Abstract
Considering the self-steepening effect in a metamaterial (MM) can significantly change its behaviour. We study the propagation of ultrashort pulses in nonlinear MMs that is governed by a generalized nonlinear Schro dinger equation with higher order effects such as pseudo-quintic nonlinearity and self-steepening effect. A class of chirped quasi-soliton solutions is obtained in the presence of the self-steepening term, and some of which are derived for the first time. The solutions comprise chirped bright quasi-solitons on a constant and zero background, kink and anti-kink quasi-solitons, and double-kink quasi-solitons. It is found that the nonlinear chirp associated with each of these waves is directly proportional to the intensity and its amplitude can be controlled by selecting the self-steepening and dispersion coefficients. Particular cases of chirp-free quasi-solitons are discussed. The conditions on MM parameters for the formation of these structures are also presented. The obtained results are important to explore much richer localized light pulses in MMs.