具有局域非均匀性的一维非线性薛定谔晶格中的孤子
Solitons in one-dimensional nonlinear Schrödinger lattices with a local inhomogeneity
摘要：
本文研究了一维离散非线性薛定谔方程带线性点亏损系统局部解的存在性、稳定性、动力学形成和迁移性.我们考虑在聚焦晶格中的吸引和排斥缺陷。我们的主要发现包括：（a）在排斥情况下，以缺陷为中心的在位模的不稳定性;（b）对于任一种足够强的缺陷，由于鞍结分叉，缺陷附近的局域模消失;（c）对于吸引缺陷，振幅形成阈值减小，而对于排斥缺陷，振幅形成阈值增大;以及d）详细说明作为初始速度和缺陷强度的函数的移动局域模与缺陷的相互作用的不同状态（俘获、俘获和反射、纯反射和纯透射）。
英文摘要：
In this paper we analyze the existence, stability, dynamical formation and mobility properties of localized solutions in a one-dimensional system described by the discrete nonlinear Schrödinger equation with a linear point defect. We consider both attractive and repulsive defects in a focusing lattice. Among our main findings are: a) the destabilization of the on--site mode centered at the defect in the repulsive case; b) the disappearance of localized modes in the vicinity of the defect due to saddle-node bifurcations for sufficiently strong defects of either type; c) the decrease of the amplitude formation threshold for attractive and its increase for repulsive defects; and d) the detailed elucidation as a function of initial speed and defect strength of the different regimes (trapping, trapping and reflection, pure reflection and pure transmission) of interaction of a moving localized mode with the defect.
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