A numerical development in the dynamical equations of solitons into ideal optical fibers
Incremental numerical method for a well-understood problem in nonlinear optics.
The authors developed a finite element method with SUPG and CAU stabilization to numerically solve soliton propagation equations in ideal optical fibers, and validated it against known analytical solutions.
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.