Optical solitons and other solutions with anti-cubic nonlinearity by Lie symmetry analysis and additional integration architectures

In this work, symmetry reduction for nonlinear Schrödinger's equation with anti-cubic nonlinearity is determined by using the invariance of equations under Lie group of transformations. Using the similarity transformations the equation is reduced into system of ordinary differential equations. Corresponding to reduced ordinary differential equations, some exact solutions are obtained. These yields bright solitons, dark solitons, singular solitons and other explicit solutions. It is also pointed out that some of the results reported earlier are particular forms of current solutions.