
SIGMA 1 (2005), 024, 12 pages nlin.SI/0512012
http://dx.doi.org/10.3842/SIGMA.2005.024
Symmetry Properties of Autonomous Integrating Factors
Sibusiso Moyo ^{a} and P.G.L. Leach ^{b}
^{a)} Department
of Mathematics, Durban Institute of Technology, PO Box 953, Steve Biko Campus, Durban 4000, Republic of South Africa
^{b)} School of Mathematical Sciences, Howard College,
University of KwaZuluNatal, Durban 4041, Republic of South Africa
Received September 27, 2005, in final form November 21,
2005; Published online December 05, 2005
Abstract
We study the symmetry properties of
autonomous integrating factors from an algebraic point of view.
The symmetries are delineated for the resulting integrals treated
as equations and symmetries of the integrals treated as functions
or configurational invariants. The succession of terms (pattern)
is noted. The general pattern for the solution symmetries for
equations in the simplest form of maximal order is given and the
properties of the associated integrals resulting from this
analysis are given.
Key words:
autonomous integrating factors; maximal symmetry.
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