THERMAL SCIENCE

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Yan Wang

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Zhong-Zhou Dong

SYMMETRY ANALYSIS OF A (2+1)-D SYSTEM

ABSTRACT
The classical Lie group method and the (2+1)-D generalized symmetry method in vector analysis are adopted to find infinitesimal symmetries for a (2+1)-D generalized Painleve Burgers system, and its various reduced systems are obtained.
KEYWORDS
classical Lie group, (2+1)-D generalized symmetry, vector analysis
PAPER SUBMITTED: 2017-05-16
PAPER REVISED: 2017-12-01
PAPER ACCEPTED: 2017-12-02
PUBLISHED ONLINE: 2018-09-10
DOI REFERENCE: https://doi.org/10.2298/TSCI1804811W
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2018, VOLUME 22, ISSUE Issue 4, PAGES [1811 - 1822]
REFERENCES
  1. Lou, S. Y., Ni, G. J. The Relations Among a Special Type of Solutions in Some (D+1)-Dimensional Nonlinear Equations, Journal of Mathematical Physics, 30 (1989), 7, pp. 1614-1620
  2. Fan, E. G., Extended Tanh-Function Method and Its Applications to Nonlinear Equations, Physics Let-ters A, 277 (2000), 4, pp. 212-218
  3. Fan, E. G., Uniformly Constructing a Series of Explicit Exact Solutions to Nonlinear Equations in Math-ematical Physics, Chaos, Solitons & Fractals, 16 (2003), 5, pp. 819-839
  4. Zhang, Y. F., et al., A Corresponding Lie Algebra of a Reductive Homogeneous Group and Its Applica-tions, Communications in Theoretical Physics, 63 (2015), 5, pp. 535-548
  5. Lou, S. Y., Extended Painleve Expansion, Nonstandard Truncation and Special Reductions of Nonlinear Evolution Equations, Zeitschrift fuer Naturforschung A, 53 (1998), 5, pp. 251-258
  6. Zhang, Y. F., Wang, Y., A New Reduction of the Self-Dual Yang-Mills Equations and Its Applications, Zeitschrift fuer Naturforschung A, 71 (2016), 7, pp. 631-638
  7. Chen, Y., et al., Exact Solutions for a New Class of Nonlinear Evolution Equations with Nonlinear Term of any Order, Chaos, Solitons & Fractals, 17 (2003), 4, pp. 675-682
  8. Wang, Y., et al., A Few New 2+1-Dimensional Nonlinear Dynamics and the Representation of Riemann Curvature Tensors, Zeitschrift fuer Naturforschung A, 71 (2016), 9, pp. 777-782
  9. Olver, P. J., Applications of Lie Groups to Differential Equations, Springer-Verlag, New York, USA, 1986
  10. Tian, C., Lie Groups and Its Applications to Differential Equations (in Chinese), Science Press, Beijing, 2001
  11. Bluman, G. W., Cole, J. D., Similarity Methods for Differential Equations, Springer-Verlag, Berlin, 1974
  12. Clarkson, P. A., Kruskal, M. D., New Similarity Reductions of the Boussinesq Equation, Journal of Mathematical Physics, 30 (1989), 10, pp. 2201-2213
  13. Clarkson, P. A., Nonclassical Symmetry Reductions of the Boussinesq Equation, Chaos, Solitons & Fractals, 5 (1995), 12, pp. 2261-2301
  14. Zhang, Y. F., Zhang, H. Q., An Extension of the Direct Method and Similarity Reductions of a General-ized Burgers Equation with an Arbitrary Derivative Function, Chinese Physics, 11 (2002), 4, pp. 319-322
  15. Lou, S. Y., Ma, H. C., Letter to the Editor: Non-Lie Symmetry Groups of (2+1)-D Nonlinear Systems Obtained from a Simple Direct Method, Journal of Physics A General Physics, 38 (2005), 7, pp. L129-L137
  16. Ma, H. C., A Simple Method to Generate Lie Point Symmetry Groups of the (3+1)-Dimensional Jimbo-Miwa Equation, Chinese Physics Letter, 22 (2005), 3, pp. 554-557
  17. Dong, Z. Z., et al., Symmetry Reduction and Exact Solutions of a Hyperbolic Monge-Ampere Equation, Chinese Annals of Mathematics, Series B, 33 (2012), 2, pp. 309-316
  18. Zhao, Z. H., Ge, W. G., Symmetry Analysis of Reaction Diffusion Equation with Distributed Delay, Communications in Nonlinear Science & Numerical Simulation, 24 (2015), 1-3, pp. 11-20
  19. Hong, K. Z., et al., Painleve Analysis and Some Solutions of (2+1)-D Generalized Burgers Equations, Communications in Theoretical Physics, 39 (2003), 4, pp. 393-394
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Symmetry analysis of a (2+1)-D system

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