We investigate numerically the existence and stability of defect solitons in nonlinear fractional Schrödinger equation. For positive defects, defect solitons are only existent in the semi-infinite gap and are stable in their whole existence domain irrespective of Lévy index. For moderate deep defects, defect solitons are existent in both the semi-infinite gap and first gap, and their instability domains occur in the low-power region of the semi-infinite gap. While for deep enough defects, stable defect solitons can be found in the second gap. Increasing the strength of defect (or Lévy index) will narrow (or broaden) the existence and stability domains.

中文翻译：

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具有缺陷晶格的非线性分数薛定谔方程支持的缺陷孤子

我们在数值上研究了非线性分数薛定谔方程中缺陷孤子的存在和稳定性。对于正缺陷，缺陷孤子只存在于半无限间隙中，并且在其整个存在域中是稳定的，与Lévy指数无关。对于中等深度缺陷，缺陷孤子存在于半无限能隙和第一能隙中，其不稳定域出现在半无限能隙的低功率区。而对于足够深的缺陷，可以在第二个间隙中找到稳定的缺陷孤子。增加缺陷强度（或 Lévy 指数）将缩小（或扩大）存在域和稳定性域。