Bilinear Structure and Exact Solutions of the Discrete Painlev\'e I Equation

Doshisha Univ.); Hiroshima Univ.); J.Satsuma(Dept. Math. Sci.; K.Kajiwara(Dept. Elecrical Eng.; Univ. Tokyo); Y.Ohta(Dept. Appl. Math.

arxiv: solv-int/9411006 · v1 · submitted 1994-11-30 · solv-int · hep-th· nlin.SI

Bilinear Structure and Exact Solutions of the Discrete Painlev\'e I Equation

Y.Ohta(Dept. Appl. Math. , Hiroshima Univ.) , K.Kajiwara(Dept. Elecrical Eng. , Doshisha Univ.) , J.Satsuma(Dept. Math. Sci. , Univ. Tokyo) This is my paper

classification solv-int hep-thnlin.SI

keywords discreteequationpainlevbilinearstructureairycasoraticorresponding

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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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Bilinear Structure and Exact Solutions of the Discrete Painlev\'e I Equation

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