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arXiv · 1504.03448

Toric networks, geometric $R$-matrices and generalized discrete Toda lattices

Rei Inoue·Thomas Lam·Pavlo Pylyavskyy
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Abstract

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 motion and a spectral map for this system. The family of commuting time evolutions arising from the action of the $R$-matrix is explicitly linearized on the Jacobian of the spectral curve. The solution to the initial value problem is constructed using Riemann theta functions.

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Rei Inoue, Thomas Lam, Pavlo Pylyavskyy. 2015-04-14. Toric networks, geometric $R$-matrices and generalized discrete Toda lattices. https://doi.org/10.1007/s00220-016-2739-z

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