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.
Highlights
In symmetry analysis of differential equations (PDEs), the computation of the maximal symmetry admitted by the system is the first step in order to use the symmetry [1,2,3]
The solving of determining equations (DTEs) for the symmetry of PDEs is a challenging problem in terms of mathematical computation
2, alternative algorithms based on the dchar-set algorithm for a differential polynomial system (DPS) for the computation of the symmetry of a system of PDEs are given; in Section 3, we give several applications of the proposed algorithms to determine the symmetry of mathematical physics equations; in Section 4, we give some concluding remarks
Summary
In symmetry analysis of (partial) differential equations (PDEs), the computation of the maximal symmetry admitted by the system is the first step in order to use the symmetry [1,2,3]. We present algorithms to deal with the classical and nonclassical symmetry computations based on the differential form Wu’s method. 2, alternative algorithms based on the dchar-set algorithm for a DPS for the computation of the symmetry of a system of PDEs are given; in Section 3, we give several applications of the proposed algorithms to determine the symmetry of mathematical physics equations; in Section 4, we give some concluding remarks. For each i, Bi , Ci ∈ K X [∂U ] have the same leading derivative as Ai. The following is the definition of the triangular form and dchar-set of a DPS. The down-arrow represents that the computation is continuous in this step, and the up-arrow shows the computation progressing into the loop step
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