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

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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

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