We consider the propagation of light beams in photorefractive media in the framework of a (1+1)-dimensional model. The Kukhtarev band transport model is introduced both in a time-dependent differential equation describing the evolution of the space charge field and in a nonlinear wave propagation equation. This latter is then numerically solved with a beam propagation method routine. The evolution in time and space of an initially diffracting laser beam is simulated as a function of initial profiles and waists. The beam is shown to go through a transient overfocused state prior to relaxing to a steady state soliton. Additional features such as the stability condition of the system or effects such as optical branching and soliton interactions are studied.