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Özel Bir Hamiltonian Denklemi için λ-Simetri ve Prelle-Singer Metodu

Year 2019, Volume: 31 Issue: 1, 62 - 69, 31.03.2019

Gülden Gün Polat

https://doi.org/10.7240/jeps.474362

Abstract

Lineer
olmayan adi diferansiyel denklemler için mevcut olan indirgeme metotlarından
önemli iki tanesi λ-simetri ve Prelle-Singer metodudur. Bu metotlar aynı
zamanda bahsi geçen denklemlerin ilk integrallerini ve integrasyon faktörlerini
bulmak için oldukça elverişlidir. Bu çalışma Riemann sıfırlarının spektral
realizasyonunu tanımlayan bir model olan özel bir Hamiltonian denklemine, bu
metotların uygulanmasını sunmayı amaçlamaktadır. Ayrıca λ-simetri ve
Prelle-Singer metotları arasındaki bağlantıya yer verilerek, bu ilişkinin
sağladığı kolaylıklar detaylarıyla açıklanacak ve Hamiltonian denklemine
uygulamaları birçok farklı durum için sunulacaktır.

Keywords

Lie simetrileri λ-simetrileri Prelle-Singer metodu integrasyon çarpanı

References

  • [1] Bluman, G.W. and Kumei, S. (1989). Symmetries and Differential Eqautions, Springer-Verlag, New York.
  • [2] Olver, P.J., (1986). Applications of Lie Groups to Differential Equations, Springer-Verlag.
  • [3] Muriel, C. ve Romero, J.L. (2001). New methods of reduction for ordinary differential equations. IMA Journal of Applied Mathematics, 66(2), 111-125.
  • [4] Muriel, C. ve Romero, J.L. (2009). First integrals, integrating factors and symmetries of second order differential equations. J. Phys. A: Math. Theor., 42(36).
  • [5] Gün Polat G. ve Özer, T. (2017). New conservation laws, Lagrangian forms and exact solutions of modified-Emden equation, Journal of Computational and Nonlinear Dynamics,12(4), 041001.
  • [6] Gün G. ve Özer, T. (2013), First integrals, integrating factors and invariant solutions of the path equation based on Noether and λ-symmetries, Abstract and Applied Analysis, Article ID 284653.
  • [7] Gün Polat G. ve Özer, T. (2016). On analysis of nonlinear dynamical systems via methods connected with λ-symmetry, Nonlinear Dynamics, 85(3), 1571-1595.
  • [8] Chandrasekar, V. K., Senthilvelan, M. Lakshmanan, M. (2005). Extended Prelle-Singer method and integrability/solvability of a class of nonlinear n.th order ordinary differential equations, Journal of Mathematical Physiscs, 12(1), 184-201.
  • [9] Mohanasubha, R., Chandrasekar, V.K., Senthilvelan, M. Lakshmanan, M. (2014). Interplay of symmetries, null forms, Darbou polynomials, integrating factors and Jacobi multipliers in integrable second-order differential equations, Proc. R. Soc. A, 470(2163), 20130656.
  • [10] Berry, M.V. (2008). Three quantum obsessions, Nonlinearity, vol. 21, T19-T26.
  • [11] Berry, M.V. ve Keating, J.P. (1999). H=xp and the Riemann zeros, in Supersymmetry and Trace Formulae: Chaos and Disorder ed J P Keating and I V Lerner, Plenum, New York, 355-367.
  • [12] Berry, M.V. ve Keating, J.P. (2011). A compact hamiltonian with the same asymptotic mean spectral density as the Riemann zeros, J. Phys. A: Math. Theor.,44, 285203.
  • [13] Sierre G. ve Rodriguez-Laguna, J. (2011). The H=xp model revisited and the Riemann zeros, Phys. Rev.Lett.,106, 200201.
  • [14] Nucci, M.C. (2014). Spectral realization of the Riemann zeros by quantizing H=w(x)(p+(l_p^2)/p) : the Lie-Noether symmetry approach, Journal of Physics, 482.
  • [15] Yaşar E. ve Yıldrım, Y. (2015). A procedure on the first integrals of second-order nonlinear ordinary differential equations, Eur. Phys. J. Plus., 130(240).
  • [16] Yıldrım, Y. (2015). İkinci Mertebe Adi Diferansiyel Denklemlerin İlk İntegralleri, Yüksek Lisans Tezi, Uludağ Üniversitesi Fen Bilimleri Enstitüsü.
  • [17] Muriel, C. ve Romero, J.L. (2003). C^∞ symmetries and reduction of equations without Lie point symmetries, J. Nonliear Math. Phys., 13(1), 167-188.
  • [18] Prelle M. ve Singer, M. (1983). Elementary First Integrals of Differential Equations, Trans. Am. Math. Soc., 279(1), 215-229.
  • [19] Duarte, L.G.S, Duarte, S.E.S, da Mota, L.A.C.P. (2001). Solving second-order ordinary differential equations by extending the Prelle-Singer method, Journal of Physics A-Mathematical and General, 34(14), 3015-3024.

Year 2019, Volume: 31 Issue: 1, 62 - 69, 31.03.2019

Gülden Gün Polat

https://doi.org/10.7240/jeps.474362

Abstract

References

  • [1] Bluman, G.W. and Kumei, S. (1989). Symmetries and Differential Eqautions, Springer-Verlag, New York.
  • [2] Olver, P.J., (1986). Applications of Lie Groups to Differential Equations, Springer-Verlag.
  • [3] Muriel, C. ve Romero, J.L. (2001). New methods of reduction for ordinary differential equations. IMA Journal of Applied Mathematics, 66(2), 111-125.
  • [4] Muriel, C. ve Romero, J.L. (2009). First integrals, integrating factors and symmetries of second order differential equations. J. Phys. A: Math. Theor., 42(36).
  • [5] Gün Polat G. ve Özer, T. (2017). New conservation laws, Lagrangian forms and exact solutions of modified-Emden equation, Journal of Computational and Nonlinear Dynamics,12(4), 041001.
  • [6] Gün G. ve Özer, T. (2013), First integrals, integrating factors and invariant solutions of the path equation based on Noether and λ-symmetries, Abstract and Applied Analysis, Article ID 284653.
  • [7] Gün Polat G. ve Özer, T. (2016). On analysis of nonlinear dynamical systems via methods connected with λ-symmetry, Nonlinear Dynamics, 85(3), 1571-1595.
  • [8] Chandrasekar, V. K., Senthilvelan, M. Lakshmanan, M. (2005). Extended Prelle-Singer method and integrability/solvability of a class of nonlinear n.th order ordinary differential equations, Journal of Mathematical Physiscs, 12(1), 184-201.
  • [9] Mohanasubha, R., Chandrasekar, V.K., Senthilvelan, M. Lakshmanan, M. (2014). Interplay of symmetries, null forms, Darbou polynomials, integrating factors and Jacobi multipliers in integrable second-order differential equations, Proc. R. Soc. A, 470(2163), 20130656.
  • [10] Berry, M.V. (2008). Three quantum obsessions, Nonlinearity, vol. 21, T19-T26.
  • [11] Berry, M.V. ve Keating, J.P. (1999). H=xp and the Riemann zeros, in Supersymmetry and Trace Formulae: Chaos and Disorder ed J P Keating and I V Lerner, Plenum, New York, 355-367.
  • [12] Berry, M.V. ve Keating, J.P. (2011). A compact hamiltonian with the same asymptotic mean spectral density as the Riemann zeros, J. Phys. A: Math. Theor.,44, 285203.
  • [13] Sierre G. ve Rodriguez-Laguna, J. (2011). The H=xp model revisited and the Riemann zeros, Phys. Rev.Lett.,106, 200201.
  • [14] Nucci, M.C. (2014). Spectral realization of the Riemann zeros by quantizing H=w(x)(p+(l_p^2)/p) : the Lie-Noether symmetry approach, Journal of Physics, 482.
  • [15] Yaşar E. ve Yıldrım, Y. (2015). A procedure on the first integrals of second-order nonlinear ordinary differential equations, Eur. Phys. J. Plus., 130(240).
  • [16] Yıldrım, Y. (2015). İkinci Mertebe Adi Diferansiyel Denklemlerin İlk İntegralleri, Yüksek Lisans Tezi, Uludağ Üniversitesi Fen Bilimleri Enstitüsü.
  • [17] Muriel, C. ve Romero, J.L. (2003). C^∞ symmetries and reduction of equations without Lie point symmetries, J. Nonliear Math. Phys., 13(1), 167-188.
  • [18] Prelle M. ve Singer, M. (1983). Elementary First Integrals of Differential Equations, Trans. Am. Math. Soc., 279(1), 215-229.
  • [19] Duarte, L.G.S, Duarte, S.E.S, da Mota, L.A.C.P. (2001). Solving second-order ordinary differential equations by extending the Prelle-Singer method, Journal of Physics A-Mathematical and General, 34(14), 3015-3024.
There are 19 citations in total.

Details

Primary Language Turkish
Subjects Engineering
Journal Section Research Articles
Authors

Gülden Gün Polat 0000-0003-3342-8380

Publication Date March 31, 2019
Published in Issue Year 2019 Volume: 31 Issue: 1

Cite

APA Gün Polat, G. (2019). Özel Bir Hamiltonian Denklemi için λ-Simetri ve Prelle-Singer Metodu. International Journal of Advances in Engineering and Pure Sciences, 31(1), 62-69. https://doi.org/10.7240/jeps.474362
AMA Gün Polat G. Özel Bir Hamiltonian Denklemi için λ-Simetri ve Prelle-Singer Metodu. JEPS. March 2019;31(1):62-69. doi:10.7240/jeps.474362
Chicago Gün Polat, Gülden. “Özel Bir Hamiltonian Denklemi için λ-Simetri Ve Prelle-Singer Metodu”. International Journal of Advances in Engineering and Pure Sciences 31, no. 1 (March 2019): 62-69. https://doi.org/10.7240/jeps.474362.
EndNote Gün Polat G (March 1, 2019) Özel Bir Hamiltonian Denklemi için λ-Simetri ve Prelle-Singer Metodu. International Journal of Advances in Engineering and Pure Sciences 31 1 62–69.
IEEE G. Gün Polat, “Özel Bir Hamiltonian Denklemi için λ-Simetri ve Prelle-Singer Metodu”, JEPS, vol. 31, no. 1, pp. 62–69, 2019, doi: 10.7240/jeps.474362.
ISNAD Gün Polat, Gülden. “Özel Bir Hamiltonian Denklemi için λ-Simetri Ve Prelle-Singer Metodu”. International Journal of Advances in Engineering and Pure Sciences 31/1 (March 2019), 62-69. https://doi.org/10.7240/jeps.474362.
JAMA Gün Polat G. Özel Bir Hamiltonian Denklemi için λ-Simetri ve Prelle-Singer Metodu. JEPS. 2019;31:62–69.
MLA Gün Polat, Gülden. “Özel Bir Hamiltonian Denklemi için λ-Simetri Ve Prelle-Singer Metodu”. International Journal of Advances in Engineering and Pure Sciences, vol. 31, no. 1, 2019, pp. 62-69, doi:10.7240/jeps.474362.
Vancouver Gün Polat G. Özel Bir Hamiltonian Denklemi için λ-Simetri ve Prelle-Singer Metodu. JEPS. 2019;31(1):62-9.