The periodic b-equation and Euler equations on the circle
The periodic b-equation and Euler equations on the circle
In this note we show that the periodic b-equation can only be realized as a Euler equation on the Lie group Diffâ(S1) of all smooth and orientation preserving diffeomorphisms on the circle if b=2, i.e., for the CamassaâHolm equation. In this case the inertia operator generating the metric on Diffâ(S1) âŚ