Propagation of ultrashort pulses at least a few tens of optical cycles in duration through a negative index material is investigated theoretically based on the generalized nonlinear Schrödinger equation with pseudo-quintic nonlinearity and self-steepening effect. Novel periodic waves of different forms are shown to exist in the system in the presence of higher-order effects. It is found that such periodic structures exhibit an interesting chirping property which depends on the light field intensity. The nonlinearity in pulse chirp is found to be caused by the presence of self-steepening effect in the negative index medium. The solutions also comprise dark, bright, and kink solitary waves. Stability of the solitary wave solutions are proved analytically using the theory of nonlinear dispersive waves. The stability of the solutions is numerically studied under finite initial perturbations.

基于具有伪五次非线性和自陡峭效应的广义非线性薛定谔方程，从理论上研究了超短脉冲在持续时间内通过负折射率材料的至少几十个光学周期的传播。在高阶效应的存在下，系统中存在不同形式的新周期波。发现这种周期性结构表现出有趣的啁啾性质，其取决于光场强度。发现脉冲啁啾的非线性是由负指数介质中自陡效应的存在引起的。解决方案还包括暗、亮和扭结孤立波。使用非线性色散波理论分析证明了孤立波解的稳定性。