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Zbl 0901.58022
MisioĊ‚ek, Gerard
A shallow water equation as a geodesic flow on the Bott-Virasoro group. (English)
[J] J. Geom. Phys. 24, No.3, 203-208 (1998). ISSN 0393-0440

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.\par In addition to these results the paper contains some rather interesting remarks.
[Th.M.Rassias (Athens)]
MSC 2000:
*37J35 Completely integrable systems, etc.
37K10 Completely integrable systems etc.
35Q53 KdV-like equations

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

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