Coupled Painlevé III systems with affine Weyl group symmetry of types $B_4^{(1)}$, $D_4^{(1)}$ and $D_5^{(2)}$

Details Coupled Painlevé III systems with affine Weyl group symmetry of types $B_4^{(1)}$, $D_4^{(1)}$ and $D_5^{(2)}$ Coupled Painlevé III systems with affine Weyl group symmetry of types $B_4^{(1)}$, $D_4^{(1)}$ and $D_5^{(2)}$

2007-04-19

arxiv.org/abs/0704.2476v2

Mathematics

Algebraic Geometry

13 pages, 5 figures

Scientific paper

We find and study four kinds of a 4-parameter family of four-dimensional
coupled Painlev\'e III systems with affine Weyl group symmetry of types
$B_4^{(1)}$, $D_4^{(1)}$ and $D_5^{(2)}$. We also show that these systems are
equivalent by an explicit birational and symplectic transformation,
respectively.

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