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On the geometry of the Painlevé V equation and a Bäcklund transformation

Published online by Cambridge University Press:  17 February 2009

W. K. Schief
W. K. Schief
Affiliation:
School of Mathematics, The University of New South Wales, Sydney, NSW 2052, Australia.
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Abstract

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It is shown that an integrable class of helicoidal surfaces in Euclidean space E3 is governed by the Painlevé V equation with four arbitrary parameters. A connection with sphere congruences is exploited to construct in a purely geometric manner an associated Bäcklund transformation.

Type
Research Article
Information
The ANZIAM Journal , Volume 44 , Issue 1 , July 2002 , pp. 141 - 148
Copyright
Copyright © Australian Mathematical Society 2002

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