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

Weaam Alhejaili, Alvaro H. Salas and Samir A. El-Tantawy ()
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Weaam Alhejaili: Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia
Alvaro H. Salas: FIZMAKO Research Group, Department of Mathematics and Statistics, Universidad Nacional de Colombia, Manizales 170001, Colombia
Samir A. El-Tantawy: Department of Physics, Faculty of Science, Port Said University, Port Said 42521, Egypt

Mathematics, 2023, vol. 11, issue 9, 1-12

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

Keywords: complex Duffing oscillators; damped complex oscillator; trigonometric functions; Jacobi elliptic functions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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