This paper presents a novel approach for studying the nonlinear Rayleigh–Taylor instability (RTI). The system deals with two rotating superposed infinite hydromagnetic Darcian flows through porous media under the influence of a uniform tangential magnetic field. The field allows the presence of currents on the surface of separation. The appropriate linear governing equations are solved and confirmed with the corresponding nonlinear boundary conditions. A nonlinear characteristic of the surface deflection is deducted. Away from the traditional techniques of the stability analysis, the work introduces a new one. The analysis depends mainly on the homotopy perturbation method (HPM). To achieve an analytical approximate periodic solution of the surface deflection, the secular terms are removed. This cancellation resulted in well-known amplitude equations. These equations are utilised to achieve stability criteria of the system. Therefore, the stability configuration is exercised in linear as well as nonlinear approaches. The mathematical procedure adopted here is simple, promising and powerful. The method may be used to treat more complicated nonlinear differential equations that arise in science, physics and engineering applications. A numerical calculation is performed to graph the implication of various parameters on the stability picture. In addition, for more convenience, the surface deflection is depicted.
