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Classification of Discrete Symmetries of Ordinary Differential Equations
Author(s) -
LainePearson F. E.,
Hydon P. E.
Publication year - 2003
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1111/1467-9590.t01-1-00234
Subject(s) - mathematics , automorphism , ordinary differential equation , homogeneous space , differential equation , differential algebraic equation , pure mathematics , mathematical analysis , lie algebra , integrating factor , algebra over a field , geometry
A simple method for determining all discrete point symmetries of a given differential equation has been developed recently. The method uses constant matrices that represent inequivalent automorphisms of the Lie algebra spanned by the Lie point symmetry generators. It may be difficult to obtain these matrices if there are three or more independent generators, because the matrix elements are determined by a large system of algebraic equations. This paper contains a classification of the automorphisms that can occur in the calculation of discrete symmetries of scalar ordinary differential equations, up to equivalence under real point transformations. (The results are also applicable to many partial differential equations.) Where these automorphisms can be realized as point transformations, we list all inequivalent realizations. By using this classification as a look‐up table, readers can calculate the discrete point symmetries of a given ordinary differential equation with very little effort.