@article {
author = {Shaban, Somayeh and Nadjafikhah, Mehdi},
title = {Computation of $\mu$-symmetry and $\mu$-conservation law for the Camassa-Holm and Hunter-Saxton equations},
journal = {AUT Journal of Mathematics and Computing},
volume = {4},
number = {2},
pages = {113-122},
year = {2023},
publisher = {Amirkabir University of Technology},
issn = {2783-2449},
eissn = {2783-2287},
doi = {10.22060/ajmc.2022.21712.1102},
abstract = {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.},
keywords = {Symmetry,$\mu$-Symmetry,conservation law,$\mu$-Conservation law,variational problem,order reduction},
url = {https://ajmc.aut.ac.ir/article_4946.html},
eprint = {https://ajmc.aut.ac.ir/article_4946_9a66e5a1235c490396ad417291e32962.pdf}
}