  We explicitly solve the classical equations of motion for strings in
backgrounds obtained as non-abelian T-duals of a homogeneous isotropic
plane-parallel wave. To construct the dual backgrounds, semi-abelian Drinfeld
doubles are used which contain the isometry group of the homogeneous plane wave
metric. The dual solutions are then found by the Poisson-Lie transformation of
the explicit solution of the original homogeneous plane wave background.
Investigating their Killing vectors, we have found that the dual backgrounds
can be transformed to the form of more general plane-parallel waves.
