Abstract
Nonlinear second-and fourth-order corrections to the critical Tonks-Frenkel parameter (which characterizes the stability of the uniformly charged flat surface of an ideal conducting incompressible fluid) are found by asymptotic calculations of the fifth order of smallness in ratio of the wave amplitude to the capillary constant of the fluid. A nonlinear integral equation for the time evolution of the unstable wave amplitude is derived and solved. It turns out that the linear stage of instability development takes a major part of the total time, while the nonlinear stage is very short. It is shown that the characteristic time of instability development on the fluid surface is a rapidly decreasing function of the initial amplitude of a virtual wave and the overcritical surface charge (i.e., the excess of the charge over the critical value).
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