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

• Autores: W.K. Schief
• Localización: Anziam journal: The Australian & New Zealand industrial and applied mahtematics journal, ISSN 1446-1811, Vol. 44, Nº 1, 2002, págs. 141-148
• Idioma: inglés
• DOI: 10.1017/s1446181100007999
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• Resumen

  • 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.