AI 中文总结
本文通过对称约化推导广义耦合非线性薛定谔系统的非简并亮孤子解，分析其呼吸特性、碰撞行为及稳定性，加深了对非简并矢量孤子的理解。
AI 中文摘要
已知广义耦合非线性薛定谔（GCNLS）方程可通过多种对称约化约化为基本矢量非线性薛定谔模型，利用这类约化可得到GCNLS系统的多种有趣孤子解。本文展示了如何通过其中一种约化推导非简并孤子解，并分析其相关特殊性质。研究发现，所得非简并孤子解呈现呼吸行为，以呼吸频率为特征；由该约化产生的矢量孤子会发生弹性碰撞并伴随标准相移，与其他耦合非线性薛定谔模型的非简并孤子类似，且在与已知亮孤子相互作用时会发生有趣的能量共享碰撞，这些碰撞场景通过适当的渐近分析得到进一步验证。此外，本文还分析了所得矢量孤子的稳定性，发现其对随机扰动具有稳定性，所得结果加深了对非简并矢量孤子性质与动力学的理解。
英文摘要
It is known that the generalized coupled nonlinear Schroedinger (GCNLS) equations can be reduced to the basic vector nonlinear Schroedinger models through various symmetry reductions. By using such reductions, soliton solutions of several interesting types can be obtained for the GCNLS system. In this paper, we show how the non-degenerate soliton solutions can be derived using one such reduction and analyze the various special features associated with the resulting soliton solutions. We find that the obtained non-degenerate soliton solutions exhibit breathing behavior, characterized by a breathing frequency. We also show that the vector solitons emerging from the reduction undergo elastic collisions with the standard phase shift, similar to the non-degenerate solitons of other coupled nonlinear Schroedinger models. Further, they undergo interesting energysharing collisions when they interact with the already known bright solitons. These collision scenarios are further confirmed by an appropriate asymptotic analysis. We have also analyzed the stability of the obtained vector solitons and found that they are stable against random perturbations. The results presented here enhance the understanding of the nature and dynamics of non-degenerate vector solitons.
Comments18 pages, 10 figures, Submitted for publication
