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Analytical solutions for the coupled Hirota equations in the firebringent fiber

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  • Wang, Pan
  • Ma, Tian-Ping
  • Qi, Feng-Hua

Abstract

Under investigation in this paper are the coupled Hirota (CH) equations, which describe the collision of two waves in the deep ocean and the propagation of the ultrashort optical pulses in a birefringent fiber. Based on the bilinear method, multi-soliton solutions for the CH equations are given. From the perspective of analysis, the interaction dynamics of solitons are obtained. The head-on and overtaking interactions of two/three solitons are analyzed. The elastic and inelastic interactions of two/three solitons are presented. The soliton velocity can be controlled by adjusting the physical parameters ϕj,(j=1,2,…N) and ϵ. The energy exchange occurs between the variables u and v before and after the collision. The local interference of two/three solitons is observed. The closer to the center of the interaction, the more significant the interference. The real and imaginary parts of the parameters ϕj,(j=1,2,…N) have the effects on the numbers of peaks and holes in the collisions. The structure of four eyes and one peak is observed during the two-soliton interaction. The three-soliton interactions are given with two peaks and local interference. It is hoped that the results of this study can provide some reference for the wave interaction in deep ocean, pulse propagation in optical fiber, financial option pricing, valuation of intangible assets in sports and so on.

Suggested Citation

  • Wang, Pan & Ma, Tian-Ping & Qi, Feng-Hua, 2021. "Analytical solutions for the coupled Hirota equations in the firebringent fiber," Applied Mathematics and Computation, Elsevier, vol. 411(C).
    • Handle: RePEc:eee:apmaco:v:411:y:2021:i:c:s0096300321005841
    DOI: 10.1016/j.amc.2021.126495
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    References listed on IDEAS

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    1. Gao, Xin-Yi & Guo, Yong-Jiang & Shan, Wen-Rui, 2021. "Oceanic studies via a variable-coefficient nonlinear dispersive-wave system in the Solar System," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    2. Du, Xia-Xia & Tian, Bo & Qu, Qi-Xing & Yuan, Yu-Qiang & Zhao, Xue-Hui, 2020. "Lie group analysis, solitons, self-adjointness and conservation laws of the modified Zakharov-Kuznetsov equation in an electron-positron-ion magnetoplasma," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    3. Gao, Xin-Yi & Guo, Yong-Jiang & Shan, Wen-Rui, 2020. "Shallow water in an open sea or a wide channel: Auto- and non-auto-Bäcklund transformations with solitons for a generalized (2+1)-dimensional dispersive long-wave system," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
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    Cited by:

    1. Yu, Weitian & Luan, Zitong & Zhang, Hongxin & Liu, Wenjun, 2022. "Collisions of three higher order dark double- and single-hump solitons in optical fiber," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    2. Zhu, Bo-Wei & Fang, Yin & Liu, Wei & Dai, Chao-Qing, 2022. "Predicting the dynamic process and model parameters of vector optical solitons under coupled higher-order effects via WL-tsPINN," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).

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