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

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

2009-02-03

arxiv.org/abs/0902.0448v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

14 pages

Scientific paper

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.

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