## THERMAL SCIENCE

International Scientific Journal

### POLYNOMIAL CHARACTERISTIC METHOD AN EASY APPROACH TO LIE SYMMETRY

**ABSTRACT**

Along the approach to Lie symmetry, it is always needed to solve an over-determined system, which is difficult and complex if not impossible. Here we suggest a new polynomial characteristic method combined with Lie algorithm to complete symmetry classification for a class of perturbed equations. A differential polynomial characteristic set algorithm is proposed to decompose the determining equations into a series of equations easy to be solved.

**KEYWORDS**

PAPER SUBMITTED: 2019-03-02

PAPER REVISED: 2019-10-27

PAPER ACCEPTED: 2019-10-28

PUBLISHED ONLINE: 2020-06-21

**THERMAL SCIENCE** YEAR

**2020**, VOLUME

**24**, ISSUE

**Issue 4**, PAGES [2629 - 2635]

- Hao, X. Z., et al., The Residual Symmetry And Exact Solutions Of The Davey-Stewartson III Equation, Computers & Mathematics with Applications, 73 (2017), 11, pp. 2404-2414
- Feng, L. L., et al., Lie Symmetries, Conservation Laws and Analytical Solutions for Two-Component Integrable Equations, Chinese Journal of Physics, 55 (2017), 3, pp. 996-1010
- Tian, S. F., et al., Lie Symmetry Analysis, Conservation Laws and Analytical Solutions for the Constant Astigmatism Equation, Chinese Journal of Physics, 55 (2017), 5, pp. 1938-1952
- Tian, Y., Symmetry Reduction a Promising Method for Heat Conduction Equations, Thermal Science, 23 (2019), 4, pp. 2219-2227
- Tian,Y., Diffusion-Convection Equations and Classical Symmetry Classification, Thermal Science, 23 (2019), 4, pp. 2151-2156
- Wei, G. M., et al., Lie Symmetry Analysis and Conservation Law of Variable-Coefficient Davey-Stewartson Equation, Computers & Mathematics with Applications, 79 (2018), 5, pp. 3420-3430
- Zhang, Z. Y., Conservation Laws of Partial Differential Equations: Symmetry, Adjoint Symmetry and Nonlinear Self-Adjointness, Computers & Mathematics with Applications, 74 (2017), 12, pp. 3129-3140
- He, J. H. Lagrangians for Self-Adjoint and Non-Self-Adjoint Equations, Applied Mathematics Letters, 26 (2013), 3, pp. 373-375
- He, J. H. Lagrangian for Nonlinear Perturbed Heat and Wave Equations, Applied Mathematics Letters, 26 (2013), 1, pp. 158-159
- He, J. H. A Modified Li-He's Variational Principle for Plasma, International Journal of Numerical Methods for Heat and Fluid Flow, On-line first, doi.org/10.1108/HFF-06-2019-0523, 2019
- He, J. H., Lagrange Crisis and Generalized Variational Principle for 3D unsteady flow, International Journal of Numerical Methods for Heat and Fluid Flow, On-line first, doi.org/10.1108/HFF-07-2019-0577, 2019
- He, J. H., Sun, C., A Variational Principle for a Thin Film Equation, Journal of Mathematical Chemistry, 57 (2019), 9, pp. 2075-2081
- Li, Y., He, C. H., A Short Remark on Kalaawy's Variational Principle for Plasma, International Journal of Numerical Methods for Heat and Fluid Flow, 27 (2017), 10, pp. 2203-2206
- Wang, Y., et al., A Variational Formulation for Anisotropic Wave Traveling in a Porous Medium, Fractals, 27 (2019), 4, 1950047
- Wang, K. L., He, C. H., A Remark on Wang's Fractal Variational Principle, Fractals, 27 (2019), 8, ID 1950134
- He, J. H., A Fractal Variational Theory for One-Dimensional Compressible Flow in a Microgravity Space, Fractals, On-line first, doi.org/10.1142/S0218348X20500243, 2019
- He, J. H., Variational Principle for the Generalized KdV-Burgers Equation with Fractal Derivatives for Shallow Water Waves, J. Appl. Comput. Mech., On-line first, doi.org/10.22055/JACM.2019.14813
- Zhang, J. J., et al., Some Analytical Methods for Singular Boundary Value Problem in a Fractal Space, Appl. Comput. Math., 18 (2019), 3, pp. 225-235
- He, J. H., A Simple Approach to One-Dimensional Convection-Diffusion Equation and Its Fractional Modification for E Reaction Arising in Rotating Disk Electrodes, Journal of Electroanalytical Chemistry, 854 (2019), 113565
- Wu, W. T., Mathematics Mechanization, Science Press, Beijing, China, 2000
- Zhang, Z. Y., Chen, Y. F., A Comparative Study of Approximate Symmetry and Approximate Homotopy Symmetry to a Class of Perturbed Nonlinear Wave Equations, Nonlinear Analysis: Theory, Methods & Applications, 74 (2011), 13, pp. 4300-4318