Properties of complex damping Helmholtz–Duffing oscillator arising in fluid mechanics

Abstract

The current paper presents the first treatment to obtain the solution of a complex Helmholtz–Duffing oscillator. This model has described the elevation of the surface waves in fluid mechanics. The non-perturbative approach is used to convert the nonlinear oscillator to a linear oscillator to derive the solution of the complex nonlinear oscillator. This paper has opened the path for a new way to study more complex nonlinear elevation of surface waves.