## THERMAL SCIENCE

International Scientific Journal

### 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**

PAPER SUBMITTED: 2017-05-16

PAPER REVISED: 2017-12-01

PAPER ACCEPTED: 2017-12-02

PUBLISHED ONLINE: 2018-09-10

**THERMAL SCIENCE** YEAR

**2018**, VOLUME

**22**, ISSUE

**4**, PAGES [1811 - 1822]

- 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
- Fan, E. G., Extended Tanh-Function Method and Its Applications to Nonlinear Equations, Physics Let-ters A, 277 (2000), 4, pp. 212-218
- 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
- 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
- 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
- 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
- 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
- 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
- Olver, P. J., Applications of Lie Groups to Differential Equations, Springer-Verlag, New York, USA, 1986
- Tian, C., Lie Groups and Its Applications to Differential Equations (in Chinese), Science Press, Beijing, 2001
- Bluman, G. W., Cole, J. D., Similarity Methods for Differential Equations, Springer-Verlag, Berlin, 1974
- Clarkson, P. A., Kruskal, M. D., New Similarity Reductions of the Boussinesq Equation, Journal of Mathematical Physics, 30 (1989), 10, pp. 2201-2213
- Clarkson, P. A., Nonclassical Symmetry Reductions of the Boussinesq Equation, Chaos, Solitons & Fractals, 5 (1995), 12, pp. 2261-2301
- 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
- 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
- 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
- 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
- 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
- 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