Non classical symmetries and the Singular Manifold Method: the Burgers equation

A generalization of the Direct Method of Clarcson and Kruskal for finding Similarity Reductions of a PDE is found and discussed. The generalization incorporates the Singular Manifold Method largely based upon the Painleve Property. The symmetries found in this way are shown to be those correspondent to the so called Non Classical Symmetries by Blumen–Cole and Olver–Rosenau. The procedure is applied to the Burgers equation.