2005/12/09 by Adrian Constantin, A. Constantin, Boris Kolev +1 · 69 citations
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Diffeomorphism #Group (periodic table) #Hamiltonian (control theory) #Homotopy and Cohomology in Algebraic Topology #Invariant (physics) #Lie algebra #Lie group #Nonlinear Waves and Solitons #Semidirect product #Sobolev space #Vector field #math-ph #math.MP #msc:35Q35 #msc:35Q53 #msc:37K10 #msc:37K65
paper · pdf · doi:10.1007/s00332-005-0707-4
published in Journal of Nonlinear Science 16(2), 109-122 (Springer Science+Business Media)
openalex publication_date 2005/12/09 · arxiv created 2009/11/26 · arxiv updated 2009/12/08 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
Each Hk Sobolev inner product defines a Hamiltonian vector field Xk on the regular dual of the Lie algebra of the diffeomorphism group of the circle. We show that only X0 and X1 are bi-Hamiltonian relatively to a modified Lie-Poisson structure.