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

By Martin Bauer, Martins Bruveris, Philipp Harms, Peter W. Michor. 2011

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The Virasoro-Bott group endowed with the right-invariant L2-metric (which is a weak Riemannian metric) has the KdV-equation as geodesic equation. We prove that this metric space has vanishing geodesic distance.

Subfields: Applied Mathematics, Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/d8811972647bc9d876e3cb670c54fb39b2ffb07e