Slowly varying envelope wave equations describing degenerate four-wave mixing (4WM) in photorefractive phase-conjugate mirrors are solved exactly, in terms of quadratures. Multigrating 4WM geometry is assumed, with the transmission and reflection gratings contributing equally and with the counterpropagating pumppump interaction accounted for. The original boundary-value problem is transformed into an initial-value problem, which is treated by an iteration procedure. It is shown that within the iterative boundary-fitting procedure the multistability of solutions takes place and that the intensity reflectivity of the mirror may become chaotic. The strange attractor thus arising is analyzed with the use of standard methods of nonlinear dynamics. 1991 Optical Society of America.