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Localized waves of the higher-order nonlinear Schrödinger-Maxwell-Bloch system with the sextic terms in an erbium-doped fiber

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Abstract

In this paper, we concentrate on the higher-order nonlinear Schrödinger-Maxwell-Bloch system with the sextic terms, which could characterize the ultra-short optical pulses in an erbium-doped fiber. Proceeding from the existing Lax pair and one-fold Darboux transformation (DT), we build an N-fold generalized DT with one spectral parameter by means of the limit procedure, and on this basis determine the Nth-order solutions of that system. The second- and third-order degenerate solitons are shown through the second-order and third-order solutions, respectively, and we also present the second-order degenerate breather through the second-order solutions. We obtain the eye-shaped rogue wave involving one hump and two valleys, rogue wave involving four valleys, as well as four-petaled rogue wave involving two humps and two valleys via the first-order solutions. Using the second-order solutions, we obtain the interaction between the two first-order rogue waves and show that the second-order rogue wave divides into three first-order rogue waves which are arranged in the triangle structure. Modifying that generalized DT, we work out the second-order and third-order mixed wave solutions, and then show the interactions between the first-order/second-order rogue wave and first-order breather.

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Notes

  1. An “ultra-short pulse” refers to a pulse with the duration of 100 fs or less [3].

  2. Many physical systems exhibit behaviour related with the occurrence of high-amplitude events with low likelihood but significant influence [30].

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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 BUPT Excellent Ph.D. Students Foundation under Grant No. CX2022156.

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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

    Yuan Shen, Bo Tian, Tian-Yu Zhou & Chong-Dong Cheng

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  1. Yuan Shen
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Shen, Y., Tian, B., Zhou, TY. et al. Localized waves of the higher-order nonlinear Schrödinger-Maxwell-Bloch system with the sextic terms in an erbium-doped fiber. Nonlinear Dyn 112, 1275–1290 (2024). https://doi.org/10.1007/s11071-023-09005-5

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