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The n-order rogue waves of Fokas-Lenells equation

Research paper by Shuwei Xu, Jingsong He, Yi Cheng, K. Porseizan

Indexed on: 26 Nov '12Published on: 26 Nov '12Published in: Nonlinear Sciences - Exactly Solvable and Integrable Systems



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.