Title

Non-classical symmetries and the singular manifold method revisited

Abstract

The connection between the singular manifold method (Painlevé 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 Painlevé analysis. This issue is also briefly discussed.

Publication Date

2-6-1998

Publication Title

Journal of Physics A: Mathematical and General

Volume

31

Issue

5

Number of Pages

1487-1494

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1088/0305-4470/31/5/016

Socpus ID

0032488759 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/0032488759

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