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Applying moving frames to finding conservation laws of the nonlinear Klein-Gordon equation | ||
| Computational Methods for Differential Equations | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 07 مرداد 1401 اصل مقاله (1.07 MB) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22034/cmde.2022.50659.2101 | ||
| نویسندگان | ||
Yousef Masoudi   1؛ Mehdi Nadjafikhah 2؛ Megerdich Toomanian3
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| 1Department of Mathematics, Islamic Azad University, Naghadeh Branch, Naghadeh, Iran. | ||
| 2Department of Pure Mathematics, School of Mathematics, Iran University of Science and Technology, Narmak, Tehran, 16846-13114, Iran. | ||
| 3Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran. | ||
| چکیده | ||
| 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 Gonçalves 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. | ||
| کلیدواژه‌ها | ||
| Nonlinear Klein-Gordon equation؛ Conservation laws؛ Moving frame؛ Differential invariants؛ Syzygy | ||
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آمار تعداد مشاهده مقاله: 12 تعداد دریافت فایل اصل مقاله: 13 |
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