Programming of the generalized nonlinear paraxial equation for the formation of solitons with Mathematica

We present the nonlinearity and dispersion effects involved in the propagation of optical solitons which can be understood by using a numerical routine to solve the generalized nonlinear paraxial equation. A sequence of code has been developed in Mathematica to explore in depth several features of the optical soliton’s formation and propagation. These numerical routines were implemented through the use of Mathematica and the results give a very clear idea of this interesting and important practical phenomenon.