Amirkabir University of TechnologyAUT Journal of Mathematics and Computing2783-24494220230301Computation of $\mu$-symmetry and $\mu$-conservation law for the Camassa-Holm and Hunter-Saxton equations113122494610.22060/ajmc.2022.21712.1102ENSomayehShabanDepartment of Mathematics, Karaj branch, Islamic Azad University, Karaj, IranMehdiNadjafikhahDepartment of Pure Mathematics, School of Mathematics, Iran University of Science and Technology, Narmak, Tehran, Iran0000-0002-1354-9786Journal Article20220822This work is intended to compute the $\mu$-symmetry and $\mu$-conservation laws for the Cammasa-Holm (CH) equation and the Hunter-Saxton (HS) equation. In other words, $\mu$-symmetry, $\mu$-symmetry reduction, variational problem, and $\mu$-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 $\mu$-conservation laws for both of them in potential form because they admit a variational problem and then using them, we obtain $\mu$-conservation laws for the CH equation and the HS equation.https://ajmc.aut.ac.ir/article_4946_662d229b183e75952b88e8f8ab32b6a4.pdf