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 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 red...
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MDPI AG
2023-04-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/9/2007 |
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| author | Weaam Alhejaili Alvaro H. Salas Samir A. El-Tantawy |
| author_facet | Weaam Alhejaili Alvaro H. Salas Samir A. El-Tantawy |
| author_sort | Weaam Alhejaili |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-11T04:12:59Z |
| format | Article |
| id | doaj.art-2f9347b351e24c79ba430dba11c895fc |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-11T04:12:59Z |
| publishDate | 2023-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-2f9347b351e24c79ba430dba11c895fc2023-11-17T23:18:47ZengMDPI AGMathematics2227-73902023-04-01119200710.3390/math11092007Ansatz and Averaging Methods for Modeling the (Un)Conserved Complex Duffing OscillatorsWeaam Alhejaili0Alvaro H. Salas1Samir A. El-Tantawy2Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi ArabiaFIZMAKO Research Group, Department of Mathematics and Statistics, Universidad Nacional de Colombia, Manizales 170001, ColombiaDepartment of Physics, Faculty of Science, Port Said University, Port Said 42521, EgyptIn 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.https://www.mdpi.com/2227-7390/11/9/2007complex Duffing oscillatorsdamped complex oscillatortrigonometric functionsJacobi elliptic functions |
| spellingShingle | Weaam Alhejaili Alvaro H. Salas Samir A. El-Tantawy Ansatz and Averaging Methods for Modeling the (Un)Conserved Complex Duffing Oscillators Mathematics complex Duffing oscillators damped complex oscillator trigonometric functions Jacobi elliptic functions |
| title | Ansatz and Averaging Methods for Modeling the (Un)Conserved Complex Duffing Oscillators |
| title_full | Ansatz and Averaging Methods for Modeling the (Un)Conserved Complex Duffing Oscillators |
| title_fullStr | Ansatz and Averaging Methods for Modeling the (Un)Conserved Complex Duffing Oscillators |
| title_full_unstemmed | Ansatz and Averaging Methods for Modeling the (Un)Conserved Complex Duffing Oscillators |
| title_short | Ansatz and Averaging Methods for Modeling the (Un)Conserved Complex Duffing Oscillators |
| title_sort | ansatz and averaging methods for modeling the un conserved complex duffing oscillators |
| topic | complex Duffing oscillators damped complex oscillator trigonometric functions Jacobi elliptic functions |
| url | https://www.mdpi.com/2227-7390/11/9/2007 |
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