Geodesic
Geodesic Flow and Two (Super) Component Analog of the Camassa–Holm Equation
Symmetry, integrability and geometry: methods and applications, Tome 2 (2006) Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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     title = {Geodesic {Flow} and {Two} {(Super)} {Component} {Analog} of the {Camassa{\textendash}Holm} {Equation}},
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}
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Partha Guha; Peter J. Olver. Geodesic Flow and Two (Super) Component Analog of the Camassa–Holm Equation. Symmetry, integrability and geometry: methods and applications, Tome 2 (2006). http://geodesic.mathdoc.fr/item/SIGMA_2006_2_a53/

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