Abstract
The equations and boundary conditions describing plane-parallel potential motions of two superposed layers of stably stratified magnetic fluid are formulated. The fluid is assumed to fill entirely a horizontal plane channel in the presence of a uniform longitudinal magnetic field induced by external sources. With reference to the case of long waves propagating over the interface between the upper and lower layers, it is shown that the action of the field may be interpreted as the result of an increase in the nondimensional surface tension by an amount proportional to the square of the undisturbed field. In the linear formulation the effect of the field on the evolution of a long-wave perturbation of the initially plane interface is investigated. Korteweg-de Vries equations with quadratic and cubic nonlinearities are derived and the action of the field on the internal solitary waves is analyzed.
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