Bilinear Structure and Exact Solutions of the Discrete Painlevé I Equation

1994/11/30 by Yuichi Ohta, Ohta, Y., Kenji Kajiwara +3
Mathematics · Physics and Astronomy · #Differential Equations and Numerical Methods #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Fractional Differential Equations Solutions #High Energy Physics - Theory (hep-th) #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.solv-int/9411006

openalex publication_date 1994/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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