Abstract
This Letter talks about the dynamics of dark optical solitons that are governed by the nonlinear Schrödinger's equation with power law nonlinearity. The solitons are considered in presence of linear attenuation, third order dispersion and self-steepening terms, all with time-dependent coefficients. The solitary wave ansatz is used to carry out the integration and an exact soliton solution is obtained. It is only necessary that these time-dependent coefficients are Riemann integrable.