Abstract
In this paper, the nonautonomous Lenells-Fokas (LF) model is investigated with the modified Darboux transformation. Such analytical solutions of the nonautonomous LF model as the breather and rogue wave are presented. It is found that the breather velocity is time dependent. The dynamics of the periodic rogue wave, composite rogue waves and oscillating rogue wave is graphically discussed. Additionally, we observe that the breather evolves into a dark solitary wave while the rogue wave becomes a bright one by proper choices of the inhomogeneous functions. Our results could be useful for the design of experiments in the optical-fiber communications.
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