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ISRN Mathematical Physics
Volume 2013 (2013), Article ID 109170, 7 pages
http://dx.doi.org/10.1155/2013/109170
Research Article

Approximate Symmetries of the Harry Dym Equation

School of Mathematics, Iran University of Science and Technology, Narmak, Tehran 1684613114, Iran

Received 27 October 2013; Accepted 17 November 2013

Academic Editors: B. Bagchi and Z. Qiao

Copyright © 2013 Mehdi Nadjafikhah and Parastoo Kabi-Nejad. 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

We derive the first-order approximate symmetries for the Harry Dym equation by the method of approximate transformation groups proposed by Baikov et al. (1989, 1996). Moreover, we investigate the structure of the Lie algebra of symmetries of the perturbed Harry Dym equation. We compute the one-dimensional optimal system of subalgebras as well as point out some approximately differential invariants with respect to the generators of Lie algebra and optimal system.