Optical solitons in medium with parabolic law nonlinearity and higher order dispersion

The nonlinear Schrodinger equation, describing the propagation of ultra-short optical solitons through parabolic law medium, has been studied analytically. The perturbations that are third-order dispersion, fourth-order dispersion, and self-steepening are taken into account. The Ricatti equation expansion approach and Ansatz method are applied. Finally, Bright, dark as well as singular solitons are constructed under some constraint conditions.