Abstract

In this work we present a finite difference scheme used to solve a higher order nonlinear Schrodinger equation. These equations are related to models of propagation of solitons travelling in fiber optics. The scheme is designed to preserve the numerical L-2 norm, and control the energy for a suitable choose on the equation's parameters. We prove the convergence of the numerical solution for this equation in a boundary domain, and we show numerical results displaying conservation properties of the schemes using solitons as initial conditions.