Elliptic analog of the Toda lattice

Details Elliptic analog of the Toda lattice Elliptic analog of the Toda lattice

1999-09-30

arxiv.org/abs/hep-th/9909224v2

Physics

High Energy Physics

High Energy Physics - Theory

25 pages, LaTeX

Scientific paper

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 $\theta$-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 $w^2-P_{N}^{el}(z)w+\Lambda^{2N}=0$, where $P_{N}^{el}(z)$ is an elliptic function with pole of order N at the point z=0.

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