Similarity reductions from extended Painlevé expansions for nonintegrable evolution equations

The use of singular manifold expansions to find exact solutions to nonintegrable evolution equations is extended to include arbitrary (resonance) coefficients in such a way as to make the resulting infinite series exactly resummable. The technique involves the use of a rescaling ansatz analogous to that used to analyze the psi-series of nonintegrable ordinary differential equations. The result is a similarity reduction of the equation in which the constrained singular manifold plays the role of a similarity variable. The method is capable of yielding new solutions corresponding to either classical or nonclassical (conditional) Lie symmetries.