NONCLASSICAL SYMMETRIES AND THE SINGULAR MANIFOLD METHOD - THE BURGERS-EQUATION

A generalization of the direct method of Clarkson 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 corresponding to the so-called nonclassical symmetries by Blumen and Cole and Olver and Rosenau. The procedure is applied to the Burgers equation.