Rogue waves and rational solutions of the nonlinear Schrödinger equation

We present a method for finding the hierarchy of rational solutions of the self-focusing nonlinear Schrödinger equation and present explicit forms for these solutions from first to fourth order. We also explain their relation to the highest amplitude part of a field that starts with a plane wave per...

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Bibliographic Details
Published inPhysical review. E, Statistical, nonlinear, and soft matter physics Vol. 80; no. 2 Pt 2; p. 026601
Main Authors Akhmediev, Nail, Ankiewicz, Adrian, Soto-Crespo, J M
Format Journal Article
LanguageEnglish
Published United States 01.08.2009
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Summary:We present a method for finding the hierarchy of rational solutions of the self-focusing nonlinear Schrödinger equation and present explicit forms for these solutions from first to fourth order. We also explain their relation to the highest amplitude part of a field that starts with a plane wave perturbed by random small amplitude radiation waves. Our work can elucidate the appearance of rogue waves in the deep ocean and can be applied to the observation of rogue light pulse waves in optical fibers.
ISSN:1539-3755
DOI:10.1103/physreve.80.026601