Symmetry, pulson solution, and conservation laws of the Holm-Hone equation. (English) Zbl 1418.35081
Summary: 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.
MSC:
| 35G20 | Nonlinear higher-order PDEs |
| 35B06 | Symmetries, invariants, etc. in context of PDEs |
| 35C07 | Traveling wave solutions |
Keywords:
fifth-order generalization of the Camassa-Holm equation; Painlevé analysis; symmetry reductions; ansatz-based methodSoftware:
GeMReferences:
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