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Lax pair, Darboux transformation, breathers and rogue waves of an \(\pmb {N}\)-coupled nonautonomous nonlinear Schrödinger system for an optical fiber or a plasma

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Abstract

Optical fibers are used in communication, biological sensors and chemical sensors. Plasma is considered to be the most abundant common form of matter in the Universe, supporting some phenomena. Considering the inhomogeneous effects, we have investigated an N-coupled nonautonomous nonlinear Schrödinger system, where N is a positive integer. With respect to the simultaneous wave propagation of N fields in an optical fiber or a plasma, we construct a Lax pair and n-fold Darboux transformation, with which we obtain the first- and second-order breather, and rogue wave solutions, where n is a positive integer. Amplitudes of the two solitons change after their interaction, while velocities of the two solitons are unchanged after their interaction via the asymptotic analysis. Characteristics of the breathers are presented. Interactions between the two breathers, and interactions between the first-order rogue waves and breather-like solitons are discussed. We find that the inhomogeneous coefficients in the system under investigation affect the backgrounds, amplitudes and trajectories of the breathers and rogue waves.

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Notes

  1. Which can be understood as an interaction behavior between the two solitons [44]

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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

    Dan-Yu Yang, Bo Tian, Meng Wang, Xin Zhao, Wen-Rui Shan & Yan Jiang

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Yang, DY., Tian, B., Wang, M. et al. Lax pair, Darboux transformation, breathers and rogue waves of an \(\pmb {N}\)-coupled nonautonomous nonlinear Schrödinger system for an optical fiber or a plasma. Nonlinear Dyn 107, 2657–2666 (2022). https://doi.org/10.1007/s11071-021-06886-2

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