Math Phys Anal Geom (2015) 18:3 DOI 10.1007/s11040-015-9170-0 Two Approaches to the Calculation of Approximate Symmetry of Ostrovsky Equation with Small Parameter Abolhassan Mahdavi · Mehdi Nadjafikhah · Megerdich Toomanian Received: 19 June 2014 / Accepted: 5 December 2014 © Springer Science+Business Media Dordrecht 2015 Abstract In this paper, two methods of approximate symmetries for partial differen- tial equations with a small parameter are applied to a perturbed nonlinear Ostrovsky equation. To compute the first-order approximate symmetry, we have applied two methods which one of them was proposed by Baikov et al. in which the infinites- imal generator is expanded in a perturbation series; whereas the other method by Fushchich and Shtelen [3] is based on the expansion of the dependent variables in perturbation series. Especially, an optimal system of one dimensional subalgebras is constructed and some invariant solutions corresponding to the resulted symmetries are obtained. Keywords Approximate symmetry · Approximate solution · Perturbed Ostrovsky equation Mathematics Subject Classification (2010) 76M60 · 35Q80 · 35Q35 · 22E70 A. Mahdavi () · M. Toomanian Department of Mathematics, Karaj Branch Islamic University, Karaj, Iran e-mail: ad.mahdavi@kiau.ac.ir M. Toomanian e-mail: megerdich.toomanian@kiau.ac.ir M. Nadjafikhah School of Mathematics, Iran University of Science and Technology, Narmak, 1684613114, Tehran, Iran e-mail: mnadjafikhah@iust.ac.ir