%0 Journal Article
%T On Noether's conservation laws of the Sine-Gordon equation using moving frames
%J International Journal of Nonlinear Analysis and Applications
%I Semnan University
%Z 2008-6822
%A Masoudi, Yousef
%A Nadjafikhah, Mehdi
%A Toomanian, Megerdich
%D 2023
%\ 01/01/2023
%V 14
%N 1
%P 2493-2506
%! On Noether's conservation laws of the Sine-Gordon equation using moving frames
%K Sine-Gordon equation
%K moving frame
%K Conservation laws
%K normalized differential invariants
%K syzygy
%R 10.22075/ijnaa.2022.24650.2791
%X 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.
%U https://ijnaa.semnan.ac.ir/article_6707_b3b5c15bc5dd880dc272609c22278a43.pdf