Characteristic Set Algorithm for Determining Approximate Symmetries of Perturbed Partial Differential Equations

In this paper, based on differential characteristic set algorithm of a differential polynomial system, an algorithm for calculating two kinds of approximate symmetries of a perturbed partial differential equation is suggested. The difficulty of solving determining equations of the approximate symmetries is overcome significantly by the algorithm. As applications of the algorithm, the approximate (potential) symmetries of three evolution equations are determined. This is also a new application of differential characteristic set (Wu´s) method in differential field.