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Topological properties and wave structures of Gilson–Pickering equation

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  • Kai, Yue
  • Li, Yaxi
  • Huang, Liuke

Abstract

The aim of this paper is to present the topological properties and wave structures of the Gilson–Pickering equation. By the traveling wave transformation, the corresponding traveling wave system of the original equation is obtained, and then a conserved quantity, namely the Hamiltonian is constructed via it. After that, the existences of the soliton and periodic solutions are established by the bifurcation method. To verify our conclusion explicitly, the corresponding exact traveling wave solutions are constructed. In particular, via the generalized trial equation method which is proposed in this paper, a special kind of soliton solution, namely the Gaussian soliton solution is given. To the best of our knowledge, this is the first time that a Gaussian soliton solution has been constructed to an equation with no logarithmic nonlinearity.

Suggested Citation

  • Kai, Yue & Li, Yaxi & Huang, Liuke, 2022. "Topological properties and wave structures of Gilson–Pickering equation," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    • Handle: RePEc:eee:chsofr:v:157:y:2022:i:c:s0960077922001102
    DOI: 10.1016/j.chaos.2022.111899
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    References listed on IDEAS

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    1. Hasan Bulut & Haci Mehmet Baskonus & Yusuf Pandir, 2013. "The Modified Trial Equation Method for Fractional Wave Equation and Time Fractional Generalized Burgers Equation," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-8, September.
    2. Kai, Yue & Chen, Shuangqing & Zheng, Bailin & Zhang, Kai & Yang, Nan & Xu, Wenlong, 2020. "Qualitative and quantitative analysis of nonlinear dynamics by the complete discrimination system for polynomial method," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
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    Cited by:

    1. Hu, Xiang & Yin, Zhixiang, 2022. "A study of the pulse propagation with a generalized Kudryashov equation," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    2. Wensheng Chen & Jalil Manafian & Khaled Hussein Mahmoud & Abdullah Saad Alsubaie & Abdullah Aldurayhim & Alabed Alkader, 2023. "Cutting-Edge Analytical and Numerical Approaches to the Gilson–Pickering Equation with Plenty of Soliton Solutions," Mathematics, MDPI, vol. 11(16), pages 1-35, August.

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