A dusty multi-ion plasma system consisting of non-isothermal (trapped) electrons, Maxwellian (isothermal) light positive ions, warm heavy negative ions and extremely massive charge fluctuating stationary dust have been considered. The dust-ion-acoustic solitary and shock waves associated with negative ion dynamics, Maxwellian (isothermal) positive ions, trapped electrons and charge fluctuating stationary dust have been investigated by employing the reductive perturbation method. The basic features of such dust-ion-acoustic solitary and shock waves have been identified. The implications of our findings in space and laboratory dusty multi-ion plasmas are discussed.

Time-dependent cylindrical and spherical dust-acoustic (DA) solitary and shock waves propagating in a strongly coupled dusty plasmas (containing strongly correlated negatively charged dust grains and weakly correlated adiabatic electrons and ions) are investigated. It is shown that cylindrical and spherical DA solitary and shock waves exist with negative potential, and that the strong correlation between the charged dust grains is a source of dissipation, and is responsible for the formation of cylindrical or spherical DA shock structures. It is also shown that the effects of a non-planar geometry (cylindrical and spherical) significantly modify the basic features (e.g. amplitude, width, speed, etc.) of DA solitary and shock waves. The implications of our results in laboratory experiments are briefly discussed.