A cubic Hamiltonian system with meromorphic solutions (Q291941)

Consider the system of equations \[ \dot{q}=p^2+zq+\alpha,\quad \dot{p}=-q^2-zp-\beta,\quad\alpha,\beta\in\mathbb{C}. \] It is a Hamiltonian system with the Hamiltonian \[ H=\frac{1}{3}(q^3+p^3)+zpq+\alpha p+\beta q. \] In the paper it is proved that this system has the Painlevé property. Actually this result follows from a general result of the paper [the author, ``Polynomial Hamiltonian sytems with movable algebraic singularities'', Preprint, \url{arXiv:1312.4030}].