Interaction of coherent states for Hartree equations

We consider the Hartree equation with a smooth kernel and an external potential, in the semiclassical regime. We analyze the propagation of two initial wave packets, and show different possible effects of the interaction, according to the size of the nonlinearity in terms of the semiclassical parameter. We show three different sorts of nonlinear phenomena. In each case, the structure of the wave as a sum of two coherent states is preserved. However, the envelope and the center (in phase space) of these two wave packets are affected by nonlinear interferences, which are described precisely.