The Painlevé property is closely connected to differential equations that are integrable via
related iso-monodromy problems. Many apparently integrable discrete analogues of the …

We present a review of what is current knowledge about discrete Painlevé equations. We
start with a historical introduction which explains how the discrete Painlevé equations made …

We review the different aspects of integrable discretizations in space and time of the
Korteweg-de Vries equation, including Miura transformations to related integrable difference …

A q-difference analog of the sixth Painlevé equation is presented. It arises as the condition
for preserving the connection matrix of linear q-difference equations, in close analogy with …

It is well known that the integrability (solvability) of a differential equation is related to the
singularity structure of its solutions in the complex domain-an observation that lies behind …

Let w (z) be an admissible finite-order meromorphic solution of the second-order difference
equation where R (z, w (z)) is rational in w (z) with coefficients that are meromorphic in z …

Surfaces with constant curvature (especially, with constant negative curvature K=—1, which
we will call shortly K-surfaces) were one of the favorite objects of investigation in differential …

A new integrable nonautonomous nonlinear ordinary difference equation is presented that
can be considered to be a discrete analogue of the Painlevé V equation. Its derivation is …

The Cargese summer school celebrated the lOOth anniversary of the Painleve property, the
property that was introduced by Painleve and subsequently by Gambier and their school to …

Some integrable discrete analogues of the Schwarz ian KdV (Krichever-Novikov) equation
and of other Mobius-invariant equations, are discussed together with their Miura chains …