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

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  • Guo Wang
  • Xuelin Yong
  • Yehui Huang
  • Jing Tian

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.

Suggested Citation

  • Guo Wang & Xuelin Yong & Yehui Huang & Jing Tian, 2019. "Symmetry, Pulson Solution, and Conservation Laws of the Holm‐Hone Equation," Advances in Mathematical Physics, John Wiley & Sons, vol. 2019(1).
    • Handle: RePEc:wly:jnlamp:v:2019:y:2019:i:1:n:4364108
    DOI: 10.1155/2019/4364108
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    References listed on IDEAS

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    1. Kalisch, Henrik & Lenells, Jonatan, 2005. "Numerical study of traveling-wave solutions for the Camassa–Holm equation," Chaos, Solitons & Fractals, Elsevier, vol. 25(2), pages 287-298.
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