An Involutive Reduction Method to Find Invariant Solutions for Partial Differential Equations

A standard approach to solve partial diffrential equations is the construction of invariant solutions. These solutions have to fulfill an additional equation called the invariant surface condition. This condition represents the invariance of the equation under a symmetry transformation. To solve the coupled system of the differential equation and its invariant surface condition we used a Mathematica-package which combines involutive and heuristic methods to simplify and solve this coupled system. The procedure is presented by some examples.