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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:
37J35Completely integrable systems, topological structure of phase space, integration methods
37K10Completely integrable systems, integrability tests, bi-Hamiltonian structures, hierarchies
35Q53KdV-like (Korteweg-de Vries) equations
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References:
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