%0 Journal Article
%T Computation of $\mu$-symmetry and $\mu$-conservation law for the Camassa-Holm and Hunter-Saxton equations
%J AUT Journal of Mathematics and Computing
%I Amirkabir University of Technology
%Z 2783-2449
%A Shaban, Somayeh
%A Nadjafikhah, Mehdi
%D 2023
%\ 03/01/2023
%V 4
%N 2
%P 113-122
%! Computation of $\mu$-symmetry and $\mu$-conservation law for the Camassa-Holm and Hunter-Saxton equations
%K Symmetry
%K $\mu$-Symmetry
%K conservation law
%K $\mu$-Conservation law
%K variational problem
%K order reduction
%R 10.22060/ajmc.2022.21712.1102
%X This 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.
%U https://ajmc.aut.ac.ir/article_4946_9a66e5a1235c490396ad417291e32962.pdf