On Splitting and Bifurcations of Dispersion Equation Solutions for Low AmplitudeWaves at Charged Interface of Two Media

A structure of dispersion equation solutions is investigated for low amplitude waves at the charged interface of two immiscible liquids of different thickness in the gravitation field when the upper (ideal, dielectric) liquid moves with respect to the lower (viscous, well-conducting) one. It is shown that the background movement of the upper liquid leads to elimination of bifurcation points of the dispersion equation solution and to splitting of oscillation modes of wave disturbances. The parametric representation of the described dispersion equation is found for the case of immobile upper liquid. Structures of solutions are given for various wave types.