Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 3 (2007), 007, 16 pages      math-ph/0610048      https://doi.org/10.3842/SIGMA.2007.007
Contribution to the Vadim Kuznetsov Memorial Issue

Multi-Hamiltonian Structures on Beauville's Integrable System and Its Variant

Rei Inoue a and Yukiko Konishi b
a) Department of Physics, Graduate School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo 113-0033, Japan
b) Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro, Tokyo 153-8914, Japan

Received October 24, 2006, in final form December 29, 2006; Published online January 08, 2007

Abstract
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.

Key words: completely integrable system; Mumford system; multi-Hamiltonian structure.

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References

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