Equations of Camassa-Holm type and the geometry of loop groups (Q478615)

The authors investigate equations on groups, specially loop groups, motivated by some of Arnold's classical work on the Riemannian geometry of diffeomorphism groups. They prove easily computable formulae for the sectional curvature in the case of the diffeomorphism group of the circle, and observe that this group has a \(CR\)-manifold structure. There are also presented examples of bona fide Hamiltonian equations in infinitely many derivatives.