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The Lagrangian fluid description is employed to solve the initial valueproblem for one-dimensional, compressible fluid flows represented by theEuler-Poisson system. Exact nonlinear and time-dependent solutions areobtained, which exhibit a variety of transient phenomena such as a densitycollapse in finite space-time or the appearance and, for the first time, asuccessive dissolution of wavelet structures during the same event. The latterare superimposed on the gross density pattern in the course of theuni-directional expansion of an initially localized density hump. Whereasself-gravitating fluids will always experience collapse, neutral fluids andfluids with repulsive forces, such as a non-neutral, pure electron fluid, canexhibit an evolution of the second type, being determined by the initialconditions. For an electron fluid, being embedded in a neutralizing ionbackground, these nonlinearities are, however, strongly diminished due to theomnipresent plasma oscillations, which weaken and alternatively change the signof the collective force.

The successive formation and disappearance of density structures in simple expanding systems