Exact Solution of selfconsistent Vlasov equation

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.

K. Morawetz · 1997