The n-order rogue waves of Fokas-Lenells equation
Shuwei Xu, Jingsong He, Yi Cheng, K. Porseizan
TL;DR
This paper derives explicit formulas for n-order rogue waves in the Fokas-Lenells equation using Darboux transformations and Taylor series expansion, advancing understanding of nonlinear pulse dynamics in optical fibers.
Contribution
It introduces a method to explicitly construct n-order rogue waves of the Fokas-Lenells equation with free parameters, extending previous solutions beyond lower orders.
Findings
Explicit n-order rogue wave solutions with 2n+3 free parameters
Application of Darboux transformation to generate solutions
Enhanced modeling of nonlinear pulse propagation in optical fibers
Abstract
Considering certain terms of the next asymptotic order beyond the nonlinear Schrodinger equation (NLS) equation, the Fokas-Lenells (FL) equation governed by the FL system arise as a model for nonlinear pulse propagation in optical fibers. The expressions of the q[n] and r[n] in the FL system are generated by n-fold Darboux transformation (DT). Further, a Taylor series expansion about the n-order breather solutions q[n] generated using DT by assuming periodic seed solutions under reduction can generate the n-order rogue waves of the FL equation explicitly with 2n+3 free parameters.
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Taxonomy
TopicsNonlinear Waves and Solitons · Ocean Waves and Remote Sensing · Coastal and Marine Dynamics