A Modified Method and Its Implementation of Constructing Symmetries and Symmetry Reductions for Nonlinear Partial Differential Equations

A method starting from an equivalent Lie group of transformations instead of Sophus Lie´s traditional procedure and using some direct subtle algebraic substitution techniques is devoted, which has been implemented in Maple and serves to seek Lie point symmetry, Lie symmetry groups, the symmetry reductions and the similarity solutions not only for partial differential equation but also for system of partial differential equations systematically and complete automatically and, all the things needed to be done are inputting the considered PDEs and then followed by an `Enter` key. Abundant nonlinear partial differential equations are analyzed effectively by the implemented approach, among of which three important examples and their corresponding results are listed in this paper.