Nonlinear Poisson structures and r-matrices

Luen-chau Li, Serge Parmentier

Research output: Contribution to journalArticlepeer-review

63 Scopus citations


We introduce quadratic Poisson structures on Lie groups associated with a class of solutions of the modified Yang-Baxter equation and apply them to the Hamiltonian description of Lax systems. The formal analog of these brackets on associative algebras provides second structures for certain integrable equations. In particular, the integrals of the Toda flow on generic orbits are shown to satisfy recursion relations. Finally, we exhibit a third order Poisson bracket for which the r-matrix approach is feasible.

Original languageEnglish (US)
Pages (from-to)545-563
Number of pages19
JournalCommunications in Mathematical Physics
Issue number4
StatePublished - Dec 1 1989

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics


Dive into the research topics of 'Nonlinear Poisson structures and r-matrices'. Together they form a unique fingerprint.

Cite this