  The modulational instability (MI) of the dust-acoustic waves (DAWs) in an
electron-positron-ion-dust plasma (containing super-thermal electrons,
positrons and ions along with negatively charged adiabatic dust grains) is
investigated by the analysis of the nonlinear Schr\"{o}dinger equation (NLSE).
To derive the NLSE, the reductive perturbation method has been employed. Two
different parametric regions for stable and unstable DAWs are observed. The
presence of super-thermal electrons, positrons and ions significantly modifies
both the stable and unstable regions. The critical wave number $k_c$ (at which
modulational instability sets in) depends on the super-thermal electron,
positron, and ion, and adiabatic dust concentrations.
