The characteristics of dust ion-acoustic waves (DIAWs) that are excited because of streaming ions and hot q-non-extensive electrons obeying a vortex-like distribution are investigated. By exploiting a pseudo-potential technique, we have derived an energy integral equation. The presence of non-extensive q-distributed hot trapped electrons and a streaming ion beam has been shown to influence soliton structure quite significantly. The evolution of the soliton-like perturbations in complex plasmas, taking into account the dissipation processes, are also investigated, obtained by numerically solving the modified Schamel, equation whose widths are dependant on electron trapping efficiency . Our illustrations indicate that compressive DIAWs develop in this plasma. As the plasmas in reality have a relative flow, such an analysis can be used to understand the DIA solitary structures observed in the mesospheric noctilucent clouds.