  We present a variational calculation of the spin wave excitation spectrum of
double--exchange ferromagnets in different dimensions. Our theory recovers the
Random Phase approximation and 1/S expansion results as limiting cases and can
be used to study the intermediate exchange coupling and electron concentration
regime relevant to the manganites. In particular, we treat exactly the long
range three--body correlations between a Fermi sea electron--hole pair and a
magnon excitation and show that they strongly affect the spin dynamics in the
parameter range relevant to experiments in the manganites. The manifestations
of these correlations are many-fold. We demonstrate that they significantly
change the ferromagnetic phase boundary. In addition to a decrease in the
magnon stiffness, we obtain an instability of the ferromagnetic state against
spin wave excitations close to the Brillouin zone boundary.Within a range of
intermediate concentrations, we find a strong softening of the spin wave
dispersion as compared to the Heisenberg ferromagnet with the same stiffness,
which changes into hardening for other concentrations. We discuss the relevance
of these results to experiments in colossal magnetoresistance ferromagnets.
