The effects of trapped and untrapped particles on an electrostatic wave packet

We present a procedure to solve the Vlasov-Poisson equations for electrostatic wave packets. We obtain a Schrödinger type of wave equation, taking the wave- particle interaction into account. We use this equation to study the propagation of one finite-amplitude wave packet. We find a change in amplitude caused by interaction between the packet and particles propagating near to the group velocity. Also, we find a modulation of the plasma in the front of the packet, caused by trapping effects.