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We explore dynamics of a density pulse induced by a local quench in aone-dimensional electron system. The spectral curvature leads to an "overturn"(population inversion) of the wave. We show that beyond this time the densityprofile develops strong oscillations with a period much larger than the Fermiwave length. The effect is studied first for the case of free fermions by meansof direct quantum simulations and via semiclassical analysis of the evolutionof Wigner function. We demonstrate then that the period of oscillations iscorrectly reproduced by a hydrodynamic theory with an appropriate dispersiveterm. Finally, we explore the effect of different types of electron-electroninteraction on the phenomenon. We show that sufficiently strong interaction[$U(r)\gg 1/mr^2$ where $m$ is the fermionic mass and $r$ the relevant spatialscale] determines the dominant dispersive term in the hydrodynamic equations.Hydrodynamic theory reveals crucial dependence of the density evolution on therelative sign of the interaction and the density perturbation.

Dynamics of waves in 1D electron systems: Density oscillations driven by population inversion