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

##### MSC:
 37J35 Completely integrable systems, topological structure of phase space, integration methods 37K10 Completely integrable systems, integrability tests, bi-Hamiltonian structures, hierarchies 35Q53 KdV-like (Korteweg-de Vries) equations
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##### References:
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