The propagation of electrostatic waves in an unmagnetized collisionlesspair-ion plasma with immobile positively charged dusts is studied for bothlarge- and small-amplitude perturbations. Using a two-fluid model forpair-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 wavemodes are studied with different mass $(m)$ and temperature $(T)$ ratios ofnegative to positive ions, as well as the effects of immobile charged dusts$(\delta)$. For large-amplitude waves, the pseudopotential approach isperformed, whereas the standard reductive perturbation technique (RPT) is usedto study the small-amplitude Korteweg-de Vries (KdV) solitons. The profiles ofthe pseudopotential, the large amplitude solitons as well as the dynamicalevolution of KdV solitons are numerically studied with the system parameters asabove. It is found that the pair-ion plasmas with positively charged dustssupport the propagation of solitary waves (SWs) with only the negativepotential. The results may be useful for the excitation of SWs in laboratorydusty pair-ion plasmas, electron-free industrial plasmas as well as forobservation in space plasmas where electron density is negligibly smallcompared to that of negative ions.
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