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

Abstract EN

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.