Averaging for split Step scheme

The split-step Fourier method for numerical solving nonlinear Schrodinger equation (NLS) can be interpreted as NLS with rapdily varying coefficients. This connection is exploited to justify the split-step approximation using averaging technique. The averaging is done up to the second order and it is explained why (in this context) symmetric split-step produces higher order scheme. The implication of this result to dispersion managed NLS (DMNLS) arising in optical communication models is discussed.