We present a Vlasov, i.e. a kinetic Eulerian simulation study of nonlinear
collisionless ion-acoustic shocks and solitons excited by an intense laser
interacting with an overdense plasma. The use of the Vlasov code avoids
problems with low particle statistics and allows a validation of
particle-in-cell results. A simple original correction to the splitting method
for the numerical integration of the Vlasov equation has been implemented in
order to ensure the charge conservation in the relativistic regime. We show
that the ion distribution is affected by the development of a turbulence driven
by the relativistic "fast" electron bunches generated at the laser-plasma
interaction surface. This leads to the onset of ion reflection at the shock
front in an initially cold plasma where only soliton solutions without ion
reflection are expected to propagate. We give a simple analytic model to
describe the onset of the turbulence as a nonlinear coupling of the ion density
with the fast electron currents, taking the pulsed nature of the relativistic
electron bunches into account