Classical r-matrices and compatible poisson structures for Lax equations on Poisson algebras

Luen Chau Li

doi:10.1007/s002200050626

Classical r-matrices and compatible poisson structures for Lax equations on Poisson algebras

Luen Chau Li

Mathematics

Research output: Contribution to journal › Article › peer-review

52 Scopus citations

Abstract

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 hierarchy, the dispersionless Toda lattice hierarchy, the dispersionless KP and modified KP hierarchies, the dispersionless Dym hierarchy, etc.

Original language	English (US)
Pages (from-to)	573-592
Number of pages	20
Journal	Communications In Mathematical Physics
Volume	203
Issue number	3
DOIs	https://doi.org/10.1007/s002200050626
State	Published - 1999

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics

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10.1007/s002200050626

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abstract = "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 hierarchy, the dispersionless Toda lattice hierarchy, the dispersionless KP and modified KP hierarchies, the dispersionless Dym hierarchy, etc.",

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AB - 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 hierarchy, the dispersionless Toda lattice hierarchy, the dispersionless KP and modified KP hierarchies, the dispersionless Dym hierarchy, etc.

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Classical r-matrices and compatible poisson structures for Lax equations on Poisson algebras

Abstract

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