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


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.


Poisson Structure Hamiltonian Formulation Toda Lattice Poisson Algebra Natural Family 
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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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