Firouzabad Institute of Higher EducationAnnals of Optimization Theory and Practice2588-36661120180201Optimal system and approximate solutions of the nonlinear filtration equation35425730010.22121/aotp.2018.115787.1009ENMohammadRahimianDepartment of Mathematics, Masjed-Soleiman Branch, Islamic Azad University, Masjed-Soleiman , IranJournal Article20171215In this paper, the problem of determining the most general Lie point approximate symmetries group for the nonlinear filtration equation with a small parameter is analyzed. By applying the basic Lie approximate symmetry method for the nonlinear filtration equation with a small parameter, the classical Lie point approximate symmetry operators are obtained. Also, the algebraic structure of the Lie algebra of approximate symmetries is discussed and an optimal system of one-dimensional subalgebras of the nonlinear filtration equation with a small parameter, symmetry algebra which creates the preliminary classification of group invariant solutions is constructed. Particularly, the Lie invariants as well as similarity reduced equations corresponding to infinitesimal symmetries and group invariant solutions associated to the symmetries are obtained.http://aotp.fabad-ihe.ac.ir/article_57300_02707fb4fef3391a9dc75c130f6ce0a9.pdf