Nonlinear nonaxisymmetric oscillations of a space-charged jet

The problem of nonlinear nonaxisymmetric oscillations of a jet of a space-charged dielectric (zero-conductivity) liquid is solved asymptotically. The solution is accurate up to second-order terms in initial deformation amplitude. It is shown that the difference between the amplitude values of second-order corrections to the solutions for perfectly conducting and perfectly dielectric liquids depends on the permittivity of the latter and may amount to several tens of percent. The permittivity of the liquid also governs the positions of internal resonances, in the vicinity of which nonlinear energy transfer between modes takes place.