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Dynamics of certain localized waves in an erbium-doped fiber system with the quintic terms

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  • Shen, Yuan

Abstract

A higher-order nonlinear Schrödinger-Maxwell-Bloch system with the quintic terms is the main focus of this study. This system is able to provide an explanation for the ultra-short optical pulses that occur in an erbium-doped fiber. We formulate an N-fold generalized Darboux transformation (DT) using the limit approach, starting with an existing Lax pair and one-fold DT, where N is a positive integer. From this, we acquire the Nth-order solutions for that system. We present the second-order degenerate soliton and breather by the application of the second-order solutions, discovering that the rogue waves with varying structures emerge in the interaction regions. The second-order rogue wave exhibiting triangular structure is obtained through the second-order solutions, while the third-order rogue waves featuring triangular and pentagonal structures are derived from the third-order solutions. We obtain the second-order and third-order mixed wave solutions by modifying that generalized DT. Interactions between the first-order rogue wave and first-order breather, as well as interactions between the second-order rogue wave and first-order breather, are derived, illustrating the generation of rogue waves with diverse structures. Furthermore, we provide the interaction between the first-order breather and second-order rogue wave exhibiting a triangular structure. The results of this study may potentially provide valuable insights for designing experiments with controlled initial conditions to excite the localized waves in optical fibers.

Suggested Citation

  • Shen, Yuan, 2025. "Dynamics of certain localized waves in an erbium-doped fiber system with the quintic terms," Chaos, Solitons & Fractals, Elsevier, vol. 192(C).
    • Handle: RePEc:eee:chsofr:v:192:y:2025:i:c:s0960077924015170
    DOI: 10.1016/j.chaos.2024.115965
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    References listed on IDEAS

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    1. Zhang, Xi & Wang, Yu-Feng & Yang, Sheng-Xiong, 2024. "Hybrid structures of the rogue waves and breather-like waves for the higher-order coupled nonlinear Schrödinger equations," Chaos, Solitons & Fractals, Elsevier, vol. 180(C).
    2. Shen, Yuan & Tian, Bo & Zhou, Tian-Yu & Cheng, Chong-Dong, 2023. "Multi-pole solitons in an inhomogeneous multi-component nonlinear optical medium," Chaos, Solitons & Fractals, Elsevier, vol. 171(C).
    3. D. R. Solli & C. Ropers & P. Koonath & B. Jalali, 2007. "Optical rogue waves," Nature, Nature, vol. 450(7172), pages 1054-1057, December.
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