A shallow water equation as a geodesic flow on the Bott-Virasoro group. (English) Zbl 0901.58022

Misiołek, Gerard

J. Geom. Phys. 24, No. 3, 203-208 (1998).

The author proves that the Camassa-Holm equation gives rise to a geodesic flow of a certain right invariant metric on the Bott-Virasoro group. It is explained that the sectional curvature of this metric is taking positive and negative signs.
In addition to these results the paper contains some rather interesting remarks.

Reviewer: Th.M.Rassias (Athens)

MSC:

37J35	Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests
37K10	Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
35Q53	KdV equations (Korteweg-de Vries equations)

Keywords:

Euler equations; Korteweg-de Vries equation; geodesic flow; Bott-Virasoro group

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