480 research outputs found
Multi-Hamiltonian Structures on Beauville's Integrable System and Its Variant
We study Beauville's completely integrable system and its variant from a
viewpoint of multi-Hamiltonian structures. We also relate our result to the
previously known Poisson structures on the Mumford system and the even Mumford
system.Comment: This is a contribution to the Vadim Kuznetsov Memorial Issue on
Integrable Systems and Related Topics, published in SIGMA (Symmetry,
Integrability and Geometry: Methods and Applications) at
http://www.emis.de/journals/SIGMA
Tropical Jacobian and the generic fiber of the ultra-discrete periodic Toda lattice are isomorphic
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
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