Bilinear Structure and Exact Solutions of the Discrete Painlev\'e I Equation

Y. Ohta; K. Kajiwara; J. Satsuma

Bilinear Structure and Exact Solutions of the Discrete Painlev\'e I Equation

solv-int 2008-02-03 v1 High Energy Physics - Theory Exactly Solvable and Integrable Systems

Authors: Y. Ohta , K. Kajiwara , J. Satsuma

Abstract

Bilinear structure for the discrete Painlev\'e I equation is investigated. The solution on semi-infinite lattice is given in terms of the Casorati determinant of discrete Airy function. Based on this fact, the discrete Painlev\'e I equation is naturally extended to a discrete coupled system. Corresponding matrix model is also mentioned.

Keywords

discrete painleve i equation bilinear structure casorati determinant discrete airy function discrete coupled system matrix model

Cite

@article{arxiv.solv-int/9411006,
  title  = {Bilinear Structure and Exact Solutions of the Discrete Painlev\'e I Equation},
  author = {Y. Ohta and K. Kajiwara and J. Satsuma},
  journal= {arXiv preprint arXiv:solv-int/9411006},
  year   = {2008}
}

Comments

6 pages in LaTeX, to appear in Proceedings of the Workshop on Symmetries and Integrability of Difference Equations, CRM Proceedings and Lecture Notes Series, AMS, 1994

Bilinear Structure and Exact Solutions of the Discrete Painlev\'e I Equation

Abstract

Keywords

Cite

Comments

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