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

TL;DR

This paper introduces a tropical analogue of Fay's trisecant identity and applies it to construct general solutions for the generalized ultradiscrete periodic Toda lattice T(M,N) with tropical spectral curves.

Contribution

It presents a novel tropical Fay's trisecant identity and uses it to solve the ultradiscrete Toda lattice T(M,N).

Findings

Constructed a general solution to T(M,N) using tropical Fay's identity.

Established a connection between tropical spectral curves and ultradiscrete integrable systems.

Extended the theory of Fay's identity to tropical geometry context.

Abstract

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).