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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
Abstract
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.
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- Copyright © Australian Mathematical Society 2002
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