%0 Journal Article
%T Applying moving frames to finding conservation laws of the nonlinear Klein-Gordon equation
%J Computational Methods for Differential Equations
%I University of Tabriz
%Z 2345-3982
%A Masoudi, Yousef
%A Nadjafikhah, Mehdi
%A Toomanian, Megerdich
%D 2023
%\ 04/01/2023
%V 11
%N 2
%P 399-411
%! Applying moving frames to finding conservation laws of the nonlinear Klein-Gordon equation
%K Nonlinear Klein-Gordon equation
%K Conservation laws
%K Moving frame
%K Differential invariants
%K Syzygy
%R 10.22034/cmde.2022.50659.2101
%X In this paper, we use a geometric approach based on the concepts of variational principle and moving frames to obtain the conservation laws related to the one-dimensional nonlinear Klein-Gordon equation. Noether’s First Theorem guarantees conservation laws, provided that the Lagrangian is invariant under a Lie group action. So, for calculating conservation laws of the Klein-Gordon equation, we first present a Lagrangian whose Euler-Lagrange equation is the Klein-Gordon equation, and then according to Gon¸calves and Mansfield’s method, we obtain the space of conservation laws in terms of vectors of invariants and the adjoint representation of a moving frame, for that Lagrangian, which is invariant under a hyperbolic group action.
%U https://cmde.tabrizu.ac.ir/article_14999_a1db7d08cd72cfdabb168f0f0ca66806.pdf