A comparison between the Split Step Fourier and Finite-Difference method in analysing the soliton collision of a type of Nonlinear Schr\"odinger equation found in the context of optical pulses

In this report a type of Schr\"odinger Equation which is found in the context of optical pulses is analysed using the $\textit{Split Step}$ and $\textit{Finite Difference}$ method. The investigation shows interesting dynamics regarding certain values for parameter $S$ as well as a comparison between the two numeric schemes demonstrating the $\textit{Split Step}$ to be superior for this problem.