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Abstract and Applied Analysis
Volume 2014, Article ID 490165, 6 pages
Research Article

Symmetries, Associated First Integrals, and Double Reduction of Difference Equations

School of Mathematics, University of the Witwatersrand, Private Bag 3, Johannesburg 2050, South Africa

Received 11 April 2014; Accepted 16 July 2014; Published 23 July 2014

Academic Editor: Igor Leite Freire

Copyright © 2014 L. Ndlovu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We determine the symmetry generators of some ordinary difference equations and proceeded to find the first integral and reduce the order of the difference equations. We show that, in some cases, the symmetry generator and first integral are associated via the “invariance condition.” That is, the first integral may be invariant under the symmetry of the original difference equation. When this condition is satisfied, we may proceed to double reduction of the difference equation.