Abstract
A reductive perturbation technique (the derivative expansion technique (DET)) is employed to derive a linear damped nonlinear Schrödinger equation (LDNLSE) for investigating the feature properties of the dissipative modulated nonlinear dust-acoustic wavepacket including rogue waves (RWs) in an electron-ion dusty plasma having superthermal electrons and ions. The modulational instability (MI) of the dissipative envelope structures is investigated and the (un)stable domain of the modulated structures is mapped precisely. The LDNLSE is solved numerically using Adomian decomposition method (ADM) in order to study the impact of the related plasma parameters on the features of the dissipative RWs. The influence of superthermal parameters and the dust-neutral collisional frequency on the profile of the dissipative dust-acoustic RWs is numerically investigated. Moreover, the accuracy of the numerical solutions is examined by estimating the global residual error in the whole space-time domain.