The reducing rank method to solve third-order Duffing equation with the homotopy perturbation

In the current work, we apply a nonstandard scheme to solve the third-order Duffing equation. This equation is produced from the strong damped Klein-Gordon equation under the traveling wave transformation. The solution and the stability conditions for the third-order Duffing equation have been discussed for the first time. The present analysis is new and used the reducing rank method with the homotopy perturbation method. A nonoscillator solution with the oscillating solutions is derived individually and frequency formula is obtained. Besides, the stability analysis is discussed.

Automated summary

This work applies a nonstandard scheme to solve the third-order Duffing equation, discussing the solution and stability conditions for the first time. The analysis is new, utilizing the reducing rank method and homotopy perturbation method. Nonoscillator and oscillating solutions are derived separately, with a frequency formula obtained, and stability analysis is also discussed.