Bright and Dark Solitons in Generalized Kerr-Like Media

In the paper the propagation of short pulses in nonlinear Kerr-like medium is considered. Pulses are described by the nonlinear Schrödinger equation in which the generalization of nonlinear dispersion term and the self-frequency shift are taken into account. The solution of the equation in the form of quadrature is derived. Both the phase and profile of the pulse intensity are obtained. The cases of propagating bright and dark solitons in saturable Kerr-like medium are analyzed. Two models of saturation are considered. The explicit analytical expressions describing the Kerr limit are reported. The relations between the medium and propagation parameters are thoroughly discussed.