  Exact solutions are derived for an n-dimensional radial wave equation with a
general power nonlinearity. The method, which is applicable more generally to
other nonlinear PDEs, involves an ansatz technique to solve a first-order PDE
system of group-invariant variables given by group foliations of the wave
equation, using the one-dimensional admitted point symmetry groups. (These
groups comprise scalings and time translations, admitted for any nonlinearity
power, in addition to space-time inversions admitted for a particular conformal
nonlinearity power). This is shown to yield not only group-invariant solutions
as derived by standard symmetry reduction, but also other exact solutions of a
more general form. In particular, solutions with interesting analytical
behavior connected with blow ups as well as static monopoles are obtained.
