# Tropical spectral curves, Fay's trisecant identity, and generalized ultradiscrete Toda lattice

@article{Inoue2010TropicalSC, title={Tropical spectral curves, Fay's trisecant identity, and generalized ultradiscrete Toda lattice}, author={Rei Inoue and Shinsuke Iwao}, journal={arXiv: Algebraic Geometry}, year={2010} }

We study the generalized ultradiscrete periodic Toda lattice T(M,N) which has tropical spectral curve. We introduce a tropical analogue of Fay's trisecant identity, and apply it to construct a general solution to T(M,N).

## 2 Citations

Toric Networks, Geometric R-Matrices and Generalized Discrete Toda Lattices

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We use the combinatorics of toric networks and the double affine geometric R-matrix to define a three-parameter family of generalizations of the discrete Toda lattice. We construct the integrals of…

Bilinear equations and Bäcklund transformation for a generalized ultradiscrete soliton solution

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Ultradiscrete soliton equations and Backlund transformation for a generalized soliton solution are presented. The equations include the ultradiscrete Korteweg–de Vries (KdV) equation or the…

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