Euler equations on homogeneous spaces and Virasoro orbits

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dc.creatorKhesin, B.
dc.creatorMisiolek, G.
dc.date2002-10-25
dc.date.accessioned2026-07-07T04:52:21Z
dc.date.available2026-07-07T04:52:21Z
dc.descriptionWe show that the following three systems related to various hydrodynamical approximations: the Korteweg--de Vries equation, the Camassa--Holm equation, and the Hunter--Saxton equation, have the same symmetry group and similar bihamiltonian structures. It turns out that their configuration space is the Virasoro group and all three dynamical systems can be regarded as equations of the geodesic flow associated to different right-invariant metrics on this group or on appropriate homogeneous spaces. In particular, we describe how Arnold's approach to the Euler equations as geodesic flows of one-sided invariant metrics extends from Lie groups to homogeneous spaces. We also show that the above three cases describe all generic bihamiltonian systems which are related to the Virasoro group and can be integrated by the translation argument principle: they correspond precisely to the three different types of generic Virasoro orbits.
dc.description26 pages, 4 figures, LaTeX. Advances in Mathematics (to appear)
dc.identifierhttps://arxiv.org/abs/math/0210397
dc.identifierhttp://arxiv.org/abs/math/0210397
dc.identifierAdvances in Mathematics, vol.176 (2003), 116-144
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/65433
dc.subjectSymplectic Geometry
dc.subjectMathematical Physics
dc.titleEuler equations on homogeneous spaces and Virasoro orbits
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