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Symmetry 2018, 10(9), 378; https://doi.org/10.3390/sym10090378

Applications of Differential Form Wu’s Method to Determine Symmetries of (Partial) Differential Equations

1
School of Arts and Siences, Shanghai Maritime University, Shanghai 201306, China
2
Department of mathematics, Inner Mongolia University of Technology, Hohhot 010057, China
*
Author to whom correspondence should be addressed.
Received: 6 July 2018 / Revised: 21 August 2018 / Accepted: 28 August 2018 / Published: 3 September 2018
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Abstract

In this paper, we present an application of Wu’s method (differential characteristic set (dchar-set) algorithm) for computing the symmetry of (partial) differential equations (PDEs) that provides a direct and systematic procedure to obtain the classical and nonclassical symmetry of the differential equations. The fundamental theory and subalgorithms used in the proposed algorithm consist of a different version of the Lie criterion for the classical symmetry of PDEs and the zero decomposition algorithm of a differential polynomial (d-pol) system (DPS). The version of the Lie criterion yields determining equations (DTEs) of symmetries of differential equations, even those including a nonsolvable equation. The decomposition algorithm is used to solve the DTEs by decomposing the zero set of the DPS associated with the DTEs into a union of a series of zero sets of dchar-sets of the system, which leads to simplification of the computations. View Full-Text
Keywords: Wu’s method; symmetry; partial differential equations; computation Wu’s method; symmetry; partial differential equations; computation
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Chaolu, T.; Bilige, S. Applications of Differential Form Wu’s Method to Determine Symmetries of (Partial) Differential Equations. Symmetry 2018, 10, 378.

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