  We present a quasi-analytical solution of a spin-orbital model of KCuF$_{3}$,
using the variational method for Green's functions. By analyzing the spectra
for different partial bosonic compositions as well as the full solution, we
show that hole propagation needs both orbiton and magnon excitations to
develop, but the orbitons dominate the picture. We further elucidate the role
of the different bosons by analyzing the self-energies for simplified models,
establishing that because of the nature of the spin-orbital ground state,
magnons alone do not produce a full quasiparticle band, in contrast to
orbitons. Finally, using the electron-hole transformation between the $e_g$
states of KCuF$_3$ and LaMnO$_3$ we suggest the qualitative scenario for
photoemission experiments in LaMnO$_3$.
