Bilinear Discrete Painleve-II and its Particular Solutions
solv-int
2009-10-28 v1 Exactly Solvable and Integrable Systems
Abstract
By analogy to the continuous Painlev\'e II equation, we present particular solutions of the discrete Painlev\'e II (d-P) 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 function for d-P. Two different forms of bilinear d-P are obtained and we show that they can be related by a simple gauge transformation.
Keywords
Cite
@article{arxiv.solv-int/9412007,
title = {Bilinear Discrete Painleve-II and its Particular Solutions},
author = {J. Satsuma and K. Kajiwara and B. Grammaticos and J. Hietarinta and A. Ramani},
journal= {arXiv preprint arXiv:solv-int/9412007},
year = {2009}
}
Comments
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