TY - JOUR
ID - 4946
TI - Computation of $\mu$-symmetry and $\mu$-conservation law for the Camassa-Holm and Hunter-Saxton equations
JO - AUT Journal of Mathematics and Computing
JA - AJMC
LA - en
SN - 2783-2449
AU - Shaban, Somayeh
AU - Nadjafikhah, Mehdi
AD - Department of Mathematics, Karaj branch, Islamic Azad University, Karaj, Iran
AD - Department of Pure Mathematics, School of Mathematics, Iran University of Science and Technology, Narmak, Tehran, Iran
Y1 - 2023
PY - 2023
VL - 4
IS - 2
SP - 113
EP - 122
KW - Symmetry
KW - $\mu$-Symmetry
KW - conservation law
KW - $\mu$-Conservation law
KW - variational problem
KW - order reduction
DO - 10.22060/ajmc.2022.21712.1102
N2 - 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.
UR - https://ajmc.aut.ac.ir/article_4946.html
L1 - https://ajmc.aut.ac.ir/article_4946_662d229b183e75952b88e8f8ab32b6a4.pdf
ER -