标题： 光学系统中强度依赖色散的黑洞孤子的稳定性 显示英文标题

标题： Stability of black solitons in optical systems with intensity-dependent dispersion

摘要： 非线性薛定谔（NLS）方程中，强度依赖色散的黑孤子与三次失焦NLS方程中的黑孤子是相同的。 我们证明，强度依赖色散在黑孤子的稳定性分析中引入了新的特性。 首先，谱稳定性问题仅在虚轴上具有孤立特征值。 其次，能量稳定性论证在具有指数权重的Sobolev空间中成立。 第三，黑孤子在添加一个小的衰减势时仍然存在，并且当它被固定在有效势的极小点时，仍保持谱稳定性。 同一模型对于每个波速都表现出一族行进的暗孤子，并且我们在黑孤子轨道稳定性的分析中结合了小波速下这些暗孤子的特性。 显示英文摘要

摘要： Black solitons are identical in the nonlinear Schr\"{o}dinger (NLS) equation with intensity-dependent dispersion and the cubic defocusing NLS equation. We prove that the intensity-dependent dispersion introduces new properties in the stability analysis of the black soliton. First, the spectral stability problem possesses only isolated eigenvalues on the imaginary axis. Second, the energetic stability argument holds in Sobolev spaces with exponential weights. Third, the black soliton persists with respect to addition of a small decaying potential and remains spectrally stable when it is pinned to the minimum points of the effective potential. The same model exhibits a family of traveling dark solitons for every wave speed and we incorporate properties of these dark solitons for small wave speeds in the analysis of orbital stability of the black soliton.