以超常介质中超短脉冲传输的归一化非线性薛定谔方程为模型,采用拟解法解析得到了自陡峭效应影响下的一组新型的精确亮、暗类孤子解。研究发现,当自陡峭效应、群速度色散和赝五阶非线性效应达到平衡时,在正折射自聚焦超常介质的反常色散区,既可以存在亮类孤子也可以存在暗类孤子,但亮、暗类孤子具有不同的脉宽、频移、速度和波数。这与自聚焦常规介质中亮孤子存在于反常色散区而暗孤子存在于正常色散区明显不同。最后,数值研究了存在条件偏离和白噪声干扰下该新型类孤子的稳定性,结果表明该亮、暗类孤子都能保持自身形状比较稳定的在超常介质中传输。

Based on the model of the generalized nonlinear Schrdinger equation describing the propagation of ultrashort pulses in metamaterials,a new type of exact bright-like and dark-like solitons under self-steepening effect was analytically obtained by the ansatz method. It was found that both bright-like and dark-like solitons,with different widths,frequency shifts,velocities and wave numbers,can exist in the anomalous dispersion regime in positive refraction region of self-focusing metamaterials when the self-steepening effect,the group velocity dispersion and the fifth-order nonlinear effect reached balances each other. This was quite different from the cases in the self-focusing ordinary materials,where bright solitons existed in the anomalous dispersion region while dark solions existed in the normal dispersion region. Finally,we numerically investigated the stability of the new types of solitons under the deviation of existence condition and the perturbation of white noise. The obtained results showed that both bright-like and dark-like solitons may stably propagate keeping their shapes.