  Nonlinear effects in the propagation of perturbations in a dusty electron-ion
plasma is studied, considering fully relativistic wave motion. A multifluid
model is considered for the particles, from which a KdV equation can be
derived. In general, two different soliton solutions are found depending on the
kind of dispersion of the KdV equation. We study when the dispersion
coefficient of this equation is positive. In this case, two kind of behavior
are possible, one associated with a slow wave mode, another with a fast wave
mode. It is shown that, depending on the value of the system parameters,
compressive and/or rarefactive solitons, or no soliton at all, can be found and
that relativistic effects for ions are much more relevant than for electrons.
It is also found that relativistic effects can strongly decrease the soliton
amplitude for the slow mode, whereas for the fast mode they can lead to
compressive-rarefactive soliton transitions and vice versa, depending on the
dust charge density in both modes.
