  Special localized wavemodes show up in several physical scenarios including
BEC in optical lattices, nonlinear photonic crystals and systems with strong
electron-phonon interaction. These result from an underlying nonlinear
contribution to the wave equation that is usually assumed to be instantaneous.
Here we demonstrate that the relaxation process of the nonlinearity has a
profound impact in the wavepacket dynamics and in the formation of localized
modes. We illustrate this phenomenology by considering the one-electron
wavepacket spreading in a $C60$ buckball structure whose dynamics is governed
by a discrete nonlinear Schroedinger equation with a Debye relaxation of the
nonlinearity. We report the full phase-diagram related to the spacial extension
of the asymptotic wavepacket and unveil a complex wavepacket dynamical
behavior.
