Solving nonlinear Schrödinger equation based on discrete split-step multi-wavelet method

Abstract

In this paper, the discrete split-step multi-wavelet method (DSSMWM) is used to solve nonlinear Schrödinger equation. When the relative amplitude error is below10 −3magnitude, relative error of amplitude evolution, relative error of pulse broadening ratio, relative phase error, and computing time is respectively achieved. Because multi-wavelet is extraordinary effective for data compression, it only needs to deal with very little data. It can be seen that although the relative amplitude error, relative error of amplitude evolution, relative error of pulse broadening rate and relative phase error changes little, but the computing time are greatly reduced.