Nonlinear corrections to the frequencies of nonaxisymmetric Modes of a space-charged dielectric liquid jet

An expression for the shape of a uniformly charged (over volume) jet of an ideal incompressible dielectric liquid as a function of time is derived with analytical asymptotic calculations of the third order of smallness in jet oscillation amplitude for the case when the initial deformation of the equilibrium surface is governed by one (in general nonaxisymmetric) mode. Analytical expressions for nonlinear corrections to the frequencies and positions of inner nonlinear degenerate three-and four-mode resonances are found.