Complete symmetry groups of ordinary differential equations and their integrals : Some basic considerations
By K. Andriopoulos, Peter G. L. Leach, G. Flessas. 2001
56 citations recorded by the source corpus.
Abstract The concept of the complete symmetry group of a differential equation introduced by J. Krause (1994, J. Math. Phys. 35 , 5734–5748) is extended to integrals of such equations. This paper is devoted to some aspects characterising complete symmetry groups. The algebras of the symmetries of both differential equations and integrals are studied in the context of equations for which the elements are represented by point or contact symmetries so that there is no ambiguity about the group. Both algebras and groups are found to be nonunique.
Subfields: Spectroscopy, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/30e671b6e78c0e1b581f22c3677feedcbde51e49
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In Statistical and Nonlinear Physics
Citations in the corpus
- The Ermakov equation: A commentary (2008, background): “Although a scalar second-order ordinary differential equation requires just three Lie symmetries [1, 2, 58, 59] to specify it completely, the complete symmetry group of (1) is not sl(2, R).”
- Symmetry group classification of ordinary differential equations: Survey of some results (2007, background): “Complete symmetry groups of equations with three symmetries [41]”