Classical $\bold{r}$-Matrices and Compatible Poisson Structures for Lax Equations on Poisson Algebras

Details Classical $\bold{r}$-Matrices and Compatible Poisson Structures for Lax Equations on Poisson Algebras Classical $\bold{r}$-Matrices and Compatible Poisson Structures for Lax Equations on Poisson Algebras

2005-06-10

arxiv.org/abs/math-ph/0506029v1

Comm. Math. Phys. 203 (1999), no. 3, 573-592

Physics

Mathematical Physics

28 pages

Scientific paper

10.1007/s002200050626

Given a classical $r$-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.

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