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 Schrödinger 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].