Nonlinear stability of rotating two superposed magnetized fluids with the technique of the homotopy perturbation

In the present work, the Rayleigh-Taylor instability of two rotating superposed magnetized fluids within the presence of a vertical or a horizontal magnetic flux has been investigated. The nonlinear theory is applied, by solving the equation of motion and uses the acceptable nonlinear boundary conditions. However, the nonlinear characteristic equation within the elevation parameter is obtained. This equation features a transcendental integro-Duffing kind. The homotopy perturbation technique has been applied by exploitation the parameter growth technique that results in constructing the nonlinear frequency. Stability conditions are derived from the frequency equation. It's illustrated that the rotation parameter plays a helpful result. It's shown that the stability behavior within the extremely uniform rotating fluids equivalents to the system while not rotation. A periodic solution for the elevation function has been performed. Numerical calculations area unit created for linear analysis furthermore the nonlinear scope. Moreover, the elevation function has been premeditated versus the time parameter. The strategy adopted here is vital and powerful for solving nonlinear generator systems with a really high nonlinearity arising in nonlinear science and engineering.