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Masoudi, Yousef, Nadjafikhah, Mehdi, Toomanian, Megerdich. (1402). Applying moving frames to finding conservation laws of the nonlinear Klein-Gordon equation. سامانه مدیریت نشریات علمی, 11(2), 399-411. doi: 10.22034/cmde.2022.50659.2101
Yousef Masoudi; Mehdi Nadjafikhah; Megerdich Toomanian. "Applying moving frames to finding conservation laws of the nonlinear Klein-Gordon equation". سامانه مدیریت نشریات علمی, 11, 2, 1402, 399-411. doi: 10.22034/cmde.2022.50659.2101
Masoudi, Yousef, Nadjafikhah, Mehdi, Toomanian, Megerdich. (1402). 'Applying moving frames to finding conservation laws of the nonlinear Klein-Gordon equation', سامانه مدیریت نشریات علمی, 11(2), pp. 399-411. doi: 10.22034/cmde.2022.50659.2101
Masoudi, Yousef, Nadjafikhah, Mehdi, Toomanian, Megerdich. Applying moving frames to finding conservation laws of the nonlinear Klein-Gordon equation. سامانه مدیریت نشریات علمی, 1402; 11(2): 399-411. doi: 10.22034/cmde.2022.50659.2101

Applying moving frames to finding conservation laws of the nonlinear Klein-Gordon equation

Computational Methods for Differential Equations
مقاله 15، دوره 11، شماره 2، تیر 2023، صفحه 399-411    اصل مقاله (337.16 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2022.50659.2101
نویسندگان
Yousef Masoudi* 1؛ Mehdi Nadjafikhah2؛ Megerdich Toomanian3
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 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. 
کلیدواژه‌ها
Nonlinear Klein-Gordon equation؛ Conservation laws؛ Moving frame؛ Differential invariants؛ Syzygy
مراجع
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