japan

Volume

83

Issue

5

Number of Pages

-

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.7566/JPSJ.83.054005

Socpus ID

84923762492 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/84923762492

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