论文标题
黑色孤子在具有强度依赖性分散体的光学系统中的稳定性
Stability of black solitons in optical systems with intensity-dependent dispersion
论文作者
论文摘要
黑色孤子子在具有强度依赖性分散体和Cubic decodocic NLS方程的非线性Schrödinger（NLS）方程中是相同的。我们证明，依赖强度的分散体引入了黑色孤子稳定性分析中的新特性。首先，光谱稳定性问题仅在假想轴上具有孤立的特征值。其次，能量稳定性参数在具有指数权重的Sobolev空间中。第三，黑色的孤子持续存在着增加较小的衰减潜力，并且当将其固定在有效电位的最小点上时，它仍然在光谱上保持稳定。同一模型为每个波速展示了一个旅行的深色孤子家族，我们将这些深色孤子的特性用于小波速度，以分析黑色孤子的轨道稳定性。
Black solitons are identical in the nonlinear Schrödinger (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.
