Equations of Camassa-Holm type and the geometry of loop groups
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.
equations with infinitely many derivatives
scientific article; zbMATH DE number 6376722
scientific article