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中文摘要：
由于其在通信领域潜在的应用前景，非局域空间孤子一直是研究热点．但空间非局域暗孤子由于其边界的特殊性，对其特别是稳定性方面研究甚少．提出了非局域暗孤子稳定性分析理论，并对热非线性体介质中1＋1维基态和二阶暗孤子的稳定性进行了数值分析和研究，得到了稳定性图．从稳定性分析图可知：在热非线性体介质中，1＋1维基态暗孤子在其存在区域总是稳定的，而1＋1维二阶暗孤子是震荡不稳定的，其不稳定区域的宽度与传播常数以及介质的非局域程度有关．为了验证非局域暗孤子稳定性分析理论的正确性，对加噪声初始输入的传输进行数值模拟得到了传输图，传输图表明稳定性分析理论的正确性．
英文摘要：
Due to its future use in communication area, nonlocal spatial optical soliton has been a hot research topic recently. However, because of its special border condition, little research has been done on spatial dark solitons especially on its linear stability. In this paper, a method to analyze linear stability of nonlocal spatial dark soliton is put forward, moreover a numerical simulation and analysis is done on the linear stability of （l＋l）-dimensional fundamental and second-order dark soliton in thermal nonlinear medium. Numerical results show that （l＋l）-dimensional fundamental nonlocal dark solitons are always stable in their entire existence domain, while second-order dark solitons are oscillatorily unstable and the width of unstable domain depends on propagation constant and nonlocality degree of thermal nonlinear medium. The propagation graphs of initial input with noise addition confirms the correctness of linear stability analysis results.
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