Ansatz and Averaging Methods for Modeling the (Un)Conserved Complex Duffing Oscillators

In this study, both the ansatz and averaging methods are carried out for analyzing complex Duffing oscillators including undamped/conserved oscillator (CDO) damped/unconserved CDO to obtain some approximate analytical solutions. To analyze conserved CDO, it is reduced two decoupled oscillators. After that, exact solution of employed derive an approximation in terms Jacobi elliptic function. damped methodologies considered. For first methodology, oscillators, method devoted oscillator. Accordingly, trigonometric functions obtained. second applied directly functions. All obtained solutions compared with fourth-order Runge–Kutta (RK4) numerical approximations. This study may help many researchers interested field plasma physics interpret their laboratory observations results.