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Advances in Mathematical Physics
Volume 2014, Article ID 695408, 16 pages
http://dx.doi.org/10.1155/2014/695408
Research Article

On New Conservation Laws of Fin Equation

1Department of Mathematics, Faculty of Science and Letters, Istanbul Technical University, Maslak, 34469 Istanbul, Turkey
2Division of Mechanics, Faculty of Civil Engineering, Istanbul Technical University, Maslak, 34469 Istanbul, Turkey

Received 12 April 2014; Accepted 17 June 2014; Published 14 August 2014

Academic Editor: Jian-Qiang Sun

Copyright © 2014 Gülden Gün Polat 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.

Abstract

We study the new conservation forms of the nonlinear fin equation in mathematical physics. In this study, first, Lie point symmetries of the fin equation are identified and classified. Then by using the relationship of Lie symmetry and -symmetry, new -functions are investigated. In addition, the Jacobi Last Multiplier method and the approach, which is based on the fact -functions are assumed to be of linear form, are considered as different procedures for lambda symmetry analysis. Finally, the corresponding new conservation laws and invariant solutions of the equation are presented.