A Bilinear Approach to the Discrete Painlevé I Equations

B. Grammaticos; T. Tamizhmani; A. Ramani; A. S. Carstea; K. M. Tamizhmani

doi:10.1143/jpsj.71.443

Journal of the Physical Society of Japan

Online ISSN : 1347-4073
Print ISSN : 0031-9015
ISSN-L : 0031-9015

A Bilinear Approach to the Discrete Painlevé I Equations

B. Grammaticos, T. Tamizhmani, A. Ramani, A. S. Carstea, K. M. Tamizhmani

著者情報

キーワード: integrability, discrete Painlevé equations, bilinear approach, Hirota method, tau function, singularity stucture

ジャーナル認証あり

2002 年 71 巻 2 号 p. 443-447

DOI https://doi.org/10.1143/jpsj.71.443

詳細

抄録

We present the list of all known to date difference and q-discrete forms of the Painlevé I equations. A new, derived here for the first time, zero-parameter, q-discrete Painlevé equation is also given. We present interrelations between some of these equations, whenever they exist, in the form of Miura transformations. Finally we give the bilinearisation of these systems.