Internal nonlinear four-mode interactions of capillary oscillations of a charged drop

Analytical expressions for the shape of a charged drop of an incompressible liquid nonlinearly oscillating upon multimode initial deformation have been obtained for the first time to within the third order of smallness. The second-order corrections to oscillation frequencies are calculated depending on the spectrum of modes determining the initial deformation. The third-order calculations show that the fundamental mode amplitude may increase due to the energy exchange with higher modes in a large number of possible four-mode resonance interactions.