143 citations · 921 across the 50 of their papers we have counts for
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Discrete and Continuous Linearizable Equations
S. Lafortune, B. Grammaticos, A. Ramani
We study the projective systems in both continuous and discrete settings. These systems are linearizable by construction and thus, obviously, integrable. We show that in the contin…
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…
A Bilinear Approach to Discrete Miura Transformations
N. Joshi, A. Ramani, B. Grammaticos
We present a systematic approach to the construction of Miura transformations for discrete Painlevé equations. Our method is based on the bilinear formalism and we start with the e…
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…
The Gambier Mapping, Revisited
B. Grammaticos, A. Ramani, S. Lafortune
We examine critically the Gambier equation and show that it is the generic linearisable equation containing, as reductions, all the second-order equations which are integrable thro…