A rigorous theoretical investigation of linear dust ion acoustic (DIA) solitary waves in an unmagnetized complex plasma consisting of ion and ion beam fluids, nonthermal electrons that are Cairns distributed and immobile dust particles were undertaken. It was found out that, for large beam speeds, three stable modes propagated as solitary waves in the beam plasma. These were the “Fast”, “Slow” and “Ion-acoustic” modes. For two stream instability to occur between ion and ion beam, it is shown that or when .
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