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N-soliton asymptotic analysis on a higher-order modified Gerdjikov-Ivanov equation in nonlinear optics

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Listed:
  • Shan, Hong-Wen
  • Tian, Bo
  • Gao, Xiao-Tian
  • Feng, Chun-Hui
  • Liu, Hao-Dong

Abstract

The study of nonlinear optics plays a certain role in the laser technology, spectroscopy, and material structure analysis. A higher-order modified Gerdjikov-Ivanov equation, which describes the propagation and interaction of the pulses in nonlinear optics, is investigated in this paper. We derive the N-fold binary Darboux transformation of the higher-order modified Gerdjikov-Ivanov equation, where N is a positive integer. For that equation under zero boundary conditions, we construct the N-soliton solutions via the obtained N-fold binary Darboux transformation and perform the asymptotic analysis on the obtained N-soliton solutions. Before and after each interaction, the N solitons pass through each other without any change in shape or velocity, while only encounter the phase shifts. Taking N=2 and N=3 as two examples, we graphically illustrate the 2 and 3 interacting solitons through the 3D plots and characteristic lines, which align with our asymptotic-analysis results. Our analysis, which still needs to be confirmed by the relevant numerical simulation and experiments, might offer some explanations for the complex and variable natural mechanisms in nonlinear optics.

Suggested Citation

  • Shan, Hong-Wen & Tian, Bo & Gao, Xiao-Tian & Feng, Chun-Hui & Liu, Hao-Dong, 2025. "N-soliton asymptotic analysis on a higher-order modified Gerdjikov-Ivanov equation in nonlinear optics," Chaos, Solitons & Fractals, Elsevier, vol. 201(P1).
    • Handle: RePEc:eee:chsofr:v:201:y:2025:i:p1:s0960077925012123
    DOI: 10.1016/j.chaos.2025.117199
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    References listed on IDEAS

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    1. Wen-Xiu Ma, 2024. "Soliton Solutions to Sasa–Satsuma-Type Modified Korteweg–De Vries Equations by Binary Darboux Transformations," Mathematics, MDPI, vol. 12(23), pages 1-15, November.
    2. Zhao, Yi-Di & Wang, Yu-Feng & Yang, Sheng-Xiong & Zhang, Xi & Chen, Yi-Xin, 2024. "Soliton, breather and rogue wave solutions of the higher-order modified Gerdjikov–Ivanov equation," Chaos, Solitons & Fractals, Elsevier, vol. 185(C).
    3. Islam, Md. Ekramul & Mannaf, Md. Abde & Khan, Kamruzzaman & Akbar, M. Ali, 2024. "Soliton’s behavior and stability analysis to a model in mathematical physics," Chaos, Solitons & Fractals, Elsevier, vol. 184(C).
    4. Han, Peng-Fei & Ye, Ru-Suo & Zhang, Yi, 2025. "Inverse scattering transform for the coupled Lakshmanan–Porsezian–Daniel equations with non-zero boundary conditions in optical fiber communications," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 232(C), pages 483-503.
    5. Zhang, Bing-Wen, 2025. "The perturbed concatenated model of the Lakshmanan–Porsezian–Daniel and the Sasa–Satsuma equations having the Kerr law in the presence of spatio-temporal dispersion and multiplicative white noise," Chaos, Solitons & Fractals, Elsevier, vol. 193(C).
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