On discrete Painleve equations associated with the lattice KdV systems andthe Painleve VI equation

A new integrable nonautonomous nonlinear ordinary difference equation is pr esented that can be considered to be a discrete analogue of the Painleve V equation. Its derivation is based on the similarity reduction on the two-di mensional lattice of integrable partial differential equations of Korteweg- de Vries (KdV) type, The new equation, which is referred to as generalized discrete Painleve equation (GDP), contains various "discrete Painleve equat ions" as subcases for special values/limits of the parameters, some of whic h have already been given in the literature. The general solution of the GD P can be expressed in terms of Painleve VI (PVI) transcendents. In fact, co ntinuous PVI emerges as the equation obeyed by the solutions of the discret e equation in terms of the lattice parameters rather than the lattice varia bles that label the lattice sites. We show that the bilinear form of PVI is embedded naturally in the lattice systems leading to the GDP, Further resu lts include the establishment of Backlund and Schlesinger transformations f or the GDP, the corresponding isomonodromic deformation problem, and the se lf-duality of its bilinear scheme.