Amirkabir University of Technology AUT Journal of Mathematics and Computing 2783-2449 2 1 2021 02 01 Conservation law and Lie symmetry analysis of Foam Drainage equation 37 44 4161 10.22060/ajmc.2020.18460.1036 EN Mehdi Nadjafikhah Department of Pure Mathematics, School of Mathematics, Iran University of Science and Technology, Narmak, Tehran, 16846-13114, Iran 0000-0002-1354-9786 Omid Chekini Department of Pure Mathematics, School of Mathematics, Iran University of Science and Technology, Narmak, Tehran, 16846-13114, Iran Journal Article 2020 05 18  In this paper, using the Lie group analysis method, we study the group invariant of the Foam Drainage equation. It shows that this equation can be reduced to ODE. Also we apply the Lie-group classical, and the nonclassical method due to Bluman and Cole to deduce symmetries of the Foam Drainage equation. and we prove that the nonclassical method applied to the equation leads to new reductions, which cannot be obtained by Lie classical symmetries. Also this paper shows how to construct directly the local conservation laws for this equation. https://ajmc.aut.ac.ir/article_4161_174f8f613332b27e9e8a5138adb7e920.pdf