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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, Hindawi, vol. 2019, pages 1-6, February.
    • Handle: RePEc:hin:jnlamp:4364108
    DOI: 10.1155/2019/4364108
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