- A symmetry analysis of degenerate four-wave-mixing equations in photorefractive crystals is carried out. Using underlying SU symmetries, a systematic derivation of conserved quantities is performed, and a method of integration of the equations is introduced. Five conserved quantities are found, suggesting that the initial four complex equations can be expressed in terms of three real quantities (Euler angles or other). However, due to the form of the equations, only one independent variable is found necessary to solve the problem. 1992 The American Physical Society.