Abstract
A theoretical study of the nonlinear behavior of the surface wave (or ripplon) propagating on the electroncharged surface of liquid helium is presented. The evolution of the wave packet is described by the nonlinear Schr\"odinger equation, and the wave is found to be either stable or unstable with respect to an amplitude perturbation depending on the choice of the wave number. Envelope solitons are formed in the onedimensional case. In two dimensions it is found that wave packets collapse when the envelope contains large wave numbers, so that the surface tension determines wave evolutions; the physical dimension of the packet shrinks and the amplitude increases. The system we consider in this paper is suitable for experimental studies of solitons and collapse phenomena because the dissipation in liquid helium is small and the ripplon dispersion relation can be easily modified by an external electric field.
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