The homotopy-perturbation method applied for solving complex-valued differential equations with strong cubic nonlinearity

In this paper the homotopy perturbation method is adopted for solving a complex-valued second-order strongly nonlinear differential equation. Homotopy with an imbedding parameter p∈[0,1] is constructed. The perturbation procedure with parameter p transforms the strongly nonlinear differential equation into a system of linear complex-valued differential equations whose solutions give the approximate solution of the initial differential equation. To illustrate the effectiveness and convenience of the suggested procedure, a Duffing equation with strong cubic nonlinearity is considered. The periodic solution in the first approximation is obtained. The solution is compared with the exact one and shows good agreement.