Starting from the three-dimensional version of a standard photorefractive model (STPM), we obtain a reduced compact Set of equations for an electric field based on the assumption of a quasi-steady-state fast recombination. The equations are suitable for evaluation of a current induced by running gratings at small-contrast approximation and also are applicable for the description of space-charge wave domains. We discuss spatial domain and subharmonic beam formation in bismuth silicon oxide (BSO) crystals in the framework of the small-contrast approximation of STPM. The experimental results confirming holographic current existence in BSO crystal are reported. (C) 2005 Optical Society of America.