Geodesic flows, bi-Hamiltonian structure and coupled KdV type systems

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We show that all the Antonowicz-Fordy type coupled KdV equations have the same symmetry group and similar bi-Hamiltonian structures. It turns out that their configuration space is Diff(S1) ⋉ C (S1), where Diff(S1), is the Bott-Virasoro group of orientation preserving diffeomorphisms of the circle, and all these systems can be interpreted as equations of a geodesic flow with respect to L2 metric on the semidirect product space Diff(S1) ⋉ C (S1).

Original languageBritish English
Pages (from-to)45-56
Number of pages12
JournalJournal of Mathematical Analysis and Applications
Issue number1
StatePublished - 1 Oct 2005


  • Bott-Virasoro group
  • Coupled KdV equations
  • Diffeomorphism
  • Geodesic flows
  • Semi-direct product


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