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We find and study four kinds of a 4-parameter family of four-dimensionalcoupled Painlev\'e III systems with affine Weyl group symmetry of types$B_4^{(1)}$, $D_4^{(1)}$ and $D_5^{(2)}$. We also show that these systems areequivalent by an explicit birational and symplectic transformation,respectively.

Coupled Painlev\'e III systems with affine Weyl group symmetry of types $B_4^{(1)}$, $D_4^{(1)}$ and $D_5^{(2)}$