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Jacobian-Elliptic-Function and Rogue-Periodic-Wave Solutions of a Fifth-Order Nonlinear Schrödinger Equation in an Optical Fiber

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Abstract

Optical fiber communication becomes the main research direction in optical networking, computing, telecommunications and data communication. In an optical fiber, a fifth-order nonlinear Schrödinger equation describing the propagation of ultrashort optical pulses is studied in this paper. We give the Jacobian-elliptic-function solutions of that equation as the seed solutions. Based on the periodic background, we combine the nonlinearization of the spectral problem with the Darboux-transformation method to derive the rogue-periodic-wave solutions. When the coefficient \(\alpha _2\) in that equation increases, the period and maximum amplitude of the onefold rogue-dn-periodic wave remain unchanged, while the minimum amplitude of the onefold rogue-dn-periodic wave rises; when the coefficient \(\alpha _1\) or \(\alpha _3\) in that equation increases, the maximum amplitude of the onefold rogue-dn-periodic wave remains unchanged, the minimum amplitude of the onefold rogue-dn-periodic wave decreases, while the period of the onefold rogue-dn-periodic becomes smaller. The conclusion of the twofold rogue-cn-periodic wave is the same as that of the onefold rogue-dn-periodic wave. When the coefficient \(\alpha _1\) in that equation increases, the maximum amplitude of the onefold rogue-cn-periodic wave remains unchanged, the minimum amplitude of the onefold rogue-cn-periodic wave rises, while the period of the onefold rogue-cn-periodic wave becomes smaller; when the coefficient \(\alpha _2\) in that equation increases, the period and maximum amplitude of the onefold rogue-cn-periodic wave remain unchanged, while the minimum amplitude of the onefold rogue-cn-periodic wave decreases; when the coefficient \(\alpha _3\) in that equation increases, the maximum amplitude of the onefold rogue-cn-periodic wave remains unchanged, the minimum amplitude of the onefold rogue-cn-periodic wave decreases, while the period of the onefold rogue-cn-periodic wave becomes smaller.

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Notes

  1. Jacobian elliptic functions are the two-periodic meromorphic functions [28].

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Acknowledgements

We express our sincere thanks to the Editors and Reviewers for their valuable comments. This work has been supported by the National Natural Science Foundation of China under Grant Nos. 11772017, 11272023 and 11471050, by the Fund of State Key Laboratory of Information Photonics and Optical Communications (Beijing University of Posts and Telecommunications), China (IPOC: 2017ZZ05), and by the Fundamental Research Funds for the Central Universities of China under Grant No. 2011BUPTYB02.

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  1. State Key Laboratory of Information Photonics and Optical Communications, and School of Science, Beijing University of Posts and Telecommunications, Beijing, 100876, China

    Cheng-Cheng Wei, Bo Tian, Xin Zhao & Yu-Qi Chen

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  1. Cheng-Cheng Wei
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  2. Bo Tian
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Correspondence to Bo Tian.

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Wei, CC., Tian, B., Zhao, X. et al. Jacobian-Elliptic-Function and Rogue-Periodic-Wave Solutions of a Fifth-Order Nonlinear Schrödinger Equation in an Optical Fiber. Qual. Theory Dyn. Syst. 22, 38 (2023). https://doi.org/10.1007/s12346-022-00720-9

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