Symmetry,Travelling Wave Solutions And Conservation Laws Of The Holm-Hone Equation

Nonlinear evolution equations can describe plasma theory,fluid mechanics,nonlinear optical and other natural phenomena.This paper mainly focus on the Holm-Hone equation by using the Lie symmetry group method.It is a fifth order Camassa-Holm type equation.It was shown that this equation is not integrable since the non-existence of a suitable Lagrangian or bi-Hamiltonian structure,Painleve analysis and the Wahquist-Estrabook method can not find suitable Lax pair.Firstly,we give the Lie point symmetry group of the Holm-Hone equation and its one-dimensional optimal system of the corresponding Lie algebra by using the classical method.Further,preliminary classifications of its symmetry reductions are investigated.Secondly,three kinds of exact solutions of the equation are obtained according to the auxiliary function method,and the specific traveling wave solutions of this equation are studied,the pulson solution is obtained by the properties of the? function.In addition,the power series solution of the equation is discussed via the ansatz-based method.Finally,some conservation laws for the fifth order equation are presented by the multiplier method.