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Mathematical Problems in Engineering
Volume 2012, Article ID 312658, 11 pages
http://dx.doi.org/10.1155/2012/312658
Research Article

On Dummy Variables of Structure-Preserving Transformations

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

Received 27 December 2011; Accepted 17 March 2012

Academic Editor: Rosana Rodriguez-Lopez

Copyright © 2012 J. C. Ndogmo. 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.

Abstract

A method is given for obtaining equivalence subgroups of a family of differential equations from the equivalence group of simpler equations of a similar form, but in which the arbitrary functions specifying the family element depend on fewer variables. Examples of applications to classical equations are presented, some of which show how the method can actually be used for a much easier determination of the equivalence group itself.