Topological properties and wave structures of Gilson–Pickering equation

Yue Kai, Yaxi Li and Liuke Huang

Chaos, Solitons & Fractals, 2022, vol. 157, issue C

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.

Keywords: Gilson–Pickering equation; Topological properties; Generalized trial equation method; Gaussian soliton solution (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:157:y:2022:i:c:s0960077922001102

DOI: 10.1016/j.chaos.2022.111899

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