A learning procedure for CNN is presented and applied in order to find the parameters of networks approximating the dynamics of certain nonlinear systems which are characterized by partial differential equations (PDE). Our results show that - depending on the training pattern - solutions of various PDE can be approximated with high accuracy by a simple CNN structure. Results for two nonlinear PDE, Burgers' equation and the Korteweg-de Vries equation, are discussed in detail.