Dynamics of topological optical solitons with time-dependent dispersion, nonlinearity and attenuation

In this paper, the dark or topological optical 1-soliton solution of the nonlinear Schrödinger’s equation is obtained. The time-dependent coefficients of the group velocity dispersion, Kerr nonlinearity and the attenuation terms are considered. This leads to the constraint relation between these coefficients for the topological solitons to exist. All what is necessary is that these time-dependent coefficients be simply Riemann integrable.