Bilinear Discrete Painleve-II and its Particular Solutions

Details Bilinear Discrete Painleve-II and its Particular Solutions Bilinear Discrete Painleve-II and its Particular Solutions

1994-12-23

arxiv.org/abs/solv-int/9412007v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

9 pages in plain TeX

Scientific paper

10.1088/0305-4470/28/12/025

By analogy to the continuous Painlev\'e II equation, we present particular solutions of the discrete Painlev\'e II (d-P$\rm_{II}$) equation. These solutions are of rational and special function (Airy) type. Our analysis is based on the bilinear formalism that allows us to obtain the $\tau$ function for d-P$\rm_{II}$. Two different forms of bilinear d-P$\rm_{II}$ are obtained and we show that they can be related by a simple gauge transformation.

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