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Bilinear Structure and Exact Solutions of the Discrete Painlevé I Equation

Y. Ohta·K. Kajiwara·J. Satsuma
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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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Y. Ohta, K. Kajiwara, J. Satsuma. 1994-11-30. Bilinear Structure and Exact Solutions of the Discrete Painlevé I Equation. https://arxiv.org/abs/solv-int/9411006

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