Non-classical symmetries and the singular manifold method revisited

The connection between the singular manifold method (Painleve expansions truncated at the constant term) and symmetry reductions of two members of a family of Cahn-Hilliard equations is considered. The conjecture that similarity information for a nonlinear partial differential equation may always be fully recovered from the singular manifold method is violated for these equations, and is thus shown to be invalid in general. Given that several earlier examples demonstrate the connection between the two techniques in some cases, it now becomes necessary to establish when such a relationship exists-a question related to a deeper understanding of Painleve analysis. This issue is also briefly discussed