CAJ | 학술논문

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。
이초상개질중초단맥충전수적귀일화비선성설정악방정위모형，채용의해법해석득도료자두초효응영향하적일조신형적정학량、암류고자해。연구발현，당자두초효응、군속도색산화안오계비선성효응체도평형시，재정절사자취초초상개질적반상색산구，기가이존재량류고자야가이존재암류고자，단량、암류고자구유불동적맥관、빈이、속도화파수。저여자취초상규개질중량고자존재우반상색산구이암고자존재우정상색산구명현불동。최후，수치연구료존재조건편리화백조성간우하해신형류고자적은정성，결과표명해량、암류고자도능보지자신형상비교은정적재초상개질중전수。
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 w hen 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 w hile 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 .