  We develop and evaluate a numerical procedure for a system of nonlinear
differential equations, which describe the propagation of solitons into ideal
dielectric optical fibers. This problem has analytical solutions known. The
numerical solutions of the system is implemented by the finite element method,
using methods of stabilization such as Streamline Upwind Petrov-Galerkin (SUPG)
and Consistent Approximate Upwind (CAU). Comparing the numerical and analytical
solutions, it was found that the numerical procedure adequately describes the
dynamics of this system.
