In this paper, we study the effect of the number of wells, inner (R[Formula: see text]) and outer (R[Formula: see text]) quantum ring radiuses, and magnetic field as controlling tools to change the nonlinearity in optical properties of GaN/AlN constant radius multi-layer quantum dots and rings. It is seen that for small R[Formula: see text] and for fixed R[Formula: see text] and R[Formula: see text], by increasing the number of wells, the nonlinearity increases, while for greater R[Formula: see text] and for fixed R[Formula: see text] and R[Formula: see text], by increasing the number of wells the nonlinearity first decreases and then increases. For systems with greater R[Formula: see text], the nonlinearity continually increases by increasing the number of wells. For fixed R[Formula: see text], the critical well number, in which the nonlinearity changes its behavior, decreases by increasing the inner quantum ring radius R[Formula: see text]. The absorption coefficient does not undertake any blue or red shifts by changing the number of wells. In the systems with more number of wells, the nonlinearity reduces more rapidly by increasing the magnetic field. Finally, by increasing the radius R[Formula: see text], the nonlinearity increases.