Symmetry in the Painlevé systems and their extensions to four-dimensional systems

Details Symmetry in the Painlevé systems and their extensions to four-dimensional systems Symmetry in the Painlevé systems and their extensions to four-dimensional systems

2007-04-18

arxiv.org/abs/0704.2393v1

Funkcialaj Ekvacioj, 51 (2008) 351-369

Mathematics

Algebraic Geometry

32 pages, 16 figures

Scientific paper

We give a new approach to the symmetries of the Painlev\'e equations
$P_{V},P_{IV},P_{III}$ and $P_{II}$, respectively. Moreover, we make natural
extensions to fourth-order analogues for each of the Painlev\'e equations
$P_{V}$ and $P_{III}$, respectively, which are natural in the sense that they
preserve the symmetries.

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