The n-order rogue waves of Fokas-Lenells equation

Considering certain terms of the next asymptotic order beyond the nonlinear Schrödinger equation, the Fokas–Lenells (FL) equation governed by the FL system arises 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 the n‐fold Darboux transformation (DT), each element of the matrix is a 2 × 2 matrix, expressed by a ratio of (2n + 1) × (2n + 1) determinant and 2n × 2n determinant of eigenfunctions. Further, a Taylor series expansion about the n‐order breather solutions q[n] generated using by DT and assuming periodic seed solutions under reduction can generate the n‐order rogue waves of the FL equation explicitly with 2n + 3 free parameters. Copyright © 2014 John Wiley & Sons, Ltd.