On the oscillations in a nonextensive complex plasma by improved differential transformation method: An application to a damped Duffing equation

In this study, the nonlinear damping oscillations in a complex non-Maxwellian plasma are investigated. For this purpose, the set of fluid equations of the present plasma model is reduced to the Burger-modified Korteweg De Vries equation (BmKdV) equation using a reductive perturbation technique. Using the traveling wave transformation, the BmKdV equation can be reduced to a damped Duffing equation. The numerical solutions to the damped Duffing equation are obtained using multistage differential transformation method (MsDTM). Also, we compared the obtained results to the semi-analytical approximations using the Pade differential transformation (PDTM) method and numerical solution, by the 4th-order Rung Kutta (RK4) method and analytical solution by He's frequency method. The impact of relevant plasma parameters, namely, negative dust concentrations and ion kinematic viscosity on the profile of dust ion-acoustic oscillations are examined. The suggested mathematical approaches can help many authors for explaining the mystery of their laboratory results. Moreover, the suggested numerical method can be applied for solving higher order nonlinearity oscillations for a long domain.