Symmetry, Pulson Solution, and Conservation Laws of the Holm‐Hone Equation

Guo Wang, Xuelin Yong, Yehui Huang and Jing Tian

Advances in Mathematical Physics, 2019, vol. 2019, issue 1

Abstract: In this paper, we focus on the Holm‐Hone equation which is a fifth‐order generalization of the Camassa‐Holm equation. It was shown that this equation is not integrable due to the nonexistence of a suitable Lagrangian or bi‐Hamiltonian structure and negative results from Painlevé analysis and the Wahlquist‐Estabrook method. We mainly study its symmetry properties, travelling wave solutions, and conservation laws. The symmetry group and its one‐dimensional optimal system are given. Furthermore, preliminary classifications of its symmetry reductions are investigated. Also we derive some solitary pattern solutions and nonanalytic first‐order pulson solution via the ansatz‐based method. Finally, some conservation laws for the fifth‐order equation are presented.

Date: 2019
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https://doi.org/10.1155/2019/4364108

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlamp:v:2019:y:2019:i:1:n:4364108

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