Bilinear Structure and Exact Solutions of the Discrete Painlevé I Equation

Abstract

Bilinear structure for the discrete Painlevé 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 Painlevé I equation is naturally extended to a discrete coupled system. Corresponding matrix model is also mentioned.

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