Clarkson, Peter and Olver, Peter J.
(1996)
*Symmetry and the Chazy equation.*
Journal of Differential Equations, 124
(1).
pp. 225-246.
ISSN 0022-0396.
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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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