  We extend previous work [Y. E. Litvinenko, Phys. Plasmas 17, 074502 (2010)]
on a direct method for finding similarity reductions of partial differential
equations such as the Grad-Shafranov equation, to the case of the generalized
Grad-Shafranov equation (GGSE) with arbitrary incompressible flow. Several
families of analytic solutions are constructed, the generalized Solov\'ev
solution being a particular case, which contain both the classical and
non-classical group-invariant solutions to the GGSE. Those solutions can
describe a variety of equilibrium configurations pertinent to toroidal
magnetically confined plasmas and planetary magnetospheres.
