  The properties of electrostatic transverse shear waves propagating in a
strongly coupled dusty plasma with an equilibrium density gradient are examined
using the generalized hydrodynamic equation. In the usual kinetic limit, the
resulting equation has similarity to zero energy Schrodinger's equation. This
has helped in obtaining some exact eigenmode solutions in both cartesian and
cylindrical geometries for certain nontrivial density profiles. The
corresponding velocity profiles and the discrete eigenfrequencies are obtained
for several interesting situations and their physics discussed.
