366 research outputs found
Classical -Matrices and Compatible Poisson Structures for Lax Equations on Poisson Algebras
Given a classical -matrix on a Poisson algebra, we show how to construct a
natural family of compatible Poisson structures for the Hamiltonian formulation
of Lax equations. Examples for which our formalism applies include the Benny
hierachy, the dispersionless Toda lattice hierachy, the dispersionless KP and
modified KP hierachies, the dispersionless Dym hierachy etc.Comment: 28 page
Spin Calogero-Moser systems associated with simple Lie algebras
We introduce spin Calogero-Moser systems associated with root systems of
simple Lie algebras and give the associated Lax representations (with spectral
parameter) and fundamental Poisson bracket relations. Our analysis is based on
a group-theoretic framework similar in spirit to the standard classical
-matrix theory for constant -matrices.Comment: 6 page
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