Nondispersive evolution of the pump mode in down-conversion processes and in the presence of Kerr nonlinearity

We show that the dynamics of appropriately designed initially uncorrelated states of a two-mode electromagnetic field exhibits a nondispersive long-time propagation of the strongly excited mode in the down-conversion regime and in the presence of a Kerr nonlinearity. The decoherence processes do not significantly affect the stability of the evolution of the excited mode. The structure of the initial states leading to a nonspreading evolution depends only on the parameters of the Hamiltonian and can be experimentally prepared and tested.