Geodesic flows on the Bott-Virasoro group with Dubinskii norm

Research output: Contribution to journalArticlepeer-review

Abstract

It is known that the Korteweg-De Vries equation, the Camassa-Holm equation and the Harry Dym (or Hunter-Saxton) equation are geodesic flows on the Bott-Virasoro group with respect to L2 and H1 right invariant metrics. In this Note we study geodesic flow on the Bott-Virasoro group with respect to the Sobolev metric of exponential type or Dubinskii metric. It is shown that the Harry Dym equation follows from linearization of this geodesic flow.

Original languageBritish English
Pages (from-to)108-114
Number of pages7
JournalApplied Mathematics E - Notes
Volume5
StatePublished - 2005

Fingerprint

Dive into the research topics of 'Geodesic flows on the Bott-Virasoro group with Dubinskii norm'. Together they form a unique fingerprint.

Cite this