English

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-PII\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 τ\tau function for d-PII\rm_{II}. Two different forms of bilinear d-PII\rm_{II} 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}
}

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9 pages in plain TeX