Symmetry and the Chazy equation

Clarkson, Peter and Olver, Peter J. (1996) Symmetry and the Chazy equation. Journal of Differential Equations, 124 (1). pp. 225-246. ISSN 0022-0396. (The full text of this publication is not available from this repository)

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Official URL
http://dx.doi.org/10.1006/jdeq.1996.0008

Abstract

There are three different actions of the unimodular Lie group SL(2, C) on a two-dimensional space. In every case, we show how an ordinary differential equation admitting SL(2) as a symmetry group can be reduced in order by three, and the solution recovered from that of the reduced equation via a pair of quadratures and the solution to a linear second order equation. A particular example is the Chazy equation, whose general solution can be expressed as a ratio of two solutions to a hypergeometric equation. The reduction method leads to an alternative formula in terms of solutions to the Lame equation, resulting in a surprising transformation between the Lame and hypergeometric equations. Finally, we discuss the Painleve analysis of the singularities of solutions to the Chazy equation.

Item Type: Article
Subjects: Q Science > QA Mathematics (inc Computing science)
Divisions: Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science
Depositing User: M.A. Ziai
Date Deposited: 15 May 2009 08:47
Last Modified: 14 May 2014 14:02
Resource URI: http://kar.kent.ac.uk/id/eprint/18879 (The current URI for this page, for reference purposes)
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