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Advances in Mathematical Physics
Volume 2013 (2013), Article ID 568632, 9 pages
Approximate Hamiltonian Symmetry Groups and Recursion Operators for Perturbed Evolution Equations
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.
- S. Lie, “On integration of a class of linear partial differential equations by means of definite integrals,” Archiv der Mathematik, vol. 6, pp. 328–368, 1881.
- V. A. Baikov, R. K. Gazizov, and N. Kh. Ibragimov, “Approximate symmetries of equations with a small parameter,” Matematicheskiĭ Sbornik, vol. 136, no. 4, pp. 435–450, 1988.
- V. A. Baikov, R. K. Gazizov, and N. H. Ibragimov, “Approximate transformation groups and deformations of symmetry Lie algebras,” in CRC Handbook of Lie Group Analysis of Differential Equations, N. H. Ibragimov, Ed., vol. 3, chapter 2, CRC Press, Boca Raton, Fla, USA, 1996.
- W. I. Fushchich and W. M. Shtelen, “On approximate symmetry and approximate solutions of the nonlinear wave equation with a small parameter,” Journal of Physics A, vol. 22, no. 18, pp. L887–L890, 1989.
- N. Euler, M. W. Shul'ga, and W.-H. Steeb, “Approximate symmetries and approximate solutions for a multidimensional Landau-Ginzburg equation,” Journal of Physics A, vol. 25, no. 18, pp. L1095–L1103, 1992.
- M. Euler, N. Euler, and A. Köhler, “On the construction of approximate solutions for a multidimensional nonlinear heat equation,” Journal of Physics A, vol. 27, no. 6, pp. 2083–2092, 1994.
- M. Pakdemirli, M. Yürüsoy, and İ. T. Dolapçi, “Comparison of approximate symmetry methods for differential equations,” Acta Applicandae Mathematicae, vol. 80, no. 3, pp. 243–271, 2004.
- R. Wiltshire, “Two approaches to the calculation of approximate symmetry exemplified using a system of advection-diffusion equations,” Journal of Computational and Applied Mathematics, vol. 197, no. 2, pp. 287–301, 2006.
- N. H. Ibragimov and V. F. Kovalev, Approximate and Renormgroup Symmetries, Nonlinear Physical Science, Springer, Berlin, Germany, 2009.
- P. J. Olver, Applications of Lie Groups to Differential Equations, vol. 107 of Graduate Texts in Mathematics, Springer, New York, NY, USA, 2nd edition, 1993.
- M. Nadjafikhah and A. Mokhtary, “Approximate symmetry analysis of Gardner equation,” http://arxiv.org/abs/1212.3604.
- Z. Zhang, “Approximate homotopy series solutions of perturbed PDEs via approximate symmetry method,” http://184.108.40.206/abs/1112.4225v2.