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The Sagdeev pseudo-potential technique and the analytic theory developed byDas et al. [J. Plasma Phys. 78, 565 (2012)] have been used to investigate thedust ion acoustic solitary structures at the acoustic speed in a collisionlessunmagnetized dusty plasma consisting of negatively charged static dust grains,adiabatic warm ions, nonthermal electrons and isothermal positrons. The presentsystem supports both positive and negative potential solitary waves at theacoustic speed, but the system does not support the coexistence of solitarystructures of opposite polarity at the acoustic speed. The system also supportsnegative potential double layer at the acoustic speed, but does not supportpositive potential double layer. Although the system supports positivepotential supersoliton at the supersonic speed, but there does not existsupersoliton of any polarity at the acoustic speed. Solitary structures havebeen investigated with the help of compositional parameter spaces and the phaseportraits of the dynamical system describing the nonlinear behaviour of thedust ion acoustic waves at the acoustic speed. For the case, when there is nopositron in the system, there exist negative potential double layer andnegative potential supersoliton at the acoustic speed and for such case, themechanism of transition of supersoliton to soliton after the formation ofdouble layer at the acoustic speed has been discussed with the help of phaseportraits. The differences between the solitary structures at the acousticspeed and the solitary structures at the supersonic speed have been analysedwith the help of phase portraits.

Dust ion acoustic solitary structures at the acoustic speed in presence of nonthermal electrons and isothermal positrons