1999/06/01 by Luen-Chau Li · 1 citation
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebra over a field #Algebraic structures and combinatorial models #Formalism (music) #Hamiltonian (control theory) #Hierarchy #Integrable system #Lattice (music) #Lax pair #Lie algebra #Mathematical analysis #Mathematical physics #Mathematics #Nonlinear Waves and Solitons #Physics #Poisson algebra #Poisson bracket #Poisson distribution #Poisson manifold #Pure mathematics #Statistics #Toda lattice #math-ph #math.MP #math.SG
paper · pdf · doi:10.1007/s002200050626
published as Comm. Math. Phys. 203 (1999), no. 3, 573-592 · 28 pages
openalex publication_date 1999/06/01 · arxiv created 2005/06/10 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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 hierachy, the dispersionless Toda lattice hierachy, the dispersionless KP and modified KP hierachies, the dispersionless Dym hierachy etc.