Numerical simulation of pulse propagation in nonlinear 1-D media

The problem of convergence of finite difference (FD) schemes for simulating the propagation of pulses in nonlinear media is analyzed. In order to establish the reliability of the numerical procedure, different FD schemes are considered and compared among themselves, with the results of a Von Neumann analysis and with the analytical solution (when available). Examples of application of the method are also provided: e.g., the propagation of semi-infinite waves and pulses in active media with periodic and exponentially decaying nonlinearities.