New optical soliton solutions of the popularized anti-cubic nonlinear Schrodinger equation versus its numerical treatment

In our current article, we will use two diverse methods namely the extended simple equation method (ESEM) and the extended direct algebraic method (EDAM) to extract the soliton solutions of popularized anti-cubic nonlinear Schrodinger equation that is very useful in the field of the optics. The obtained rational solutions via these two reliable, effective techniques denote the importance of these methods. Moreover, we will implement the differential transform method (DTM) which is one of the most, new semi-analytical and numerical methods to construct the corresponding numerical solutions for all achieved soliton solutions by the above two methods. We will compare between the soliton solutions introduced by the two suggested methods with the numerical solutions obtained by the DTM. It is clear that there exist similarity and convergence between the traveling wave solutions achieved by the ESEM, EDAM and the numerical solutions achieved by DTM. The novelty of our achieved solutions will appear when it compared by [1].