  Here, we show that electrostatic solitons in a plasma with turbulent heating
of the electrons through an accelerating electric field, can form with very
high velocities, reaching up to several order of magnitudes larger than the
ion-sound speed. We call these solitons hypersonic solitons. The possible
parameter regime, where this work may be relevant, can be found the so-called
``dead zones'' of a protoplanetary disk. These zones are stable to
magnetorotational instability but the resultant turbulence can in effect heat
the electrons make them follow a highly non-Maxwellian velocity distribution.
We show that these hypersonic solitons can also reach very high velocities.
With electron velocity distribution described by Davydov distribution function,
we argue that these solitons can be an effective mechanism for energy
equilibration in such a situation through soliton decay and radiation.
