SELF-DUALITY AND SCHLESINGER CHAINS FOR THE ASYMMETRIC D-P-II AND QP(III) EQUATIONS

We analyse two asymmetric discrete Painleve equations, namely d-P-II a nd q-P-III which an known to be discrete forms of P-III and P-VI respe ctively. We show that both equations are self-dual. This means that th e same equation governs the evolution along the discrete independent v ariable and the transformations under the action of the Schlesinger tr ansforms along the parameters of the discrete Painleve. A bilinear for mulation of the self-dual equation is given as a system of nonautonomo us Hirota-Miwa equations.