Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 2 (2006), 054, 9 pages      nlin.SI/0605041      https://doi.org/10.3842/SIGMA.2006.054

Geodesic Flow and Two (Super) Component Analog of the Camassa-Holm Equation

Partha Guha a and Peter J. Olver b
a) S.N. Bose National Centre for Basic Sciences, JD Block, Sector-3, Salt Lake, Calcutta-700098, India
b) School of Mathematics, University of Minnesota, Minneapolis, MN 55455, USA

Received March 08, 2006, in final form May 08, 2006; Published online May 23, 2006

Abstract
We derive the 2-component Camassa-Holm equation and corresponding N = 1 super generalization as geodesic flows with respect to the H1 metric on the extended Bott-Virasoro and superconformal groups, respectively.

Key words: geodesic flow; diffeomorphism; Virasoro orbit; Sobolev norm.

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