131 citations · 826 across the 43 of their papers we have counts for
19 papers · 1 filter
Singularity confinement and algebraic entropy: the case of the discrete Painlevé equations
Y. Ohta, K. M. Tamizhmani, B. Grammaticos +1
We examine the validity of the results obtained with the singularity confinement integrability criterion in the case of discrete Painlevé equations. The method used is based on the…
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…
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…