Nonlinear dynamics of magnetic fluids with a relative motion in the presence of an oblique magnetic field

The Kelvin–Helmholtz (KH) model of superposed magnetic fluids is studied, in this work, using the concepts of KH, Benjamin–Feir and superharmonic instability. A plane interface of two incompressible inviscid magnetic fluids of different densities, permeabilities and surface tension is considered. The fluids moving with uniform velocities parallel to their interface are stressed by an oblique magnetic field. The linear relation between the oblique magnetic field and the KH instability is analyzed. The nonlinear studies of the discussed sample are studied through the Schrödinger equations and the Klein–Gordon equation. The existence conditions of Stokes waves with their instability conditions were united to have general conditions. In these conditions, we realize the properties of the existence and instability simultaneously. These conditions are discussed analytically and graphically.