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Communications in Mathematical Physics

, Volume 203, Issue 3, pp 573–592 | Cite as

Classical r-Matrices and Compatible Poisson Structures for Lax Equations on Poisson Algebras

  • Luen-Chau Li

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.

Keywords

Poisson Structure Hamiltonian Formulation Toda Lattice Poisson Algebra Natural Family 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Luen-Chau Li
    • 1
  1. 1.Department of Mathematics, Pennsylvania State University, University Park, PA 16802, USA.¶E-mail: luenli@math.psu.eduUS

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