Dual pairs in fluid dynamics

Abstract

This paper is a rigorous study of the dual pair structure of the ideal fluid and the dual pair structure for the $n$-dimensional Camassa-Holm (EPDiff) equation, including the proofs of the necessary transitivity results. In the case of the ideal fluid, we show that a careful definition of the momentum maps leads naturally to central extensions of diffeomorphism groups such as the group of quantomorphisms and the Ismagilov central extension.

33 pages

References in corpus (1)

• An integrable shallow water equation with peaked solitons

Cited by in corpus (1)

• The n:m resonance dual pair