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Wave behaviors for fractional generalized nonlinear Schrödinger equation via Riemann–Hilbert method

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  • Liu, Jinshan
  • Dong, Huanhe
  • Zhang, Yong

Abstract

This paper aims to study the explicit fractional generalized nonlinear Schrödinger (fGNLS) equation by the Riemann–Hilbert (RH) method and to explore the impact of the order of fractional derivatives ϵ on solitons. Firstly, utilizing the recursion operator of the generalized nonlinear Schrödinger (GNLS) equation, the anomalous dispersion relation is constructed. Secondly, the explicit form of the fGNLS equation is obtained by the anomalous dispersion relation and the completeness. Then, the N-soliton solutions are acquired through RH problems. We found that the energy of the solitons decreases with the increase of the order of fractional derivatives ϵ. Specifically, we demonstrate that the fractional one-soliton solution constitutes a valid solution of the fGNLS equation by the Darboux transform.

Suggested Citation

  • Liu, Jinshan & Dong, Huanhe & Zhang, Yong, 2024. "Wave behaviors for fractional generalized nonlinear Schrödinger equation via Riemann–Hilbert method," Chaos, Solitons & Fractals, Elsevier, vol. 185(C).
    • Handle: RePEc:eee:chsofr:v:185:y:2024:i:c:s0960077924007148
    DOI: 10.1016/j.chaos.2024.115162
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    References listed on IDEAS

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    2. 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.
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