64 citations · 239 across the 16 of their papers we have counts for
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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…
The Gambier Mapping
B. Grammaticos, A. Ramani
We propose a discrete form for an equation due to Gambier and which belongs to the class of the fifty second order equations that possess the Painleve property. In the continuous c…
Casorati Determinant Solutions for the Discrete Painlevé III Equation
Kenji Kajiwara, Yasuhiro Ohta, Junkichi Satsuma
The discrete Painlevé III equation is investigated based on the bilinear formalism. It is shown that it admits the solutions expressed by the Casorati determinant whose entries are…
Integrable Trilinear PDE's
J. Hietarinta, B. Grammaticos, A. Ramani
In a recent publication we proposed an extension of Hirota's bilinear formalism to arbitrary multilinearities. The trilinear (and higher) operators were constructed from the requir…
Continuous vacua in bilinear soliton equations
J. Hietarinta, A. Ramani, B. Grammaticos
We discuss the freedom in the background field (vacuum) on top of which the solitons are built. If the Hirota bilinear form of a soliton equation is given by $A(D_{\vec x})\bd GF=0…
Linearization And Solutions Of The Discrete Painlevé-III Equation
B. Grammaticos, F. W. Nijhoff, V. Papageorgiou +1
We present particular solutions of the discrete Painlevé III (d-P) equation of rational and special function (Bessel) type. These solutions allow us to establish a close…
Casorati Determinant Solutions for the Discrete Painlevé-II Equation
Kenji Kajiwara, Yasuhiro Ohta, Junkichi Satsuma +2
We present a class of solutions to the discrete Painlevé-II equation for particular values of its parameters. It is shown that these solutions can be expressed in terms of Casorati…