Stock´s waves at conducting liquid surface in static and SHF electric fields

Summary form only given. The problem of the description of nonlinear Stock´s waves on the surface of a conducting liquid with an electrical field applied at the liquid-vacuum boundary is investigated. Mathematical model was developed that takes into account the effects of electric field in nonlinear approximation with any accuracy required. The ratio of the wave amplitude to its length was employed as a small parameter. Due to that the problem of the effects of electric field on the profile of an arbitrary two-dimensional surface wave could have been solved. Basing on these results, the problem of non-linear wave bifurcation from a zero level was solved. The existence of a Stock´s wave is proved. The formula of approximating the profile of a wave and dispersion equation with the third order of accuracy is obtained. The influence of weak non-linearity to development of instability near to a threshold is investigated