Coupled Painlevé III systems with affine Weyl group symmetry of types $B_5^{(1)},D_5^{(1)}$ and $D_6^{(2)}$

Details Coupled Painlevé III systems with affine Weyl group symmetry of types $B_5^{(1)},D_5^{(1)}$ and $D_6^{(2)}$ Coupled Painlevé III systems with affine Weyl group symmetry of types $B_5^{(1)},D_5^{(1)}$ and $D_6^{(2)}$

2007-04-19

arxiv.org/abs/0704.2467v1

Mathematics

Algebraic Geometry

13 pages, 5 figures

Scientific paper

We find and study four kinds of five-parameter family of six-dimensional
coupled Painlev\'e III systems with affine Weyl group symmetry of types
$D_5^{(1)},B_5^{(1)}$ and $D_6^{(2)}$. We show that each system is equivalent
by an explicit birational and symplectic transformation, respectively. We also
show that we characterize each system from the viewpoint of holomorphy.

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