Hamiltonian flows on the space of star-shaped curves
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We provide a geometric interpretation of the KdV equation as an evolution equation on the space of closed curves in the centroaffine plane. There is a natural symplectic structure on this space and the KdV-flow is generated by a Hamiltonian given by the total centroaffine curvature. In this way we obtain another example for a soliton equation coming naturally from a differential geometric problem . Furthermore, we present a group action of the diffeomorphism group of the circle on the space of closed centroaffine curves.
1991 Mathematics Subject Classification35Q53 53A15
Key words and phraseKdV equation affine curves
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