Geometry of inhomogeneous Poisson brackets, multicomponent Harry Dym hierarchies and multicomponent Hunter-Saxton equations

Andrey Yu. Konyaev

We introduce a natural class of multicomponent local Poisson structures ${\mathcal{P}}_k+{\mathcal{P}}_1$, where ${\mathcal{P}}_1$ is a local Poisson bracket of order one and $\mathcal P_…