Exotic galilean symmetry and non-commutative mechanics.
Geodesic flows on the Bott-Virasoro group with Dubinskii norm.
Geometrical methods in hydrodynamics
We describe some recent results on a specific nonlinear hydrodynamical problem where the geometric approach gives insight into a variety of aspects.
Geometry of fluid motion
We survey two problems illustrating geometric-topological and Hamiltonian methods in fluid mechanics: energy relaxation of a magnetic field and conservation laws for ideal fluid motion. More details and results, as well as a guide to the literature on these topics can be found in [3].
Invariant manifold of hyperbolic-elliptic type for nonlinear wave equation.
Ito equation as a geodesic flow on
The Ito equation is shown to be a geodesic flow of metric on the semidirect product space , where is the group of orientation preserving Sobolev diffeomorphisms of the circle. We also study a geodesic flow of a metric.
Projective structure and integrable geodesic flows on the extension of Bott-Virasoro group.
Self-consistent-field method and -functional method on group manifold in soliton theory: a review and new results.