Discretising systematically the Painlevé equations
Integrable discrete analogues of the Painlevé equations have been constructed by Grammaticos, Ramani, et.\ al.\ some time ago. In the present paper it is shown that this can be done using the systematic discretisation procedure introduced by the authors in [J. Phys. A, Math. Theor. 43, No. 31, Article ID 315203, 15 p. (2010; Zbl 1222.39009)]. This is achieved by applying the discretisation method directly to the Hamiltonian equations of motion which define each Painlevé equation. These are in general of Riccati type (after a simple change of variables).
scientific article; zbMATH DE number 5862551