Marcelo Cavalcanti, Wellington Correa, Mauricio Sepúlveda, Rodrigo Véjar:
Study of stability and conservative numerical methods for a high order nonlinear Schrödinger equation
In this work we present a finite difference scheme used to solve a high order nonlinear Schrödinger equation. These equations can model the propagation of solitons travelling in fiber optics. The scheme is designed to preserve the numerical L2 norm and the energy, for a suitable initial condition. We show numerical results displaying conservation properties of the schemes using solitons as initial conditions.