Higher-order Peregrine combs and Peregrine walls for the variable-coefficient Lenells-Fokas equation. (February 2017) - Wang, Zi-Qi; Wang, Xin; Wang, Lei; Sun, Wen-Rong; Qi, Feng-Hua
Abstract: In this paper, we study the variable-coefficient Lenells-Fokas (LF) model. Under large periodic modulations in the variable coefficients of the LF model, the generalized Akhmediev breathers develop into the breather multiple births (BMBs) from which we obtain the Peregrine combs (PCs). The PCs can be considered as the limiting case of the BMBs and be transformed into the Peregrine walls (PWs) with a specific amplitude of periodic modulation. We further investigate the spatiotemporal characteristics of the PCs and PWs analytically. Based on the second-order breather and rogue-wave solutions, we derive the corresponding higher-order structures (higher-order PCs and PWs) under proper periodic modulations. What is particularly noteworthy is that the second-order PC can be converted into the Peregrine pyramid which exhibits the higher amplitude and thickness. Our results could be helpful for the design of experiments in the optical fiber communications. Highlights: The breather multiple births, Peregrine comb and Peregrine wall. The novel dynamics of the higher-order Peregrine comb and Peregrine wall. The mechanisms of the Peregrine comb and Peregrine wall.