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Split-step Fourier method for nonlinear Schrodinger equation

Various versions of the split-step Fourier method (SSFM) for the nonlinear Schrodinger equation (NLSE) are presented. New versions are introduced, namely: the operator exponential scheme (OES) and the simplified one (SOES). Comparison between these schemes is made. The approach for comparison is to (a) fix the accuracy; (b) leave mesh parameters (∆t, ∆x) free and compare the computing time required to attain such accuracy for various choices of the parameters. The results of our study suggest OES and SOES as effective numerical schemes for NLSE.