SIMILARITY REDUCTIONS FROM EXTENDED PAINLEVE 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.