%0 Journal Article
%T The periodic b-equation and Euler equations on the circle
%A J. Escher
%A J. Seiler
%J Mathematics
%D 2010
%I arXiv
%R 10.1063/1.3405494
%X In this note we show that the periodic b-equation can only be realized as an Euler equation on the Lie group Diff(S^1) of all smooth and orientiation preserving diffeomorphisms on the cirlce if b=2, i.e. for the Camassa-Holm equation. In this case the inertia operator generating the metric on Diff(S^1) is given by A=1-d^2/dx^2. In contrast, the Degasperis-Procesi equation, for which b=3, is not an Euler equation on Diff(S^1) for any inertia operator. Our result generalizes a recent result of B. Kolev.
%U http://arxiv.org/abs/1001.2987v1