Highly dispersive optical solitons in the nonlinear Schrödinger’s equation having polynomial law of the refractive index change

In this paper, we apply the unified Riccati equation expansion method, as well as two forms of auxiliary equation methodology, to find highly dispersive optical solitons in the nonlinear Schrödinger’s equation having a polynomial law of the refractive index change. Bright, dark and singular solitons as well as periodic and Jacobi elliptic solutions are obtained that are presented together with their existence criteria.