  The propagation of electrostatic waves in an unmagnetized collisionless
pair-ion plasma with immobile positively charged dusts is studied for both
large- and small-amplitude perturbations. Using a two-fluid model for
pair-ions, it is shown that there appear two linear ion modes, namely the
"fast" and "slow" waves in dusty pair-ion plasmas. The properties of these wave
modes are studied with different mass $(m)$ and temperature $(T)$ ratios of
negative to positive ions, as well as the effects of immobile charged dusts
$(\delta)$. For large-amplitude waves, the pseudopotential approach is
performed, whereas the standard reductive perturbation technique (RPT) is used
to study the small-amplitude Korteweg-de Vries (KdV) solitons. The profiles of
the pseudopotential, the large amplitude solitons as well as the dynamical
evolution of KdV solitons are numerically studied with the system parameters as
above. It is found that the pair-ion plasmas with positively charged dusts
support the propagation of solitary waves (SWs) with only the negative
potential. The results may be useful for the excitation of SWs in laboratory
dusty pair-ion plasmas, electron-free industrial plasmas as well as for
observation in space plasmas where electron density is negligibly small
compared to that of negative ions.
