  The dispersion of the high-energy phonon modes in the electron doped
high-temperature superconductor Nd$_{1.85}$Ce$_{0.15}$CuO$_4$ has been studied
by inelastic neutron scattering. The frequencies of phonon modes with Cu-O
bond-stretching character drop abruptly when going from the Brillouin zone
center along the [100]-direction; this dispersion is qualitatively similar to
observations in the hole-doped cuprates. We also find a softening of the
bond-stretching modes along the [110]-direction but which is weaker and
exhibits a sinusoidal dispersion. The phonon anomalies are discussed in
comparison to hole-doped cuprate superconductors and other metallic
perovskites.
