  A complex plasma medium (containing Cairns nonthermal electron species,
adiabatically warm inertial ion species, and stationary positively charged dust
(PCD) species (making a plasma system very complex) is considered. The effects
of PCD species, nonthermal electron species, and adiabatic ion-temperature on
ion-acoustic (IA) solitary waves (SWs) and double layers (DLs) are investigated
by the pseudo-potential approach, which is valid for the arbitrary amplitude
time-independent SWs and DLs. It is observed that the presence of the PCD
species reduces the phase speed of the IA waves, and consequently supports the
IA subsonic compressive SWs in such electron-ion-PCD plasmas. On the other
hand, the increase in both adiabatic ion-temperature and the number of
nonthermal or fast electrons causes to reduce the possibility for the formation
of the subsonic SWs, and thus convert subsonic SWs into supersonic ones. It is
also observed that after at a certain value of the nonthermal parameter, the IA
supersonic SWs with both positive and negative potentials as well as the DLs
with only negative potential exist. The applications of the work in space
environments (viz. Earth's mesosphere, cometary tails, Jupiter's magnetosphere,
etc.) and laboratory devices, where the warm ion and nonthermal electron
species along with PCD species have been observed, are briefly discussed.
