Abstract
We derive exact analytical soliton solutions of the dark and gray type for a family of the Chen–Lee–Liu equation which arises in the context of temporal pulses along optical fibers associated with the self-steepening nonlinearity. It is found that the chirp associated to these solutions is directly proportional to the intensity of the wave and includes both linear and nonlinear contributions. Moreover, the parametric conditions for the existence of the chirped soliton structures are also presented.