Tropical Jacobian and the generic fiber of the ultra-discrete periodic Toda lattice are isomorphic

Abstract

We prove that the general isolevel set of the ultra-discrete periodic Toda lattice is isomorphic to the tropical Jacobian associated with the tropical spectral curve. This result implies that the theta function solution obtained in the authors' previous paper is the complete solution. We also propose a method to solve the initial value problem.Comment: 14 page