Elliptic solutions to difference non-linear equations and related many-body problems

@inproceedings{IKrichever1997EllipticST,
  title={Elliptic solutions to difference non-linear equations and related many-body problems},
  author={I.Krichever and P.Wiegmann and A.Zabrodin},
  year={1997}
}
We study algebro-geometric (finite-gap) and elliptic solutions of fully discretized KP or 2D Toda equations. In bilinear form they are Hirota’s difference equation for τ -functions. Starting from a given algebraic curve, we express the τ -function and the Baker-Akhiezer function in terms of the Riemann theta function. We show that the elliptic solutions, when the τ -function is an elliptic polynomial, form a subclass of the general algebro-geometric solutions. We construct the algebraic curves of… 

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