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

Yuan Shen

Chaos, Solitons & Fractals, 2025, vol. 192, issue C

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.

Keywords: The higher-order nonlinear Schrödinger-Maxwell-Bloch system with the quintic terms; Darboux transformation; Soliton; Breather; Rogue wave; Mixed wave (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:192:y:2025:i:c:s0960077924015170

DOI: 10.1016/j.chaos.2024.115965

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