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**An algorithm for the complete symmetry classification of differential equations based on Wu’s method.**
*(English)*
Zbl 1204.35021

An alternative algorithm using Wu’s method (differential characteristic set algorithm) is proposed for complete symmetry classification of partial differential equations involving arbitrary parameters. Such classification is determined by decomposing the solution set of the determining equations into a union of a series of zero sets of differential characteristic sets of the corresponding differential polynomial system. Each branch of the resulting decomposition yields a class of symmetries and the corresponding parameters. The proposed algorithm makes the classification direct and systematic, which also provides a novel application of Wu’s method to differential equations. To show the efficiency of the algorithm, complete potential symmetry classifications are given for linear and nonlinear wave equations with an arbitrary function parameter and both classical and nonclassical symmetries of a parametric Burgers equation as illustrative examples.

Reviewer: Ma Wen-Xiu (Tampa)

### MSC:

35B06 | Symmetries, invariants, etc. in context of PDEs |

35A30 | Geometric theory, characteristics, transformations in context of PDEs |

58J70 | Invariance and symmetry properties for PDEs on manifolds |

35K05 | Heat equation |

58J72 | Correspondences and other transformation methods (e.g., Lie-Bäcklund) for PDEs on manifolds |

35A25 | Other special methods applied to PDEs |

### Keywords:

Lie symmetries; differential characteristic set algorithm; parametric differential equations; linear wave equations; nonlinear wave equations; parametric Burgers equation
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\textit{T. Chaolu} and \textit{P. Jing}, J. Eng. Math. 66, No. 1--3, 181--199 (2010; Zbl 1204.35021)

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