A Lie symmetry approach to nonlinear Schrödinger’s equation with non-Kerr law nonlinearity

This paper obtains the stationary 1-soliton solution of the nonlinear Schrödinger’s equation in non-Kerr law media. The types of nonlinearity that are considered are Kerr law, power law, parabolic law and the dual-power law. The technique that is used to carry out the integration of this equation is the Lie symmetry analysis.