Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-682214120230101On Noether's conservation laws of the Sine-Gordon equation using moving frames24932506670710.22075/ijnaa.2022.24650.2791ENYousef MasoudiDepartment of Mathematics, Naghadeh Branch, Islamic Azad University, Naghadeh, Iran0000-0001-8346-5695Mehdi NadjafikhahDepartment of Pure Mathematics, School of Mathematics, Iran University of Science and Technology, Narmak, Tehran, 16846-13114, IranMegerdich ToomanianDepartment of Mathematics, Karaj Branch, Islamic Azad University, Karaj, IranJournal Article20210925The 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.https://ijnaa.semnan.ac.ir/article_6707_b3b5c15bc5dd880dc272609c22278a43.pdf