Document Type

Article

Rights

This item is available under a Creative Commons License for non-commercial use only

Disciplines

Pure mathematics, Applied mathematics

Publication Details

Journal of Geometric Mechanics

Abstract

The geodesic equations of a class of right invariant metrics on the semi-direct product of two Diff(S) groups are studied. The equations are explicitly described, they have the form of a system of coupled equations of Camassa-Holm type and possess singular (peakon) solutions. Their integrability is further investigated, however no compatible bi-Hamiltonian structures on the corresponding dual Lie algebra are found.

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