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An algorithm for the complete symmetry classification of differential equations based on Wu’s method

Journal of Engineering Mathematics volume 66, pages 181–199 (2010)Cite this article

Abstract

In this paper, an alternative algorithm which uses Wu’s method (differential characteristic set algorithm) for the complete symmetry classification of (partial) differential equations containing arbitrary parameter is proposed. The classification is determined by decomposing the solution set of determining equations into a union of a series of zero sets of differential characteristic sets of the corresponding differential polynomial system of the determining equations. Each branch of the decomposition yields a class of symmetries and associated parameters. The algorithm makes the classification become direct and systematic. This is also a new application of Wu’s method in the field of differential equations. As illustrative examples of our algorithm, the complete potential symmetry classifications of linear and nonlinear wave equations with an arbitrary function parameter and both classical and nonclassical symmetries of a parametric Burgers equation are presented.

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Authors and Affiliations

  1. Shanghai Maritime University, Shanghai, 200135, China

    Temuer Chaolu

  2. Inner Mongolia University of Technology, Hohhot, 010051, China

    Pang Jing

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  1. Temuer Chaolu
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  2. Pang Jing
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Correspondence to Temuer Chaolu.

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Chaolu, T., Jing, P. An algorithm for the complete symmetry classification of differential equations based on Wu’s method. J Eng Math 66, 181–199 (2010). https://doi.org/10.1007/s10665-009-9344-5

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  • DOI: https://doi.org/10.1007/s10665-009-9344-5

Keywords

  • Differential characteristic set algorithm
  • Parametric differential equations
  • Symmetry classification
  • Wu’s method