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

Abstract

The solutions of the discrete Painlevé 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 Painlevé equation I as a special case.

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References in corpus (1)

• Hyperelliptic Solutions of KdV and KP equations: Reevaluation of Baker's Study on Hyperelliptic Sigma Functions

Cited by in corpus (1)

• Toda Equations and $\sigma$-Functions of Genera One and Two