title: Breather transition dynamics, Peregrine combs and walls, and modulation instability in a variable-coefficient nonlinear Schrödinger equation with higher-order effects.
abstract: We study a variable-coefficient nonlinear Schrödinger (vc-NLS) equation with higher-order effects. We show that the breather solution can be converted into four types of nonlinear waves on constant backgrounds including the multipeak solitons, antidark soliton, periodic wave, and W-shaped soliton. In particular, the transition condition requiring the group velocity dispersion (GVD) and third-order dispersion (TOD) to scale linearly is obtained analytically. We display several kinds of elastic interactions between the transformed nonlinear waves. We discuss the dispersion management of the multipeak soliton, which indicates that the GVD coefficient controls the number of peaks of the wave while the TOD coefficient has compression effect. The gain or loss has influence on the amplitudes of the multipeak soliton. We further derive the breather multiple births and Peregrine combs by using multiple compression points of Akhmediev breathers and Peregrine rogue waves in optical fiber systems with periodic GVD modulation. In particular, we demonstrate that the Peregrine comb can be converted into a Peregrine wall by the proper choice of the amplitude of the periodic GVD modulation. The Peregrine wall can be seen as an intermediate state between rogue waves and W-shaped solitons. We finally find that the modulational stability regions with zero growth rate coincide with the transition condition using rogue wave eigenvalues. Our results could be useful for the experimental control and manipulation of the formation of generalized Peregrine rogue waves in diverse physical systems modeled by vc-NLS equation with higher-order effects.
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: School of Energy Power and Mechanical Engneering, North China Electric Power University, Beijing 102206, People's Republic of China.
authors.forename: Jian-Hui
authors.initials: JH
authors.lastname: Zhang
authors.affiliation: School of Physics, Northwest University, Xi'an 710069, People's Republic of China.
authors.forename: Chong
authors.initials: C
authors.lastname: Liu
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 Information, Beijing Wuzi University, Beijing 101149, People's Republic of China.
authors.forename: Feng-Hua
authors.initials: FH
authors.lastname: Qi