Four-dimensional Painlev\'e systems of types $D_5^{(1)}$ and $B_4^{(1)}$

Abstract

We find and study a five-parameter family of four-dimensional coupled Painlev\'e V systems with affine Weyl group symmetry of type $D_5^{(1)}$. We then give an explicit description of a confluence from those systems to a four-parameter family of four-dimensional coupled Painlev\'e III systems with affine Weyl group symmetry of type $B_4^{(1)}$.