On geodesic exponential maps of the Virasoro group

By Adrian Constantin, Thomas Kappeler, Boris Kolev, P. Topalov. 2007

174 citations recorded by the source corpus.

Subfields: Geometry and Topology, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/a0b6ba1d116d2fba9df50f0c7a68d8ff47e3c898

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Citations in the corpus

Stability of peakons for the Degasperis‐Procesi equation (2007, methodology): “Furthermore, the Camassa-Holm equation is a re-expression of geodesic flow on the diffeomorphism group [5, 10] and on the Bott-Virasoro group [9, 28], while no such geometric derivation of the Degasperis-Procesi equation is available.”
Some Geometric Evolution Equations Arising as Geodesic Equations on Groups of Diffeomorphisms Including the Hamiltonian Approach (2006, background): “The mistake was corrected in [12], for the more general case of the Virasoro group.”
Vanishing geodesic distance for the Riemannian metric with geodesic equation the KdV-equation (2011, background): “This might be related to the fact that the Riemannian exponential mapping is not a diffeomorphism near 0, see [2] for Diff(S(1)) and [3] for the Virasoro group over S(1).”
Well-posedness, wave breaking and peakons for a modified μ-Camassa-Holm equation (2014, unknown): “the discussion in the paper [12].”
On the Regularity of the Composition of Diffeomorphisms (2011, methodology): “In particular, Riemann exponential maps have been studied in [10], [11], [20], [21].”
Inverse scattering transform for the Camassa–Holm equation (2006, background): “CH arises also as an equation of the geodesic flow for the H1 right-invariant metrics on the Bott-Virasoro group (if ω > 0) and on the diffeomorphism group (if ω = 0) [34, 13, 8, 12].”
On the global existence and wave-breaking criteria for the two-component Camassa-Holm system (2010, background): “This is related to the geodesic equation which is on the diffeomorphism group of the circle [14] or on the Bott–Virasoro group [13,28,29].”
Geodesic distance for right invariant Sobolev metrics of fractional order on the diffeomorphism group (2011, methodology): “This interpretation was extended to other PDEs used in hydrodynamics, some of which are: Burgers’ equation as the geodesic equation for Diffc(R) with the L2-metric, Camassa-Holm equation for Diffc(R) with the H1-metric or KdV for the Virasoro-Bott group with the L2-metric in [21].”