Amirkabir University of Technology AUT Journal of Modeling and Simulation 2588-2953 51 2 2019 12 01 Approximate symmetries and invariant solutions for the generalizations of the Burgers- Korteweg-de Vries mod 249 254 4266 10.22060/miscj.2021.19554.5240 EN Hamid Razzaghi Department of Mathematics, Payame Noor University, Tehran, Iran Mehdi Nadjafikhah School of Mathematics, Iran University of Science and Technology, Narmak, Tehran, Iran 0000-0002-1354-9786 Yousef Alipour Fakhri Department of Mathematics, Payame Noor University, Tehran, Iran Journal Article 2018 04 28 In this paper the generalizations of the Burgers-Korteweg-de Vries model with small parameter derived by Kudryshov <em>et al</em>[ N.A. Kudryashov, D.I. Sinelshchikov. Extended models of non-linear waves in liquid with gas bubbles, International Journal of Non-Linear Mechanics 63 (2014) 31-38] is studied. A comprehensive study on the approximate symmetry analysis of the waves models is presented. First, we obtain approximate symmetry for the equation. Subsequently, in a physical application, using the first-order approximate symmetries, corresponding approximate invariant solutions to the perturbed non-linear models are obtained. Perturbed model Approximate symmetry Approximate invariant solution Waves in liquid with gas bubbles https://miscj.aut.ac.ir/article_4266_0e139b17a92b2df7d6c3c840e51465fe.pdf