title: Modulational instability, higher-order localized wave structures, and nonlinear wave interactions for a nonautonomous Lenells-Fokas equation in inhomogeneous fibers.
abstract: 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.
authors.affiliation: Department of Mathematics and Physics, North China Electric Power University, Beijing 102206, People's Republic of China.
authors.forename: Lei
authors.initials: L
authors.lastname: Wang
authors.affiliation: Institute of Electrical and Electronic Engineering, North China Electric Power University, Beijing 102206, People's Republic of China.
authors.forename: Yu-Jie
authors.initials: YJ
authors.lastname: Zhu
authors.affiliation: School of Information, Beijing Wuzi University, Beijing 101149, People's Republic of China.
authors.forename: Feng-Hua
authors.initials: FH
authors.lastname: Qi
authors.affiliation: Department of Mathematics and Physics, North China Electric Power University, Beijing 102206, People's Republic of China.
authors.forename: Min
authors.initials: M
authors.lastname: Li
authors.affiliation: School of Mathematics, Taiyuan University of Technology, Taiyuan 030024, People's Republic of China.
authors.forename: Rui
authors.initials: R
authors.lastname: Guo