Exact optical solitons in metamaterials with anti-cubic law of nonlinearity by Lie group method

In this paper, using Lie point symmetry analysis, we study the dynamics of the solitons for the nonlinear Schrodinger’s equation with anti-cubic nonlinearity. Some new doubly periodic solutions are obtained that degenerate to dark and bright soliton solutions. In our of best knowledge, the obtained solutions are new. Those obtained results have important applications in the understanding the nonlinear propagation theory of solitons in metamaterials.