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arXiv · 0809.2399

Coupled Painlevé systems in dimension four with affine Weyl group symmetry of types $A_4^{(2)}$ and $A_1^{(1)}$

Yusuke Sasano
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Abstract

We find a two-parameter family of coupled Painlevé systems in dimension four with affine Weyl group symmetry of type $A_4^{(2)}$. For a degenerate system of $A_4^{(2)}$ system, we also find a one-parameter family of coupled Painlevé systems in dimension four with affine Weyl group symmetry of type $A_1^{(1)}$. We show that for each system, we give its symmetry and holomorphy conditions. These symmetries, holomorphy conditions and invariant divisors are new. Moreover, we find a one-parameter family of partial differential systems in three variables with $W(A_1^{(1)})$-symmetry. We show the relation between its polynomial Hamiltonian system and an autonomous version of the system of type $A_1^{(1)}$.

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BibTeXRIS

Yusuke Sasano. 2010-12-07. Coupled Painlevé systems in dimension four with affine Weyl group symmetry of types $A_4^{(2)}$ and $A_1^{(1)}$. https://arxiv.org/abs/0809.2399

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