Casorati Determinant Solutions for the Discrete Painlevé-II Equation

Details Casorati Determinant Solutions for the Discrete Painlevé-II Equation Casorati Determinant Solutions for the Discrete Painlevé-II Equation

1993-10-20

arxiv.org/abs/solv-int/9310002v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

13 pages in plain TeX

Scientific paper

10.1088/0305-4470/27/3/030

We present a class of solutions to the discrete Painlev\'e-II equation for
particular values of its parameters. It is shown that these solutions can be
expressed in terms of Casorati determinants whose entries are discrete Airy
functions. The analogy between the $\tau$ function for the discrete P$_{\rm
\romanno2}$ and the that of the discrete Toda molecule equation is pointed out.

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