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Symmetry reductions and exact solutions to the Sharma–Tasso–Olever equation

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Języki publikacji
EN
Abstrakty
EN
In the present paper, the Sharma–Tasso–Olever (STO) equation is considered by the Lie symmetry analysis. All of the geometric vector fields to the STO equation are obtained, and then the symmetry reductions and exact solutions of the equation are investigated. Our results witness that symmetry analysis is a very efficient and powerful technique in finding the solutions of the proposed equation.
Wydawca
Rocznik
Strony
107--114
Opis fizyczny
Bibliogr. 22 poz.
Twórcy
autor
  • School of Mathematics and Statistics, Hexi University, 734000 Zhangye, China
Bibliografia
  • [1] B. Ahmed, R. Morris, E. Krishnan, P. Leach and A. Biswas, Shock-waves and other solutions to the Sharma-Tasso-Olver equation with Lie point symmetry and travelling-waves approach, Appl. Math. Inf. Sci. 8 (2014), 2675-2681.
  • [2] W. Baiser, Multisummability of formal power series solutions of partial differential equations with constant coefficients, J. Differential Equations 201 (2004), 63-74.
  • [3] A. Chen, Multi-kink solutions and soliton fission and fusion of Sharma-Tasso-Olver equation, Phys. Lett. A 374 (2010), 2340-2345.
  • [4] M. Craddock and K. Lennox, Lie group symmetries as integral transforms of fundamental solutions, J. Differential Equations 232 (2007), 652-674.
  • [5] F. Güngör and C. Özemir, Lie symmetries of a generalized Kuznetsov-Zabolotskaya-Khokhlv equation, Math. Anal. Appl. 423 (2015), 623-638.
  • [6] M. Lakshmanan and P. Kaliappan, Lie transformations, nonlinear evolution equations and Painlevé forms, J. Math. Phys. 24 (1983), 795-806.
  • [7] H. Liu and Y. Geng, Symmetry reductions and exact solutions to the systems of carbon nanotubes conveying fluid, J. Differential Equations 254 (2013), 2289-2303.
  • [8] H. Liu, J. Li and L. Liu, Lie symmetry analysis, optimal systems and exact solutions to the fifth-order KdV types of equations, J. Math. Anal. Appl. 368 (2010), 551-558.
  • [9] H. Liu, J. Li and L. Liu, Conservation law classification and integrability of generalized nonlinear second-order equation, Commun. Theor. Phys. (Beijing) 56 (2011), 987-991.
  • [10] A. Mikhailov, A. Shabat and V. Sokolov, The symmetry approach to classification of integrable equations, in: What is Integrability?, Springer Ser. Nonlinear Dyn., Springer, Berlin (1991), 115-184.
  • [11] B. Muatjetjeja and C. 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 Differential Equations, Grad. Texts in Math. 107, Springer, New York, 1993.
  • [13] J. Pan and W. Chen, A new auxiliary equation method and its Application to the Sharma-Tasso-Olver model, Phys. Lett. A 373(2009), 3118-3121.
  • [14] P. Razborova, A. H. Kara and A. Biswas, Additional conservation laws for Rosenau-KdV-RLW equation with power law non-linearity by Lie symmetry, Nonlinear Dynam. 79 (2015), 743-748.
  • [15] W. Rudin, Principles of Mathematical Analysis, China Machine Press, Beijing, 2004.
  • [16] Y. Shang, Y. Huang and W. Yuan, Bäcklund transformations and abundant exact explicit solutions of the Sharma-Tasso-Olver equation, Appl. Math. Comput 217 (2011), 7172-7183.
  • [17] W. Sinkala, P. Leach and J. O'Hara, Invariance properties of a general-pricing equation, J. Differential Equations 244 (2008), 2820-2835.
  • [18] S. Wang, X. Tang and S. Lou, Soliton fission and fusion: Burgers equation and Sharma-Tasso-Olver equation, Chaos Solitons Fractals 21 (2004), 231-239.
  • [19] A. Wazwaz, New soiitons and kinks solutions to the Sharma-Tasso-Olver equation, Appl. Math. Comput. 188 (2007), 1205-1213.
  • [20] P. Winternitz, Lie groups and solutions of nonlinear partial differential equations, Lecture Notes in Phys. 47 (1951), 752-755.
  • [21] B. Xue and C. M. Wu, Conservation laws and Darboux transformation for Sharma-Tasso-Olver equation, Commun. Theor. Phys. 58 (2012), 317-322.
  • [22] Y. Zhou, F. Yang and Q. Liu, Reduction of the Sharma-Tasso-Olver equation and series solutions, Commun. Nonlinear Sci. Numer. Simul 16 (2011), 641-646.
Uwagi
Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-6a996b39-a42e-4d2d-9f20-2a8c1dbba43c
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