Toda Equations and $σ$-Functions of Genera One and Two

Details Toda Equations and $σ$-Functions of Genera One and Two Toda Equations and $σ$-Functions of Genera One and Two

2003-05-04

arxiv.org/abs/math-ph/0305008v1

Physics

Mathematical Physics

16 pages

Scientific paper

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.

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