Wave-like equations of the non linear VLASOV equation for a one dimensional electron plasma are discussed analytically and numerically. The quasilinear theory is derived in a simple way and some conclusions are drawn from it. It is found that, if the initial conditions of the harmonics of the electrical field differ by orders of magnitude the type of the solution varies appreciably. — The numerical solution is obtained by integrating the characteristic function of the distribution function f, i. e. it’s FOURIER transform in space and velocity. It is shown that this method is in principle superior to the direct integration of f. Stable and instable cases are discussed. Good agreement between theory and numerical computations is found.