AI 中文总结
本文针对描述光纤激光器和非平衡现象的三次复金兹堡-朗道方程，识别出新型孤子与周期波解，开展稳定性分析并验证其准稳定性。
AI 中文摘要
针对由三次复金兹堡-朗道方程描述脉冲传播的非线性耗散介质，本文识别出新型孤子和周期波。研究发现，脉冲振幅的动力学方程支持两种具有不同函数形式的 distinct 扭结孤子与反扭结孤子，且所得扭结孤子与反扭结孤子波形在相同的固定逆速度下出现。结果还表明，周期波可呈现多种波形，如 sn、cn、dn 及其有理形式。在长波极限下，推导得到的周期波退化为不同的亮孤子脉冲和暗孤子脉冲。本文基于非线性光学中的色散波理论开展稳定性分析，结果显示，在由复金兹堡-朗道方程描述的被动锁模激光器语境下，部分椭圆函数解和孤子解为准稳定解。
英文摘要
New types of soliton and periodic waves are identified for a nonlinear dissipative medium where the pulse propagation is governed by the cubic complex Ginzburg-Landau equation. We find that the dynamical equation for the pulse amplitude supports two distinct types of kink and antikink solitons with different functional forms. It is found that the obtained kink and antikink soliton waveforms occur under the same fixed inverse velocity. The results also indicate that the periodic waves can propagate with variety of wave forms such as sn, cn, dn and their rational forms as well. It is also shown that in the long-wave limit, the derived periodic waves degenerate into different bright and dark soliton pulses. The stability analysis based on the theory of dispersive waves in nonlinear optics is developed. It is shown that some elliptic and soliton solutions are quasi-stable in the context of passive mode locking lasers described by complex Ginzburg-Landau equation.
Comments14 pages, 7 figures
