TY - JOUR
ID - 57300
TI - Optimal system and approximate solutions of the nonlinear filtration equation
JO - Annals of Optimization Theory and Practice
JA - AOTP
LA - en
SN - 2588-3666
AU - Rahimian, Mohammad
AD - Department of Mathematics, Masjed-Soleiman Branch, Islamic Azad University, Masjed-Soleiman , Iran
Y1 - 2018
PY - 2018
VL - 1
IS - 1
SP - 35
EP - 42
KW - Lie group analysis
KW - Approximate symmetry
KW - Optimal system
KW - Invariant solution
KW - Filtration equation
DO - 10.22121/aotp.2018.115787.1009
N2 - In 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.
UR - http://aotp.fabad-ihe.ac.ir/article_57300.html
L1 - http://aotp.fabad-ihe.ac.ir/article_57300_02707fb4fef3391a9dc75c130f6ce0a9.pdf
ER -