耦合Sasa-Satsuma系统在简并与非简并 regime下的矢量Akhmediev呼吸子及状态跃迁
Vector Akhmediev Breathers and State Transitions in the Degenerate and Nondegenerate Regimes for the Coupled Sasa-Satsuma System
中文总结 AI 辅助
针对耦合Sasa-Satsuma系统，研究其简并与非简并 regime下的矢量Akhmediev呼吸子，分析三种波数构型的特性，揭示简并与非简并区域的模式交叉现象，通过解析与数值方法验证相关结论。
中文摘要 AI 辅助
我们研究了描述两个耦合超短光脉冲包络的耦合Sasa-Satsuma系统在简并与非简并 regime下的矢量Akhmediev呼吸子（ABs）。基于双分量背景的载波波数关系，我们考察了三种构型：单个消失波数、一对相反波数以及两个大小不等的非零波数。这些构型具有不同的最大非简并度。对于每种构型，我们推导了约化谱方程，构建了存在图，并将所得分支与调制不稳定性增益谱进行比较。由于载波波数对称性不同，非简并型模式可出现在光谱简并区域，而简并型模式也可能出现在光谱非简并区域。此外，简并 regime下所有可允许的分支均满足状态跃迁条件且对应周期波状态，此类分支也存在于非简并 regime中。对代表性解的直接数值模拟进一步证实了这些解析预测。
英文摘要
We investigate vector Akhmediev breathers (ABs) in the degenerate and nondegenerate regimes for the coupled Sasa-Satsuma system describing two coupled ultrashort optical pulse envelopes. Based on the carrier-wavenumber relations of the two-component background, we examine three configurations: a single vanishing wavenumber, a pair of opposite wavenumbers, and two nonzero wavenumbers of unequal magnitudes. These configurations admit distinct maximal degrees of nondegeneracy. For each configuration, we derive the reduced spectral equations, construct the existence diagrams, and compare the resulting branches with the modulation-instability gain spectra. Owing to the distinct carrier-wavenumber symmetries, nondegenerate-type modes can occur in spectrally degenerate regions, whereas degenerate-type ones may also appear in spectrally nondegenerate regions. Moreover, all admissible branches in the degenerate regimes satisfy the state-transition condition and correspond to periodic-wave states, while such branches are also present in nondegenerate regimes. Direct numerical simulations of representative solutions further confirm the analytical predictions.
