Title

Non-classical symmetries and the singular manifold method revisited

Authors

Authors

U. Tanriver;S. R. Choudhury

Comments

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Abbreviated Journal Title

J. Phys. A-Math. Gen.

Keywords

PARTIAL-DIFFERENTIAL EQUATIONS; INVARIANT PAINLEVE ANALYSIS; FITZHUGH-NAGUMO EQUATION; CAHN-HILLIARD EQUATIONS; SIMILARITY; REDUCTIONS; NONCLASSICAL SYMMETRIES; EVOLUTION-EQUATIONS; LONG-WAVE; LAX; PAIRS; EXPANSIONS; Physics, Multidisciplinary; Physics, Mathematical

Abstract

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.

Journal Title

Journal of Physics a-Mathematical and General

Volume

31

Issue/Number

5

Publication Date

1-1-1998

Document Type

Article

Language

English

First Page

1487

Last Page

1494

WOS Identifier

WOS:000071991200016

ISSN

0305-4470

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