Elliptic analog of the Toda lattice
Abstract
The actionangle variables for Nparticle Hamiltonian system with the Hamiltonian $H=\sum_{n=0}^{N1} \ln sh^{2}(p_n/2)+\ln(\wp(x_nx_{n+1}) \wp(x_n+x_{n+1})), x_N=x_0,$ 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 $w^2P_{N}^{el}(z)w+\Lambda^{2N}=0$, where $P_{N}^{el}(z)$ is an elliptic function with pole of order N at the point z=0.
 Publication:

arXiv eprints
 Pub Date:
 September 1999
 DOI:
 10.48550/arXiv.hepth/9909224
 arXiv:
 arXiv:hepth/9909224
 Bibcode:
 1999hep.th....9224K
 Keywords:

 High Energy Physics  Theory
 EPrint:
 25 pages, LaTeX