Computation of µ-symmetry and µ-conservation law for the Camassa-Holm and Hunter-Saxton equations

This work is intended to compute the µ-symmetry and µ-conservation laws for the Cammasa-Holm (CH) equation and the Hunter-Saxton (HS) equation. In other words, µ-symmetry, µ-symmetry reduction, variational problem, and µ-conservation laws for the CH equation and the HS equation are provided. Since the CH equation and the HS equation are of odd order, they do not admit a variational problem. First we obtain µ-conservation laws for both of them in potential form because they admit a variational problem and then using them, we obtain µ-conservation laws for the CH equation and the HS equation.