Vanishing geodesic distance for the Riemannian metric with geodesic equation the KdV-equation

Abstract

The Virasoro-Bott group endowed with the right-invariant $L^2$-metric (which is a weak Riemannian metric) has the KdV-equation as geodesic equation. We prove that this metric space has vanishing geodesic distance.

10 pages, 1 figure; typos corrected. Title changed. It agrees with the published version