A procedure for systematically calculating a wide class of exact, nonlinear wave solutions of the Vlasov equation that are stationary in the wave frame is given. The essential feature of the method is the expansion of the current density in an infinite series of the vector potential or the expansion of the charge density in an infinite series in the scalar potential. The potentials obey a differential equation of the form of the equation of motion for a point particle in a conservative potential. This nonlinear differential equation has numerous analytic solutions depending on the choice of physical parameters.