Self-duality and Schlesinger chains for the asymmetric \(\text{d-P}_{\text{II}}\) and \(\text{q-P}_{\text{III}}\) equations
Two discrete equations \(d-P_{\text{II}}\) and \(d-P_{\text{III}}\), known as discrete forms of Painlevé equations \(P_{\text{III}}\) and \(P_{\text{VI}}\), respectively, are studied. Both equations are self-dual, i.e. the same equation governs the evolution along the discrete independent variable and in the direction of the parameters. These equations can be represented by a system of Hirota-Miwe equations governing the evolution in any direction of the independent variable or the parameter.
asymmetric \(d-P_{\text{ II}}\) and \(q-P_{\text{III}}\) equations
scientific article; zbMATH DE number 1213896