Rogue waves of the Fokas-Lenells equation

2012/09/25 by Jingsong He, Shuwei Xu, Kuppuswamy Porsezian · 1 citation
Mathematics · Physics and Astronomy · #math-ph #math.AP #math.MP #nlin.SI

paper · pdf · doi:10.1143/jpsj.81.124007

7 pages, 3 figures

arxiv created 2012/09/25 · arxiv updated 2015/06/11

Abstract

The Fokas-Lenells (FL) equation arises as a model eqution which describes for nonlinear pulse propagation in optical fibers by retaining terms up to the next leading asymptotic order (in the leading asymptotic order the nonlinear Schrödinger (NLS) equation results). Here we present an explicit analytical representation for the rogue waves of the FL equation. This representation is constructed by deriving an appropriate Darboux transformation (DT) and utilizing a Taylor series expansion of the associated breather solution. when certain higher-order nonlinear effects are considered, the propagation of rogue waves in optical fibers is given.

Cited by

• Asymptotic analysis of N-elliptic localized solutions for the Fokas--Lenells equation
• Miura transformation in bidifferential calculus and a vectorial Darboux transformation for the Fokas-Lenells equation

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