Numerical methods for a class of generalized nonlinear Schrodinger equations

Abstract

We present and analyze di erent splitting algorithms for numerical solution of the both classical and generalized nonlinear Schr odinger equations describing propagation of wave packets with special emphasis on applications to nonlinear ber-optics. The considered generalizations take into account the higher-order corrections of the linear di erential dispersion operator as well as the saturation of nonlinearity and the self-steepening of the eld envelope function. For stabilization of the pseudo-spectral splitting schemes for generalized Schr odinger equations a regularization based on the approximation of the derivatives by the low number of Fourier modes is proposed. To illustrate the theoretically predicted performance of these schemes several numerical experiments have been done. In particular, we compute real-world examples of extreme pulses propagating in silica bers.