An efficient numerical method is developed for solving nonlinear wave equations by studying
the propagation and stability properties of solitary waves (solitons) of the regularized long wave
(RLW) equation in one space dimension using a combination of leap frog for time dependence and
a pseudospectral (Fourier transform) treatment of the space dependence. Our schemes follow very
accurately these solutions, which are given by simple closed formulas. Studying the interaction of
two such solitons and three solitary waves interaction for the RLW equation. Our implementation
employs the fast Fourier transform (FFT) algorithm.