  A precise theoretical investigation has been made on dust-acoustic (DA) waves
(DAWs) in a four components dusty plasma medium having inertial warm adiabatic
dust grains and inertialess $q$-distributed electrons as well as isothermal
ions and positrons. The nonlinear and dispersive parameters of the nonlinear
Schr\"{o}dinger equation (NLSE), which develops by using reductive
perturbations technique, have been used to recognize the stable and unstable
parametric regions of the DAWs as well as associated DA rogue waves (DARWs) in
the unstable parametric regime of the DAWs. The effects of the light positrons
and massive dust grains in determining the amplitude and width of the DARWs
associated with DAWs are examined. The findings of our present investigation
may be useful for understanding different nonlinear electrostatic phenomena in
both space and laboratory plasmas.
