Symmetries in the system of type $D_4^{(1)}$

Abstract

In this paper, we propose a 4-parameter family of coupled Painlevé III systems in dimension four with affine Weyl group symmetry of type $D_4^{(1)}$. We also propose its symmetric form in which the $D_4^{(1)}$-symmetries become clearly visible.

4 pages, 1 figure

References in corpus (2)

• An augmentation of the phase space of the system of type A^{(1)}_4
• Coupled Painlevé VI systems in dimension four with affine Weyl group symmetry of type $D_6^{(1)}$, II

Cited by in corpus (10)

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• Coupled Painlevé systems in dimension four with affine Weyl group symmetry of types $A_4^{(2)}$ and $A_1^{(1)}$
• Coupled Painlevé III systems with affine Weyl group symmetry of types $B_5^{(1)},D_5^{(1)}$ and $D_6^{(2)}$
• Ordinary differential systems in dimension three with affine Weyl group symmetry of types $D_4^{(1)},B_3^{(1)},G_2^{(1)},D_3^{(2)}$ and $A_2^{(2)}$
• Ordinary differential system in dinension six with affine Weyl group symmetry of type $D_4^{(2)}$
• On some Hamiltonian structures of coupled Painlevé II systems in dimension four
• Coupled Painlevé III system with affine Weyl group symmetry of type $D_6^{(1)}$
• Coupled Painlevé systems with affine Weyl group symmetry of types $A_7^{(2)},A_5^{(2)}$ and $D_4^{(3)}$