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The n ‐order rogue waves of Fokas–Lenells equation
Author(s) -
Xu Shuwei,
He Jingsong,
Cheng Yi,
Porseizan K.
Publication year - 2015
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3133
Subject(s) - mathematics , rogue wave , eigenfunction , breather , mathematical physics , order (exchange) , matrix (chemical analysis) , nonlinear system , mathematical analysis , transformation (genetics) , nonlinear schrödinger equation , taylor series , reduction (mathematics) , eigenvalues and eigenvectors , schrödinger equation , physics , quantum mechanics , geometry , chemistry , biochemistry , gene , chromatography , finance , economics
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 (2 n + 1) × (2 n + 1) determinant and 2 n × 2 n 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 2 n + 3 free parameters. Copyright © 2014 John Wiley & Sons, Ltd.
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