  Based on the Vlasov-Maxwell equations describing the self-consistent
nonlinear beam dynamics and collective processes, the evolution of an intense
sheet beam propagating through a periodic focusing field has been studied. In
an earlier paper [1] it has been shown that in the case of a beam with uniform
phase space density the Vlasov-Maxwell equations can be replaced exactly by the
macroscopic warm fluid-Maxwell equations with a triple adiabatic pressure law.
In this paper we demonstrate that starting from the macroscopic fluid-Maxwell
equations a nonlinear Schroedinger equation for the slowly varying wave
amplitude (or a set of coupled nonlinear Schroedinger equations for the wave
amplitudes in the case of multi-wave interactions) can be derived. Properties
of the nonlinear Schroedinger equation are discussed, together with soliton
formation in intense particle beams.
