A new finite element scheme for optical temporal soliton analysis

In order to get insights for more complex nonlinear scalar or vectorial simulations, which could include simultaneous spatial and temporal soliton analysis, a comparison among the most common two step-by-step finite element method (SbS/FEM) algorithms, the FE scheme and the well known split step/Fourier method (SS/FM), has been performed. To reach this goal, as a model, the dimensionless nonlinear Schrodinger equation, associated to the Kerr nonlinearity type, has been adopted. This equation describes optical temporal solitons propagating through a nonlinear monomode optical fibre (NMOF). From a numerical point of view this example constitutes a very good test provided that the collision can create numerical instabilities due to the complex shape adopted by the pulses during the colliding interaction