Amirkabir University of TechnologyAUT Journal of Mathematics and Computing2120210201Conservation law and Lie symmetry analysis of foam drainage equation3744416110.22060/ajmc.2020.18460.1036ENMehdiNadjafikhahSchool of Mathematics, Iran University of Science and Technology0000-0002-1354-9786OmidChekiniSchool of Mathematics, Iran University of Science and TechnologyJournal Article20200518In 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 equationhttps://ajmc.aut.ac.ir/article_4161_afc061bca696a62e35f9dcb82217760b.pdf