In this work, the propagation characteristics of electromagnetics waves in dieletric waveguides with arbitarily non-linear materiais, represented by a distribution of refractive index that depends on the local intensity of the signal, is presented. The waveguides here considered are analysed by means of an unidimensional equation. Due to the non- linearity of the materials this equation has analytical solution only for few types of non-linearities. To permit a more abrangent study, a numerical solution for the non- linear wave equation was developed. This solution is applied to the study of propagation characteristics of dielectric waveguides with different distributions of refractive index, either for TE and TM polarization. It is shown that these waveguides have propagation properties, like hysteresis and optical bi-stability, that fine applications in optical devices and optical computers. It´s also made a study of the stability of the solution of non-linear wave equation, showing that some portions of the solutions are usntable that is, they are a function of the observation point in the waveguide. The possibility of CAOS for unstable solutions, when the power is gradually increased, was also observed. At each step of this work, all results are compared with those of other methods of the literature.