On Noether's conservation laws of the Sine-Gordon equation using moving frames

Document Type : Research Paper


1 Department of Mathematics, Naghadeh Branch, Islamic Azad University, Naghadeh, Iran

2 Department of Pure Mathematics, School of Mathematics, Iran University of Science and Technology, Narmak, Tehran, 16846-13114, Iran

3 Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran


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 Noether’s First Theorem and Mansfield’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.