TY - JOUR
ID - 6707
TI - On Noether's conservation laws of the Sine-Gordon equation using moving frames
JO - International Journal of Nonlinear Analysis and Applications
JA - IJNAA
LA - en
SN - 2008-6822
AU - Masoudi, Yousef
AU - Nadjafikhah, Mehdi
AU - Toomanian, Megerdich
AD - Department of Mathematics, Naghadeh Branch, Islamic Azad University, Naghadeh, Iran
AD - Department of Pure Mathematics, School of Mathematics, Iran University of Science and Technology, Narmak, Tehran, 16846-13114, Iran
AD - Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran
Y1 - 2023
PY - 2023
VL - 14
IS - 1
SP - 2493
EP - 2506
KW - Sine-Gordon equation
KW - moving frame
KW - Conservation laws
KW - normalized differential invariants
KW - syzygy
DO - 10.22075/ijnaa.2022.24650.2791
N2 - The wide significance of the problem of finding conservation laws in a great number of applications in mechanics and physics is beyond any doubt. The aim of this paper is to obtain conservation laws of the Sine-Gordon equation via the concept of moving frames and the variational principle. For this purpose, we first present a Lagrangian whose Euler-Lagrange equation is the Sine-Gordon equation, and then by Noetherâ€™s First Theorem and Mansfieldâ€™s method, we obtain the space of conservation laws in terms of invariants and the adjoint representation of a moving frame, for that Lagrangian, which is invariant under HRT group action.
UR - https://ijnaa.semnan.ac.ir/article_6707.html
L1 - https://ijnaa.semnan.ac.ir/article_6707_b3b5c15bc5dd880dc272609c22278a43.pdf
ER -