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.


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)
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