Preprint A488/2006
Bi-Hamiltonian Aspects of a Matrix Harry Dym Hierarchy

Jorge Zubelli | Fontanelli, Laura | Lorenzoni, Paolo | Pedroni, Marco

**Keywords: **
Harry Dym. Solitons. Integrable Systems. Inverse Problems. Bihamiltonian systems. Nonlinear evolution equations.

We study the Harry Dym hierarchy of nonlinear
evolution equations from the bi-Hamiltonian view point. This is done by
using the concept of an $\CS$-hierarchy, which permits us to
define a matrix Harry Dym hierarchy. We conclude by showing that
the conserved densities of the matrix Harry Dym equation can be found
by means of a Riccati-type equation.