Bright and dark solitons in metamaterials obtained by extended F-expansion method

Abstract

The ultra-short pulse equation in a metamaterial is solved by the extended F-expansion method. The new phenomena and characteristics of solitons, caused by the anomalous self-steepening effect and the second-order nonlinear dispersion in metamaterials, are discussed. The results show that the second-order nonlinear dispersion in the positive-index region may take the place of the linear dispersion to form the bright and dark solitons. Due to the switchable sign of the anomalous self-steepening effect in the positive-index and negative-index regions, the bright and dark solitons separately exist in the anomalous and normal dispersion regions under some specific conditions. The moving directions of the centers of bright and dark solitons can be controlled by the sign of the anomalous self-steepening effect or by the combination of the anomalous self-steepening effect and third-order linear dispersion.