We investigate the nonlinear dynamics of an unmagnetized dusty plasma comprising of four components, such as positively and negatively charged mobile dust, the Boltzmann distributed electrons, and nonthermal ions. The associated set of fluid equations is recasted into the celebrated nonlinear Schrodinger equation (NLSE) by invoking the standard reductive perturbation method. We have constructed a set of solitary antikink pulses by employing the exponential function method (EFM). It is found that the nonthermal ionic variable plays a key role in determining the electrostatic structure in the dusty plasma. The present investigation may have potential applications in predicting the nature of electrostatic solitary structures noticed in Saturn's ring.