  Recent inelastic neutron scattering experiments in CeIn$_{3}$ and
CePd$_{2}$Si$_{2}$ single crystals measured spin wave excitations at low
temperatures. These two heavy fermion compounds exhibit antiferromagnetic
long-range order, but a strong competition between the
Ruderman-Kittel-Kasuya-Yosida(RKKY) interaction and Kondo effect is evidenced
by their nearly equal N\'eel and Kondo temperatures. Our aim is to show how
magnons such as measured in the antiferromagnetic phase of these Ce compounds,
can be described with a microscopic Heisenberg-Kondo model introduced by
J.R.Iglesias, C.Lacroix and B.Coqblin, used before for studies of the
non-magnetic phase. The model includes the correlated Ce-$4 f$ electrons
hybridized with the conduction band, where we also allow for correlations, and
we consider competing
  RKKY (Heisenberg-like $J_{H} $) and Kondo ($J_{K}$) antiferromagnetic
couplings. Carrying on a series of unitary transformations, we perturbatively
derive a second-order effective Hamiltonian which, projected onto the
antiferromagnetic electron ground state, describes the spin wave excitations,
renormalized by their interaction with correlated itinerant electrons. We
numerically study how the different parameters of the model influence the
renormalization of the magnons, yielding useful information for the analysis of
inelastic neutron scattering experiments in antiferromagnetic heavy fermion
compounds. We also compare our results with the available experimental data,
finding good agreement with the spin wave measurements in cubic CeIn$_3$.
