@article {
author = {Masoudi, Yousef and Nadjafikhah, Mehdi and Toomanian, Megerdich},
title = {Applying moving frames to finding conservation laws of the nonlinear Klein-Gordon equation},
journal = {Computational Methods for Differential Equations},
volume = {11},
number = {2},
pages = {399-411},
year = {2023},
publisher = {University of Tabriz},
issn = {2345-3982},
eissn = {2383-2533},
doi = {10.22034/cmde.2022.50659.2101},
abstract = {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. },
keywords = {Nonlinear Klein-Gordon equation,Conservation laws,Moving frame,Differential invariants,Syzygy},
url = {https://cmde.tabrizu.ac.ir/article_14999.html},
eprint = {https://cmde.tabrizu.ac.ir/article_14999_a1db7d08cd72cfdabb168f0f0ca66806.pdf}
}