Advances in Mathematical Physics
Volume 2013 (2013), Article ID 568632, 9 pages
http://dx.doi.org/10.1155/2013/568632
Research Article

Approximate Hamiltonian Symmetry Groups and Recursion Operators for Perturbed Evolution Equations

M. Nadjafikhah1 and A. Mokhtary2

1School of Mathematics, Iran University of Science and Technology, Narmak, Tehran 1684613114, Iran
2Department of Complementary Education, Payame Noor University, Tehran 19395-3697, Iran

Received 11 October 2012; Revised 18 December 2012; Accepted 1 January 2013

Academic Editor: Rutwig Campoamor-Stursberg

Copyright © 2013 M. Nadjafikhah and A. Mokhtary. 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

The method of approximate transformation groups, which was proposed by Baikov et al. (1988 and 1996), is extended on Hamiltonian and bi-Hamiltonian systems of evolution equations. Indeed, as a main consequence, this extended procedure is applied in order to compute the approximate conservation laws and approximate recursion operators corresponding to these types of equations. In particular, as an application, a comprehensive analysis of the problem of approximate conservation laws and approximate recursion operators associated to the Gardner equation with the small parameters is presented.