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Generalized (n,N−n)-fold Darboux transformation and localized waves for an integrable reduced spin Hirota-Maxwell-Bloch system in an erbium doped fiber

Author

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  • Liu, Shao-Hua
  • Tian, Bo
  • Gao, Xiao-Tian

Abstract

In this paper, under investigation is an integrable reduced spin Hirota-Maxwell-Bloch (rsHMB) system, which describes the transmission of the femtosecond pulses in an erbium doped fiber. Based on the existing N-fold Darboux transformation, we establish a generalized (n,N−n)-fold Darboux transformation for the rsHMB system, where n and N are the positive integers (n≤N). The Nth-order degenerate soliton and Nth-order rogue-wave solutions for the rsHMB system are obtained via the generalized (1,N−1)-fold Darboux transformation. By means of the generalized (2,N−2)-fold Darboux transformation, we derive the Nth-order hybrid wave solutions describing the interaction between the (N−1)th-order rogue wave and the first-order breather. The above solutions are discussed graphically, which exhibit the diverse wave structures including the triangle and pentagon, among others.

Suggested Citation

  • Liu, Shao-Hua & Tian, Bo & Gao, Xiao-Tian, 2024. "Generalized (n,N−n)-fold Darboux transformation and localized waves for an integrable reduced spin Hirota-Maxwell-Bloch system in an erbium doped fiber," Chaos, Solitons & Fractals, Elsevier, vol. 186(C).
    • Handle: RePEc:eee:chsofr:v:186:y:2024:i:c:s0960077924008373
    DOI: 10.1016/j.chaos.2024.115285
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