A heuristic approach to the prediction of a periodic solution for a damping nonlinear oscillator with the non-perturbative technique - El-Dib, Yusry O.; Elgazery, Nasser S.; Alyousef, Haifa A. (Frontiers in Physics, 2023)
The present work attracts attention to obtaining a new result of the periodic solution of a damped nonlinear Duffing oscillatory as well as a damped Klein-Gordon equation. It is known that the frequency response equation in the Duffing equation can be derived from the homotopy analysis, only, in the absence of the damping force. We suggest a suitable new scheme successfully to produce a periodic solution without losing the damping coefficient. The novel strategy is centered on establishing an alternate equation apart from any difficulty in handling the influence of the linear damped term. This technique is successful in obtaining new results towards a periodic solution, frequency equation, and the corresponding stability conditions. The analysis may be extended to investigate the damping parametric Duffing equation. This methodology yields a more effective outcome of the damped nonlinear oscillators. With the help of this procedure, one can analyze many problems in the domain of physical engineering that involve oscillators and a linear damping influence produced by the HPM. Moreover, this method can help all interested plasma authors for modeling different nonlinear acoustic oscillations in plasma.