Formation and propagation of dark solitons in metamaterials

We use an extended Tanh-function expansion method to solve the nonlinear equation for ultrashort pulse propagation in matamaterial, and obtain dark solitary solutions in various cases. Further, we study the influence of the controllable self-steepening effect and the second-order nonlinear dispersion on the formation and propagation of dark solitons in metarnaterials. It is found that the negative self-steepening effect in metamaterial makes the soliton center move to the leading side,opposite to the moving direction of soliton in ordinary materials in which the self-steepening effect is always positive. Most importantly, due to the role of the second-order nonlinear dispersion, dark solitons can be formed in the medium without linear dispersion or with an anomalous linear dispersion.