Journal of Nonlinear Mathematical Physics

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Volume 17, Issue 1, March 2010, Pages 7 - 11

On the Geodesic Flow on the Group of Diffeomorphisms of the Circle with a Fractional Sobolev Right-Invariant Metric

Authors
Marcus Wunsch
Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606-8502, Japan,mwunsch@kurims.kyoto-u.ac.jp
Received 29 June 2009, Accepted 9 September 2009, Available Online 7 January 2021.
DOI
10.1142/S1402925110000544How to use a DOI?
Keywords
Geodesic flow; fractional Sobolev metric; generalized CLM equation
Abstract

We show that the geodesic flow on the infinite-dimensional group of diffeomorphisms of the circle, endowed with a fractional Sobolev metric at the identity, is described by the generalized Constantin–Lax–Majda equation with parameter a=−12.

Copyright
© 2010 The Authors. Published by Atlantis Press and Taylor & Francis
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
17 - 1
Pages
7 - 11
Publication Date
2021/01/07
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
10.1142/S1402925110000544How to use a DOI?
Copyright
© 2010 The Authors. Published by Atlantis Press and Taylor & Francis
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

risenwbib
TY  - JOUR
AU  - Marcus Wunsch
PY  - 2021
DA  - 2021/01/07
TI  - On the Geodesic Flow on the Group of Diffeomorphisms of the Circle with a Fractional Sobolev Right-Invariant Metric
JO  - Journal of Nonlinear Mathematical Physics
SP  - 7
EP  - 11
VL  - 17
IS  - 1
SN  - 1776-0852
UR  - https://doi.org/10.1142/S1402925110000544
DO  - 10.1142/S1402925110000544
ID  - Wunsch2021
ER  -