Bilinear Structure and Exact Solutions of the Discrete Painlevé I Equation
Y. Ohta, K. Kajiwara, J. Satsuma
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.
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