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Solitons and breathers for a generalized nonlinear Schrödinger equation via the binary Bell polynomials

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  • Jiang, Yan
  • Qu, Qi-Xing

Abstract

In this paper, we investigate a generalized nonlinear Schrödinger equation with two certain terms in the single-mode optical fibers. Via the binary Bell polynomials, a more general bilinear form and analytic solutions are obtained. On the basis of those solutions, we present the parametric regions for the existence of the solitons and breathers on a nonzero background. From the soliton solutions, we prove the soliton interaction to be elastic through the asymptotic analysis. The interactions can be observed between (i) two dark solitons, (ii) two anti-dark solitons, and (iii) one dark and one anti-dark solitons, and relevant parametric conditions of the three types of interactions are given. From the breather solutions, the general breathers, Akhmediev breathers and Kuznetsov–Ma breathers can be respectively derived with the different parametric conditions. Besides, we obtain some rational solutions by taking the limit of the breather solutions. Based on those rational solutions, the parametric conditions for the soliton interactions and rogue waves are given.

Suggested Citation

  • Jiang, Yan & Qu, Qi-Xing, 2021. "Solitons and breathers for a generalized nonlinear Schrödinger equation via the binary Bell polynomials," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 179(C), pages 57-68.
    • Handle: RePEc:eee:matcom:v:179:y:2021:i:c:p:57-68
    DOI: 10.1016/j.matcom.2020.07.020
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    References listed on IDEAS

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    1. 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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    1. Yu, Weitian & Liu, Wenjun & Zhang, Hongxin, 2022. "Soliton molecules in the kink, antikink and oscillatory background," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).

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