Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)


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 KwaZulu-Natal, 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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