  An analytical solution of the selfconsistent Vlasov equation is presented.
The time evolution is entirely determined by the initial distribution function.
The largest Lyapunov exponent is calculated analytically. For special
parameters of the model potential positive Lyapunov exponent is possible. This
model may serve as a check for numerical codes solving selfconsistent Vlasov
equations. The here presented method is also applicable for any system with
analytical solution of the Hamilton equation for the formfactor of the
potential.
