  When both Hamiltonian operators of a bi-Hamiltonian system are pure
differential operators, we show that the generalized Kupershmidt deformation
(GKD) developed from the Kupershmidt deformation in \cite{kd} offers an useful
way to construct new integrable system starting from the bi-Hamiltonian system.
We construct some new integrable systems by means of the generalized
Kupershmidt deformation in the cases of Harry Dym hierarchy, classical
Boussinesq hierarchy and coupled KdV hierarchy. We show that the GKD of Harry
Dym equation, GKD of classical Boussinesq equation and GKD of coupled KdV
equation are equivalent to the new integrable Rosochatius deformations of these
soliton equations with self-consistent sources. We present the Lax Pair for
these new systems. Therefore the generalized Kupershmidt deformation provides a
new way to construct new integrable systems from bi-Hamiltonian systems and
also offers a new approach to obtain the Rosochatius deformation of soliton
equation with self-consistent sources.
