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solv-int1999
The hunting for the discrete Painlevé VI is over
B. Grammaticos, A. Ramani
We present the discrete, q-, form of the Painlevé VI equation written as a three-point mapping and analyse the structure of its singularities. This discrete equation goes over to P…
solv-int1998
On Discrete Painleve Equations Associated with the Lattice KdV Systems and the Painleve VI Equation
F. W. Nijhoff, A. Ramani, B. Grammaticos +1
A new integrable nonautonomous nonlinear ordinary difference equation is presented which can be considered to be a discrete analogue of the Painleve V equation. Its derivation is b…
solv-int1998
Schlesinger Transformations for Linearisable Equations
A. Ramani, B. Grammaticos, S. Lafortune
We introduce the Schlesinger transformations of the Gambier equation. The latter can be written, in both the continuous and discrete cases, as a system of two coupled Riccati equat…