  Analyses of recent helioseismic data have produced ample evidence for
substantial dynamical variation of the differential rotation within the solar
convection zone. Given the inevitable difficulties in resolving the precise
nature of variations at deeper layers, much effort has recently gone into
determining theoretically the expected modes of behaviour, using nonlinear
dynamo models. Two important limitations of these models are that they have so
far included only one form of nonlinearity, and as yet they have not taken into
account the density stratification in the solar convection zone. Here we
address both of these issues by studying the effects of including density
stratification, as well as including an alpha--quenching nonlinearity in
addition to the previously studied effects of the Lorentz force on the
differential rotation. We find that observationally important features found in
the earlier uniform density models remain qualitatively unchanged, although
there are quantitative differences. This is important as it provides more
realistic theoretical predictions to be compared with and guide observations,
especially in the deeper regions where the uncertainties in the inversions are
larger. However the presence of an effective alpha-quenching nonlinearity
significantly reduces the amplitudes of the oscillations.
