  We present a parallel version of the well-known Split-Step Fourier method
(SSF) for solving the Nonlinear Schr\"odinger equation, a mathematical model
describing wave packet propagation in fiber optic lines. The algorithm is
implemented under both distributed and shared memory programming paradigms on
the Silicon Graphics/Cray Research Origin 200. The 1D Fast-Fourier Transform
(FFT) is parallelized by writing the 1D FFT as a 2D matrix and performing
independent 1D sequential FFTs on the rows and columns of this matrix. We can
attain almost perfect speedup in SSF for small numbers of processors depending
on both problem size and communication contention. The parallel algorithm is
applicable to other computational problems constrained by the speed of the 1D
FFT.
