Ritt-Wu Characteristic Set Method for Laurent Partial Differential Polynomial Systems

2019 ◽  
Vol 32 (1) ◽  
pp. 62-77 ◽  
Author(s):  
Youren Hu ◽  
Xiao-Shan Gao
Keyword(s):  
Polynomial Systems ◽  
Differential Polynomial ◽  
Characteristic Set ◽  
Partial Differential ◽  
Characteristic Set Method

scholarly journals Characteristic set method for differential–difference polynomial systems

2009 ◽  
Vol 44 (9) ◽  
pp. 1137-1163 ◽  
Author(s):  
X.S. Gao ◽  
J. Van der Hoeven ◽  
C.M. Yuan ◽  
G.L. Zhang
Keyword(s):  
Polynomial Systems ◽  
Characteristic Set ◽  
Difference Polynomial ◽  
Characteristic Set Method

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

Symmetry ◽  
2018 ◽  
Vol 10 (9) ◽  
pp. 378 ◽  
Author(s):  
Temuer Chaolu ◽  
Sudao Bilige
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Differential Polynomial ◽  
Decomposition Algorithm ◽  
Partial Differential ◽  
Wu’S Method ◽  
Classical Symmetry ◽  
Symmetries Of Differential Equations ◽  
Wu's Method ◽  
Nonclassical Symmetry

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.

Sign in / Sign up

Export Citation Format

Share Document