Integrable property, Lie symmetry analysis and explicit solutions to the generalized [formula omitted] model

Abstract

In this paper, the combination of Painlevé analysis and Lie group method is performed, the Painlevé properties (PPs) and Bäcklund transformations (BTs) of the nonlinear ϕ4 types of equations are obtained under some conditions. Then, all of the point symmetries of the generalized ϕ4 model are given by Lie group classification method. Furthermore, the exact solutions to the equations are investigated by the symmetry reductions and analytic method.