Planar dust-acoustic waves in electron–positron–ion–dust plasmas with dust-size distribution under higher-order transverse perturbations

Propagation of small but finite nonlinear dust-acoustic solitary waves are investigated in a planar unmagnetized dusty plasma, which consists of electrons, positrons, ions and negatively charged dust particles with different sizes and masses. A Kadomtsev–Petviashvili (KP) equation is obtained by using reductive perturbation method. The effect of positron density and positron–electron temperature ratio on dust-acoustic solitary structures are studied. Numerical results show that the increase in positron number density increases the amplitude of hump-like solitons but decreases the dip-like solitary waves. Furthermore, increase in the positron–electron temperature ratio results in the decrease of the amplitude of dip-like solitary waves. It seems that both the dip and hump-like solitary waves can exist in this system. Our results also suggest that the dust-size distribution has a significant role on the amplitude of the solitary waves.