Symmetry analysis and conservation laws for higher order CamassaHolm equation

Document Type : Research Paper


1 Department of Mathematics, Eslamabad-E-Gharb Branch, Islamic Azad University, Eslamabad-E-Gharb, Iran.

2 Department of Pure Mathematics, School of Mathematics, Iran University of Science and Technology, Narmak, Tehran, 16846-13114, Iran.


In this paper, Lie symmetry group method is applied to study for the higher order Camassa-Holm equation. Complete analysis of symmetries and nonclassical symmetries is discussed. Furthermore, optimal system, preliminary classification of its group invariant solutions and symmetry reduction are investigated. Finally conservation laws for the higher order Camassa-Holm equation which conserved quantities arise from multipliers by using homotopy operator are presented.