The split-step Fourier method for solving numerically nonlinear Schrödinger equations (NLS) is considered as NLS with rapidly varying coefficients. This connection is exploited to justify the split-step approximation using an averaging technique. The averaging is done up to the second order and it is explained why (in this context) symmetric split-step produces a higher order scheme. The same approach is applied to dispersion managed NLS to show that anti-symmetric dispersion maps lead to higher order validity of the corresponding averaged equation.
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics
- Physics and Astronomy(all)
- Applied Mathematics