Application of the split operator Fourier transform method to the solution of the nonlinear Schrodinger equation

The nonlinear Schrodinger equation arises naturally in a variety of physical processes; in particular, it is fundamentally important to nonlinear optics. Both the analytic and numerical solutions of this equation have been extensively investigated; a recent review by Taha and Ablowitz1 suggests that for soliton propagation problems the method of Hardin and Tapped2 is the superior numerical method. In this paper, the split operator Fourier transform (SOFT) method, originally due to Fleck et al.,3 is demonstrated to be applicable to the nonlinear Schrodinger equation. For the particular soliton problem studied,4 the results obtained with the SOFT method are found to be an order of magnitude more accurate than those obtained with the Hardin-Tappert method.