TY - JOUR
ID - 14999
TI - Applying moving frames to finding conservation laws of the nonlinear Klein-Gordon equation
JO - Computational Methods for Differential Equations
JA - CMDE
LA - en
SN - 2345-3982
AU - Masoudi, Yousef
AU - Nadjafikhah, Mehdi
AU - Toomanian, Megerdich
AD - Department of Mathematics, Islamic Azad University, Naghadeh Branch, Naghadeh, Iran.
AD - Department of Pure Mathematics, School of Mathematics, Iran University of Science and Technology, Narmak, Tehran, 16846-13114, Iran.
AD - Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran.
Y1 - 2023
PY - 2023
VL - 11
IS - 2
SP - 399
EP - 411
KW - Nonlinear Klein-Gordon equation
KW - Conservation laws
KW - Moving frame
KW - Differential invariants
KW - Syzygy
DO - 10.22034/cmde.2022.50659.2101
N2 - 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.
UR - https://cmde.tabrizu.ac.ir/article_14999.html
L1 - https://cmde.tabrizu.ac.ir/article_14999_a1db7d08cd72cfdabb168f0f0ca66806.pdf
ER -