Two Approaches to the Calculation of Approximate Symmetry of Ostrovsky Equation with Small Parameter

In this paper, two methods of approximate symmetries for partial differential 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 infinitesimal 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