The problem of convergence of finite difference (FD) schemes for simulating
the propagation of pulses in nonlinear media is analyzed. In order to esta
blish 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 ap
plication of the method are also provided: e.g., the propagation of semi-in
finite waves and pulses in active media with periodic and exponentially dec
aying nonlinearities. (C) 1999 Acoustical Society of America. [S0001-4966(9
9)00810-3].