This article is cited in 34 papers

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

Partha Guha^a, Peter J. Olver<sup>b

a</sup> 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

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

Keywords: geodesic flow; diffeomorphism; Virasoro orbit; Sobolev norm.

MSC: 53A07; 53B50

Received: March 8, 2006; in final form May 8, 2006; Published online May 23, 2006

Language: English

DOI: 10.3842/SIGMA.2006.054

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ArXiv: nlin.SI/0605041