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Toda Equations and σ-Functions of Genera One and Two

Shigeki Matsutani
2003 Journal of Nonlinear Mathematical Physics  
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.
doi:10.2991/jnmp.2003.10.4.8 fatcat:qujdll6jizfirll6cvmejuef3i