Painlevé Test, Generalized Symmetries, B?cklund Transformations and Exact Solutions to the Third-Order Burgers-Equations
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  • 作者：Hanze Liu
  • 关键词：Third ; order Burger’s equation ; Integrability ; Generalized symmetry ; B?cklund transformation ; Exact solution ; 17B80 ; 22E70 ; 35C05
  • 刊名：Journal of Statistical Physics
  • 出版年：2015
  • 出版时间：January 2015
  • 年：2015
  • 卷：158
  • 期：2
  • 页码：433-446
  • 全文大小：214 KB
  • 参考文献：1. Liu, H., Li, J., Zhang, Q.: Lie symmetry analysis and exact explicit solutions for general Burgers-equation. J. Comput. Appl. Math. 228, 1- (2009) CrossRef
    2. Liu, H., Li, J., Liu, L.: The recursion operator method for generalized symmetries and B?cklund transformations of the Burgers-equations. J. Appl. Math. Comput. 42, 159-70 (2013) CrossRef
    3. Conte, R., Musette, M.: The Painlevé Handbook. Springer, Dordrecht (2008)
    4. Weiss, J., Tabor, M., Carnevale, G.: The Painlevé property for partial differential equations. J. Math. Phys. 24, 522-26 (1983) CrossRef
    5. Newell, A., et al.: A unified approach to Painlevé expansions. Physics D 29, 1-8 (1987) CrossRef
    6. Cariello, F., Tabor, M.: The Painlevé expansions for nonintegrable evolution equations. Physics D 39, 77-4 (1989) CrossRef
    7. Clarkson, P.: Painlevé analysis and the complete integrability of a generalized variable-coefficient Kadomtsev–Petviashvili equation. IMA J. Appl. Math. 44, 27-3 (1990) CrossRef
    8. Olver, P.: Applications of Lie groups to differential equations. Graduate Texts in Mathematics. Springer, New York (1993)
    9. Bluman, G., Anco, S.: Symmetry and integration methods for differential equations. Applied Mathematical Sciences. Applied Mathematical Sciences, New York (2002)
    10. Chou, T.: New strong symmetries, symmetries and Lie algebra for Burgers-equation. Sci. China Ser. A 10, 1009-018 (1987). (in Chinese)
    11. Cheng, Y., et al.: Connections among symmetries, B?cklund transformation and the Painlevé property for Burgers-hierarchies. Acta Math. Appl. Sin. 14, 180-84 (1991). (in Chinese)
    12. Liu, H., Li, J.: Lie symmetry analysis and exact solutions for the short pulse equation. Nonlinear Anal. TMA 71, 2126-133 (2009) CrossRef
    13. Liu, H., Li, J., Liu, L.: Painlevé analysis. Lie symmetries, and exact solutions for the time-dependent coefficients Gardner equations. Nonlinear Dyn. 59, 497-02 (2010) CrossRef
    14. Liu, H., Li, J., Liu, L.: Symmetry and conservation law classification and exact solutions to the generalized KdV types of equations. Int. J. Bifur. Chaos 22(1250188), 1-1 (2012)
    15. Liu, H., Li, J., Liu, L.: Lie symmetry analysis, B?cklund transformations and exact solutions to (2 + 1)-dimensional Burgers-types of equations. Commun. Theor. Phys. 57, 737-42 (2012) CrossRef
    16. Liu, H., Geng, Y.: Symmetry reductions and exact solutions to the systems of carbon nanotubes conveying fluid. J. Differ. Equ. 254, 2289-303 (2013) CrossRef
    17. Fokas, A., Fuchssteiner, B.: On the structure of sympletic operators and hereditary symmetries. Lett. Nuovo Cimento 28, 299-03 (1980) CrossRef
    18. Tian, C.: Transformation of equations and transformation of symmetries. Acta Math. Appl. Sin. 12, 238-49 (1989). (in Chinese)
    19. Calogero, F., Eckhaus, W.: Nonlinear evolution equations, rescalings, model PDEs and their integrability: I. Inverse Probl. 3, 229-62 (1987)
文摘
In this paper, the Painlevé analysis is performed on the physical form of the third-order Burgers-equation, the Painlevé property and integrability (C-integrable) of the equation is verified. Then, the generalized symmetries of the equation are presented and the generalized symmetries of the other equation are given by the symmetry transformation method. The B?cklund Transformations of the equations are constructed based on the symmetries, respectively. Furthermore, the exact explicit solutions to the equations are investigated in terms of the symmetries, B?cklund transformations and transformations of the equations.
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