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

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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.

Original languageEnglish (US)
Pages (from-to)573-592
Number of pages20
JournalCommunications In Mathematical Physics
Volume203
Issue number3
DOIs
StatePublished - Jan 1 1999

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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