THERMAL SCIENCE

International Scientific Journal

Authors of this Paper

External Links

Yi Tian

,

Kang-Le Wang

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
Lie algorithm, differential polynomial characteristic set algorithm, symmetry classification
PAPER SUBMITTED: 2019-03-02
PAPER REVISED: 2019-10-27
PAPER ACCEPTED: 2019-10-28
PUBLISHED ONLINE: 2020-06-21
DOI REFERENCE: https://doi.org/10.2298/TSCI2004629T
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2020, VOLUME 24, ISSUE Issue 4, PAGES [2629 - 2635]
REFERENCES
  1. 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
  2. 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
  3. 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
  4. Tian, Y., Symmetry Reduction a Promising Method for Heat Conduction Equations, Thermal Science, 23 (2019), 4, pp. 2219-2227
  5. Tian,Y., Diffusion-Convection Equations and Classical Symmetry Classification, Thermal Science, 23 (2019), 4, pp. 2151-2156
  6. 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
  7. 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
  8. He, J. H. Lagrangians for Self-Adjoint and Non-Self-Adjoint Equations, Applied Mathematics Letters, 26 (2013), 3, pp. 373-375
  9. He, J. H. Lagrangian for Nonlinear Perturbed Heat and Wave Equations, Applied Mathematics Letters, 26 (2013), 1, pp. 158-159
  10. 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
  11. 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
  12. He, J. H., Sun, C., A Variational Principle for a Thin Film Equation, Journal of Mathematical Chemistry, 57 (2019), 9, pp. 2075-2081
  13. 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
  14. Wang, Y., et al., A Variational Formulation for Anisotropic Wave Traveling in a Porous Medium, Fractals, 27 (2019), 4, 1950047
  15. Wang, K. L., He, C. H., A Remark on Wang's Fractal Variational Principle, Fractals, 27 (2019), 8, ID 1950134
  16. 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
  17. 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
  18. 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
  19. 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
  20. Wu, W. T., Mathematics Mechanization, Science Press, Beijing, China, 2000
  21. 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
PDF VERSION [DOWNLOAD]
Polynomial characteristic method an easy approach to lie symmetry

© 2024 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence