VII-th International Conference "SOLITONS, COLLAPSES AND TURBULENCE: Achievements, Developments and Perspectives" (SCT-14) in honor of Vladimir Zakharov's 75th birthday August, 04-08, 2014 Chernogolovka, Russia

New reductions of Gauss-Codazzi equations in three-dimensional Euclidean space to the sixth Painlev\'e equation
Date/Time: 15:10 04-Aug-2014
Abstract:
The Gauss-Codazzi equations govern the geometry of surfaces in R${}^n$.
In 1897, Hazzi\-dakis found a reduction to a codimension three P6 equation in the case $n=3$.
Our motivation is to find a reduction to the full (codimension zero) P6.
Since the Gauss-Codazzi equations are underdetermined (three equations in four unknowns), we first restrict them to a determined system and compute its Lie point symmetries.
This allows us to find three more reductions to P6, with respective codimensions three, two, two.

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{\bf References:}
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%\bibitem{BE2000}
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%http://www-sfb288.math.tu-berlin.de

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%\bibitem{CMBook}
R.~Conte and M.~Musette,
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Authors
Conte Robert (Presenter)

Grundland A M

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