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SYMMETRY REDUCTIONS AND EXACT SOLUTIONS TO THE SEVENTH-ORDER KDV TYPES OF EQUATION

Yıl 2015, Cilt: 3 Sayı: 2, 122 - 130, 01.10.2015

Öz

In present paper, the seventh-order KdV types of equation is considered by the Lie symmetry analysis. All of the geometric vector elds of the KdV equation are obtained, then the symmetry reductions and exact solutions to the KdV equation are investigated by the dynamical system and the power series method.

Kaynakça

  • [1] M. Craddock, K. Lennox, Lie group symmetries as integral transforms of fundamental solutions, J. Differential Equations, 232 (2007), 652-674.
  • [2] F. Gungor, C.  Ozemir, Lie symmetries of a generalized Kuznetsov-Zabolotskaya-Khokhlov equation, J. Math. Anal. Appl., 423 (2015), 623-638.
  • [3] M. Lakshmanan, P. Kaliappan, Lie transformations, nonlinear evolution equations and Painleve forms, J. Math. Phys., 24 (1983), 795-806.
  • [4] H. Liu, J. Li, Lie symmetry analysis and exact solutions for the extended mKdV equation, Acta Appl. Math., 109 (2010), 1107-1119.
  • [5] H. Liu, J. Li, F. Chen, Exact periodic wave solutions for the hKdV equation, Nonlinear Anal., 70 (2009), 2376-2381.
  • [6] H. Liu, J. Li, L. Liu, Lie symmetry analysis, optimal systems and exact solutions to the fth-order KdV types of equations, J. Math. Anal. Appl., 368 (2010), 551-558.
  • [7] H. Liu, J. Li, L. Liu, Conservation law classi cation and integrability of generalized nonlinear second-order equation, Commun. Theor. Phys. (Beijing), 56 (2011), 987-991.
  • [8] H. Liu, Y. Geng, Symmetry reductions and exact solutions to the systems of carbon nanotubes conveying uid, J. Differential Equations, 254 (2013), 2289-2303.
  • [9] W. Balser, Multisummability of formal power series solutions of partial differential equations with constant coecients, J. Di erential Equations, 201 (2004), 63-74.
  • [10] A.B. Mikhailov, A.B. Shabat, V.V. Sokolov, The symmetry approach to classi cation of integrable equation, in: What is Integrability?, Springer Series on Nonlinear Dynamics, Berlin, 1991.
  • [11] B. Muatjetjeja, C.M. Khalique, Symmetry analysis and conservation laws for a coupled (2+1)- dimensional hyperbolic system, Commun. Nonlinear Sci. Numer. Simul., 22 (2015), 1252- 1262.
  • [12] P.J. Olver, Applications of Lie Groups to Di erential Equations, Grad. Texts in Math., vol. 107, Springer, New York, 1993.
  • [13] P. Razborova, A.H. Kara, A. Biswas, Additional conservation laws for Rosenau-KdV-RLW equation with power law nonlinearity by Lie symmetry, Nonlinear Dynam., 79 (2015), 743- 748.
  • [14] W. Sinkala, P. Leach, J. O'Hara, Invariance properties of a general-pricing equation, J. Differential Equations, 244 (2008), 2820-2835.
  • [15] P. Winternitz, Lie groups and solutions of nonlinear partial di erential equations, in: Lecture Notes in Physics, CRM-1841, Canada 1993.
Yıl 2015, Cilt: 3 Sayı: 2, 122 - 130, 01.10.2015

Öz

Kaynakça

  • [1] M. Craddock, K. Lennox, Lie group symmetries as integral transforms of fundamental solutions, J. Differential Equations, 232 (2007), 652-674.
  • [2] F. Gungor, C.  Ozemir, Lie symmetries of a generalized Kuznetsov-Zabolotskaya-Khokhlov equation, J. Math. Anal. Appl., 423 (2015), 623-638.
  • [3] M. Lakshmanan, P. Kaliappan, Lie transformations, nonlinear evolution equations and Painleve forms, J. Math. Phys., 24 (1983), 795-806.
  • [4] H. Liu, J. Li, Lie symmetry analysis and exact solutions for the extended mKdV equation, Acta Appl. Math., 109 (2010), 1107-1119.
  • [5] H. Liu, J. Li, F. Chen, Exact periodic wave solutions for the hKdV equation, Nonlinear Anal., 70 (2009), 2376-2381.
  • [6] H. Liu, J. Li, L. Liu, Lie symmetry analysis, optimal systems and exact solutions to the fth-order KdV types of equations, J. Math. Anal. Appl., 368 (2010), 551-558.
  • [7] H. Liu, J. Li, L. Liu, Conservation law classi cation and integrability of generalized nonlinear second-order equation, Commun. Theor. Phys. (Beijing), 56 (2011), 987-991.
  • [8] H. Liu, Y. Geng, Symmetry reductions and exact solutions to the systems of carbon nanotubes conveying uid, J. Differential Equations, 254 (2013), 2289-2303.
  • [9] W. Balser, Multisummability of formal power series solutions of partial differential equations with constant coecients, J. Di erential Equations, 201 (2004), 63-74.
  • [10] A.B. Mikhailov, A.B. Shabat, V.V. Sokolov, The symmetry approach to classi cation of integrable equation, in: What is Integrability?, Springer Series on Nonlinear Dynamics, Berlin, 1991.
  • [11] B. Muatjetjeja, C.M. Khalique, Symmetry analysis and conservation laws for a coupled (2+1)- dimensional hyperbolic system, Commun. Nonlinear Sci. Numer. Simul., 22 (2015), 1252- 1262.
  • [12] P.J. Olver, Applications of Lie Groups to Di erential Equations, Grad. Texts in Math., vol. 107, Springer, New York, 1993.
  • [13] P. Razborova, A.H. Kara, A. Biswas, Additional conservation laws for Rosenau-KdV-RLW equation with power law nonlinearity by Lie symmetry, Nonlinear Dynam., 79 (2015), 743- 748.
  • [14] W. Sinkala, P. Leach, J. O'Hara, Invariance properties of a general-pricing equation, J. Differential Equations, 244 (2008), 2820-2835.
  • [15] P. Winternitz, Lie groups and solutions of nonlinear partial di erential equations, in: Lecture Notes in Physics, CRM-1841, Canada 1993.
Toplam 15 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Mühendislik
Bölüm Articles
Yazarlar

Youwei Zhang

Yayımlanma Tarihi 1 Ekim 2015
Gönderilme Tarihi 10 Temmuz 2014
Yayımlandığı Sayı Yıl 2015 Cilt: 3 Sayı: 2

Kaynak Göster

APA Zhang, Y. (2015). SYMMETRY REDUCTIONS AND EXACT SOLUTIONS TO THE SEVENTH-ORDER KDV TYPES OF EQUATION. Konuralp Journal of Mathematics, 3(2), 122-130.
AMA Zhang Y. SYMMETRY REDUCTIONS AND EXACT SOLUTIONS TO THE SEVENTH-ORDER KDV TYPES OF EQUATION. Konuralp J. Math. Ekim 2015;3(2):122-130.
Chicago Zhang, Youwei. “SYMMETRY REDUCTIONS AND EXACT SOLUTIONS TO THE SEVENTH-ORDER KDV TYPES OF EQUATION”. Konuralp Journal of Mathematics 3, sy. 2 (Ekim 2015): 122-30.
EndNote Zhang Y (01 Ekim 2015) SYMMETRY REDUCTIONS AND EXACT SOLUTIONS TO THE SEVENTH-ORDER KDV TYPES OF EQUATION. Konuralp Journal of Mathematics 3 2 122–130.
IEEE Y. Zhang, “SYMMETRY REDUCTIONS AND EXACT SOLUTIONS TO THE SEVENTH-ORDER KDV TYPES OF EQUATION”, Konuralp J. Math., c. 3, sy. 2, ss. 122–130, 2015.
ISNAD Zhang, Youwei. “SYMMETRY REDUCTIONS AND EXACT SOLUTIONS TO THE SEVENTH-ORDER KDV TYPES OF EQUATION”. Konuralp Journal of Mathematics 3/2 (Ekim 2015), 122-130.
JAMA Zhang Y. SYMMETRY REDUCTIONS AND EXACT SOLUTIONS TO THE SEVENTH-ORDER KDV TYPES OF EQUATION. Konuralp J. Math. 2015;3:122–130.
MLA Zhang, Youwei. “SYMMETRY REDUCTIONS AND EXACT SOLUTIONS TO THE SEVENTH-ORDER KDV TYPES OF EQUATION”. Konuralp Journal of Mathematics, c. 3, sy. 2, 2015, ss. 122-30.
Vancouver Zhang Y. SYMMETRY REDUCTIONS AND EXACT SOLUTIONS TO THE SEVENTH-ORDER KDV TYPES OF EQUATION. Konuralp J. Math. 2015;3(2):122-30.
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