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Rogue waves in a resonant erbium-doped fiber system with higher-order effects

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  • Zhang, Yu
  • Li, Chuanzhong
  • He, Jingsong

Abstract

We mainly investigate a coupled system of the generalized nonlinear Schrödinger equation and the Maxwell–Bloch equations which describes the wave propagation in an erbium-doped nonlinear fiber with higher-order effects including the forth-order dispersion and quintic non-Kerr nonlinearity. We derive the one-fold Darboux transformation of this system and construct the determinant representation of the n-fold Darboux transformation. Then the determinant representation of the nth new solutions (E[n], p[n], η[n]) which were generated from the known seed solutions (E, p, η) is established through the n-fold Darboux transformation. The solutions (E[n], p[n], η[n]) provide the bright and dark breather solutions of this system. Furthermore, we construct the determinant representation of the nth-order bright and dark rogue waves by Taylor expansions and also discuss the hybrid solutions which are the nonlinear superposition of the rogue wave and breather solutions.

Suggested Citation

  • Zhang, Yu & Li, Chuanzhong & He, Jingsong, 2016. "Rogue waves in a resonant erbium-doped fiber system with higher-order effects," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 826-841.
    • Handle: RePEc:eee:apmaco:v:273:y:2016:i:c:p:826-841
    DOI: 10.1016/j.amc.2015.10.015
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    References listed on IDEAS

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    1. Hai-Qiang Zhang & Bo Tian & Xiang-Hua Meng & Xing Lü & Wen-Jun Liu, 2009. "Conservation laws, soliton solutions and modulational instability for the higher-order dispersive nonlinear Schrödinger equation," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 72(2), pages 233-239, November.
    2. 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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