On Some Hamiltonian Structures of Coupled Painlevé Ii Systems in Dimension Four

We find and study a two-parameter family of coupled Painlevé II systems in dimension four with affine Weyl group symmetry of several types. In this paper, we study coupled Painlevé II systems in dimension four dx dt = ∂H ∂y , dy dt = − ∂H ∂x , dz dt = ∂H ∂w , dw dt = − ∂H ∂z (1) with the following Hamiltonian Here x, y, z and w denote unknown complex… CONTINUE READING