  Using the Calogero model as an example, we show that the transport in
interacting non-dissipative electronic systems is essentially non-linear.
Non-linear effects are due to the curvature of the electronic spectrum near the
Fermi energy. As is typical for non-linear systems, propagating wave packets
are unstable. At finite time shock wave singularities develop, the wave packet
collapses, and oscillatory features arise. They evolve into regularly
structured localized pulses carrying a fractionally quantized charge - {\it
soliton trains}. We briefly discuss perspectives of observation of Quantum
Shock Waves in edge states of Fractional Quantum Hall Effect and a direct
measurement of the fractional charge.
