Grey Solitons in Saturable Media with Nonlinear Dispersion and Self-Frequency Shift

In the paper a special form of the generalized nonlinear Schrödinger equation in saturable medium with nonlinear dispersion and the self-frequency shift terms is considered. The solutions describing both the intensity and phase profiles of grey solitons propagating in this medium are obtained. Four cases of medium with or without saturation and with or without higher order terms are considered. For a square-two-level model of saturation analytical explicit solutions are derived. The relations between the medium and propagation parameters of solitons are discussed.