Toda Equations and σ-Functions of Genera One and Two
classification
🧮 math-ph
math.AGmath.MP
keywords
functionsleveltodaequationsgenerasigmaultradiscreteappears
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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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