Coupled Painlevé systems with affine Weyl group symmetry of types $D_3^{(2)}$ and $D_5^{(2)}$

Details Coupled Painlevé systems with affine Weyl group symmetry of types $D_3^{(2)}$ and $D_5^{(2)}$ Coupled Painlevé systems with affine Weyl group symmetry of types $D_3^{(2)}$ and $D_5^{(2)}$

2007-05-31

arxiv.org/abs/0705.4540v2

Mathematics

Algebraic Geometry

8 pages

Scientific paper

In this paper, we find a two-parameter family of coupled Painlev\'e systems in dimension four with affine Weyl group symmetry of type $D_3^{(2)}$. We also find a four-parameter family of 2-coupled $D_3^{(2)}$-systems in dimension eight with affine Weyl group symmetry of type $D_5^{(2)}$. We show that for each system, we give its symmetry and holomorphy conditions, respectively. These symmetries, holomorphy conditions and invariant divisors are new.

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