510 citations · 819 across the 11 of their papers we have counts for
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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…
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…
On Integrability and Chaos in Discrete Systems
M. J. Ablowitz, Y. Ohta, A. D. Trubatch
The scalar nonlinear Schrodinger (NLS) equation and a suitable discretization are well known integrable systems which exhibit the phenomena of ``effective'' chaos. Vector generaliz…
Cellular Automata and Ultra-Discrete Painlevé Equations
B. Grammaticos, Y. Ohta, A. Ramani +2
Starting from integrable cellular automata we present a novel form of Painlevé equations. These equations are discrete in both the independent variable and the dependent one. We sh…
From Discrete to Continuous Painlevé Equations: A Bilinear Approach
Y. Ohta, A. Ramani, B. Grammaticos +1
We present the bilinear forms of the (continuous) Painlevé equations obtained from the continuous limit of the analogous expresssions for the discrete ones. The advantage of this m…