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arXiv · hep-th/9909224

Elliptic analog of the Toda lattice

I. M. Krichever
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Abstract

The action-angle variables for N-particle Hamiltonian system with the Hamiltonian $H=\sum_{n=0}^{N-1} \ln sh^{-2}(p_n/2)+\ln(\wp(x_n-x_{n+1})- \wp(x_n+x_{n+1})), x_N=x_0,$ are constructed, and the system is solved in terms of the Riemann $θ$-functions. It is shown that this system describes pole dynamics of the elliptic solutions of 2D Toda lattice corresponding to spectral curves defined by the equation $w^2-P_{N}^{el}(z)w+Λ^{2N}=0$, where $P_{N}^{el}(z)$ is an elliptic function with pole of order N at the point z=0.

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I. M. Krichever. 1999-11-04. Elliptic analog of the Toda lattice. https://arxiv.org/abs/hep-th/9909224

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