Rogue waves of the Fokas-Lenells equation
Jingsong He, Shuwei Xu, Kuppuswamy Porsezian
TL;DR
This paper derives explicit rogue wave solutions for the Fokas-Lenells equation, a model for nonlinear pulse propagation in optical fibers, using Darboux transformation and Taylor series expansion.
Contribution
It provides the first explicit analytical rogue wave solutions for the Fokas-Lenells equation, incorporating higher-order nonlinear effects.
Findings
Explicit rogue wave solutions derived
Darboux transformation used for solution construction
Higher-order nonlinear effects included in analysis
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 Schr\"odinger (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.
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