On some Hamiltonian structures of coupled Painlevé II systems in dimension four

Abstract

We find and study a two-parameter family of coupled Painlevé II systems in dimension four with affine Weyl group symmetry of several types. Moreover, we find a three-parameter family of polynomial Hamiltonian systems in two variables $t,s$. Setting $s=0$, we can obtain an autonomous version of the coupled Painlevé II systems. We also show its symmetry and holomorphy conditions.

9 pages

References in corpus (2)

• An augmentation of the phase space of the system of type A^{(1)}_4
• Symmetries in the system of type $D_4^{(1)}$