دانشگاه تبریز
فهرست نشریات دارای اعتبار وزارت علوم، تحقیقات و فناوری
پایگاه استنادی علوم جهان اسلام (ISC)

 آمار

تعداد نشریات44
تعداد شماره‌ها1,339
تعداد مقالات16,461
تعداد مشاهده مقاله53,439,257
تعداد دریافت فایل اصل مقاله16,002,441
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
  • [1] A. Bihlo, J. Jackaman, and F. Valiquette, Invariant variational schemes for ordinary differential equations, Studies in Applied Mathematics, 148 (2022), 991–1020.
  • [2] M. Dehghan and A. Shokri, A numerical method for solution of the two-dimensional sine-Gordon equation using the radial basis functions, Mathematics and Computers in Simulation, 79 (2008), 700–715.
  • [3] M. Fels and P. J. Olver, Moving coframes: II. Regularization and theoretical foundations, Acta Applicandae Mathematica, 55 (1999), 127–208.
  • [4] T. M. N. Gon¸calves and E. L. Mansfield, Moving frames and conservation laws for Euclidean invariant La- grangians, Studies in Applied Mathematics, 130 (2013), 134–166.
  • [5] T. M. N. Gon¸calves and E. L. Mansfield, Moving Frames and Noether’s Conservation Laws - the General Case, Vol. 4, Forum of Mathematics, Sigma, Cambridge University Press, 2016.
  • [6] T. M. N. Gon¸calves and E. L. Mansfield, On moving frames and Noether’s conservation laws, Studies in Applied Mathematics, 128 (2012), 1–29.
  • [7] D. Kaya and S. M. El-Sayed, A numerical solution of the Klein-Gordon equation and convergence of the decom- position method, Applied mathematics and computation, 156 (2004), 341–353.
  • [8] P. Kim, Invariantization of numerical schemes using moving frames, BIT Numerical Mathematics, 47 (2007), 525–546.
  • [9] I. A. Kogan and P. J. Olver, Invariant Euler–Lagrange equations and the invariant variational bicomplex, Acta Applicandae Mathematica, 76 (2003), 137–193.
  • [10] E. L. Mansfield, A practical guide to the invariant calculus, Vol. 26, Cambridge University Press, New York, 2010.
  • [11] E. Noether, Invariant variation problems, Transport theory and statistical physics, 1 (1971), 186–207.
  • [12] P. J. Olver, Applications of Lie groups to differential equations, Vol. 107, Springer Science and Business Media, 2000.
  • [13] E. Ozbenli and P. Vedula, Construction of invariant compact finite-difference schemes, Physical Review E, 101 (2020), 023303.
  • [14] E. Ozbenli and P. Vedula, High order accurate finite difference schemes based on symmetry preservation, Journal of Computational Physics, 349 (2017), 376–398.
  • [15] E. Ozbenli and P. Vedula, Numerical solution of modified differential equations based on symmetry preservation, Physical Review E, 96 (2017), 063304.
  • [16] F. Shakeri and M. Dehghan, Numerical solution of the Klein-Gordon equation via He’s variational iteration method, Nonlinear Dynamics, 51 (2008), 89–97.
  • [17] Sirendaoreji, Auxiliary equation method and new solutions of Klein-Gordon equations, Chaos Solitons and Fractals, 31 (2007), 943–950.
  • [18] A. M. Wazwaz, New travelling wave solutions to the Boussinesq and the Klein-Gordon equations, Communications in Nonlinear Science and Numerical Simulation, 13 (2008), 889–901.
  • [19] A. M. Wazwaz, The modified decomposition method for analytic treatment of differential equations, Applied mathematics and computation, 173 (2006), 165–176.
آمار
تعداد مشاهده مقاله: 261
تعداد دریافت فایل اصل مقاله: 402


سامانه مدیریت نشریات علمی. قدرت گرفته از سیناوب