The n-order rogue waves of Fokas-Lenells equation

Considering certain terms of the next asymptotic order beyond the nonlinear Schrodinger 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 2x2 matrix, expressed by a ratio of (2n+1)x(2n+1) determinant and 2nx2n 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 (c) 2014 John Wiley & Sons, Ltd.