Bilinear Structure and Exact Solutions of the Discrete Painlevé I Equation

Details Bilinear Structure and Exact Solutions of the Discrete Painlevé I Equation Bilinear Structure and Exact Solutions of the Discrete Painlevé I Equation

1994-11-30

arxiv.org/abs/solv-int/9411006v1

Physics

High Energy Physics

High Energy Physics - Theory

6 pages in LaTeX, to appear in Proceedings of the Workshop on Symmetries and Integrability of Difference Equations, CRM Procee

Scientific paper

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.

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