Abstract
Nonlinear differential equations that control the propagation of a surface wave through the surface disconnection between two fluids are described by the Helmholtz-Duffing oscillator having imaginary damping forces. This oscillator is solved without using any perturbation techniques. This study is relevant in many fields such as nanotechnology. Along with the nonlinear analysis, the periodic solution and the stability criteria are established. Numerical calculations for stability conditions showed vital changes in the stability behavior due to the presence of the rotation ratio. Published under an exclusive license by AIP Publishing.