Nonlinear Poisson structures and r-matrices

Luen-chau Li, Serge Parmentier

Research output: Contribution to journalArticle

59 Citations (Scopus)

Abstract

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
Volume125
Issue number4
DOIs
StatePublished - Dec 1 1989

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Recursion Relations
Yang-Baxter Equation
Integrable Equation
Poisson Structure
Poisson Bracket
Associative Algebra
R-matrix
Modified Equations
Brackets
brackets
Orbit
Analogue
matrices
algebra
analogs
orbits
Class

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

Li, Luen-chau ; Parmentier, Serge. / Nonlinear Poisson structures and r-matrices. In: Communications in Mathematical Physics. 1989 ; Vol. 125, No. 4. pp. 545-563.
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Nonlinear Poisson structures and r-matrices. / Li, Luen-chau; Parmentier, Serge.

In: Communications in Mathematical Physics, Vol. 125, No. 4, 01.12.1989, p. 545-563.

Research output: Contribution to journalArticle

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