Results in Mathematics

, Volume 27, Issue 3–4, pp 328–332

Hamiltonian flows on the space of star-shaped curves

Article

Abstract

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 [1]. Furthermore, we present a group action of the diffeomorphism group of the circle on the space of closed centroaffine curves.

1991 Mathematics Subject Classification

35Q53 53A15 

Key words and phrase

KdV equation affine curves 

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Copyright information

© Birkhäuser Verlag, Basel 1995

Authors and Affiliations

  1. 1.Fachbereich MathematikBerlin

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