Elliptic and Hyperelliptic Solutions of Discrete Painlevé I and Its Extensions to Higher Order Difference Equations

Details Elliptic and Hyperelliptic Solutions of Discrete Painlevé I and Its Extensions to Higher Order Difference Equations Elliptic and Hyperelliptic Solutions of Discrete Painlevé I and Its Extensions to Higher Order Difference Equations

2001-05-23

arxiv.org/abs/math-ph/0105030v2

Physics

Mathematical Physics

AMS-TeX, 11 pages

Scientific paper

10.1016/S0375-9601(02)00784-3

The solutions of the discrete Painlev\'e equation I were constructed in terms
of elliptic and hyperelliptic $\psi$ functions for algebraic curves of genera
one and two. For the case of genus two, there appear higher order difference
equations which naturally contain the discrete Painlev\'e equation I as a
special case.

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