Modulational instability, higher-order localized wave structures, and nonlinear wave interactions for a nonautonomous Lenells-Fokas equation in inhomogeneous fibers

In this paper, the nonautonomous Lenells-Fokas (LF) model is investigated. The modulational instability analysis of the solutions with variable coefficients in the presence of a small perturbation is studied. Higher-order soliton, breather, earthwormon, and rogue wave solutions of the nonautonomous...

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Published in:Chaos (Woodbury, N.Y.) N.Y.), 2015-06, Vol.25 (6), p.063111-063111
Main Authors: Wang, Lei, Zhu, Yu-Jie, Qi, Feng-Hua, Li, Min, Guo, Rui
Format: Article
Language:English
Subjects:
Breathers
Design of experiments
Diamonds
Elastic scattering
Mathematical models
Optical communication
Optical fibers
Solitary waves
Stability analysis
Structural stability
Wave interaction
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Summary:In this paper, the nonautonomous Lenells-Fokas (LF) model is investigated. The modulational instability analysis of the solutions with variable coefficients in the presence of a small perturbation is studied. Higher-order soliton, breather, earthwormon, and rogue wave solutions of the nonautonomous LF model are derived via the n-fold variable-coefficient Darboux transformation. The solitons and earthwormons display the elastic collisions. It is found that the nonautonomous LF model admits the higher-order periodic rogue waves, composite rogue waves (rogue wave pair), and oscillating rogue waves, whose dynamics can be controlled by the inhomogeneous nonlinear parameters. Based on the second-order rogue wave, a diamond structure consisting of four first-order rogue waves is observed. In addition, the semirational solutions (the mixed rational-exponential solutions) of the nonautonomous LF model are obtained, which can be used to describe the interactions between the rogue waves and breathers. Our results could be helpful for the design of experiments in the optical fiber communications.
ISSN:1054-1500
1089-7682
DOI:10.1063/1.4922025