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Dynamics of localized waves for the higher-order nonlinear Schrödinger equation with self-steepening and cubic–quintic nonlinear terms in optical fibers

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Abstract

Under investigation in this paper is the dynamics of localized waves for the higher-order nonlinear Schrödinger equation with self-steepening and cubic–quintic nonlinear terms, which describes the propagation of ultrashort pulses in optical fibers. Firstly, based on Lax pair, the Nth-fold Darboux transformation is constructed. Secondly, the N-soliton solutions are obtained and the interactions of solitons are analyzed graphically. Moreover, the Akhmediev breather, space-time period breather and line breather are derived. The interactions of two breathers are shown and discussed. In addition, the first-order usual rogue wave and line rogue wave are given and investigated. And the different structures of second- and third-order rogue wave are observed. Finally, the interaction solutions between rogue wave and one-breather are constructed. These results in the present work could be used to understand related physical phenomena in nonlinear optics and relevant fields.

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Funding

This work was supported by the National Natural Science Foundation of China [grant numbers 11801597].

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Authors and Affiliations

  1. College of Science, Minzu University of China, Beijing, 100081, China

    Sheng-Xiong Yang, Yu-Feng Wang & Xi Zhang

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  1. Sheng-Xiong Yang
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  2. Yu-Feng Wang
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Yang, SX., Wang, YF. & Zhang, X. Dynamics of localized waves for the higher-order nonlinear Schrödinger equation with self-steepening and cubic–quintic nonlinear terms in optical fibers. Nonlinear Dyn 111, 17439–17454 (2023). https://doi.org/10.1007/s11071-023-08755-6

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