University of Tabriz Computational Methods for Differential Equations 2345-3982 11 1 2023 01 01 Approximate symmetry group analysis and similarity reductions of the perturbed mKdV-KS equation 175 182 14435 10.22034/cmde.2022.48341.2022 EN Mehdi Jafari Department of Mathematics, Payame Noor University, PO BOX 19395-4697, Tehran, Iran. Razie Darvazebanzade Department of Mathematics, Payame Noor University, PO BOX 19395-4697, Tehran, Iran. Journal Article 2021 10 09 In this paper, we apply the approximate symmetry transformation group to obtain the approximate symmetry group of the perturbed mKdV-KS equation which is a modified Korteweg-de Vries (mKdV) equation with a higher singularity perturbed term as the Kuramoto-Sivashinsky (KS) equation. Also, an optimal system of one-dimensional subalgebras of symmetry algebra is constructed and the corresponding differential invariants and some approximately invariant solutions of the equation are computed.  Perturbed mKdV-KS equation Approximate symmetry Approximately invariant solution Optimal system https://cmde.tabrizu.ac.ir/article_14435_2acb98a54724c87f05f5ed80210cf245.pdf