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

Abstract

We study the Toda equations in the continuous level, discrete level and ultradiscrete level in terms of elliptic and hyperelliptic $\sigma$ and $\psi$ functions of genera one and two. The ultradiscrete Toda equation appears as a discrete-valuation of recursion relations of $\psi$ functions.

16 pages

References in corpus (3)

• Hyperelliptic Solutions of KdV and KP equations: Reevaluation of Baker's Study on Hyperelliptic Sigma Functions
• Elliptic and Hyperelliptic Solutions of Discrete Painlevé I and Its Extensions to Higher Order Difference Equations
• Lotka-Volterra Equation over a Finite Ring Z/p^N Z

Cited by in corpus (1)

• Quasi-periodic and periodic solutions of the Toda lattice via the hyperelliptic sigma function