Existence of Korteweg-de Vries solitons and relevance of relativistic effects in a dusty electron-ion plasma

Nonlinear effects in the propagation of perturbations in a dusty electron-ion plasma are 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 kinds 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.