中文摘要：

非局域体介质中的暗孤子及表面亮孤子由于在光通信领域的潜在应用而受到极大关注，然而到目前为止却没有对非局域表面暗孤子的研究．在线性介质和非局域非线性介质的分界面上，数值模拟得到了1＋1维非局域基态和二阶表面暗孤子，研究了它们的波形与传播常数和介质非局域程度的关系，基于它们的稳定性分析进行了理论推导和数值模拟．稳定性分析结果表明：1＋1维非局域基态表面暗孤子在其存在区域总是稳定的，而二阶表面暗孤子是区域不稳定的，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系，且受传播常数的影响更大．加噪声的初始输入传输图验证了稳定性分析结果的正确性．

英文摘要：

Due to their future applications in optical communication, nonlocal dark solitons in bulk medium and surface bright solitons have received much attention recently. However, nonlocal surface dark solitons have not been investigated till now. In this paper, 1＋1 dimensional nonlocal fundamental and second-order surface dark solitons have been found numerically at the interface between thermal nonlinear medium and linear medium. The relation between the Wave shape of nonlocal surface dark soliton and propagation constant and nonlocality degree is investigated. Moreover, the stability of them is analyzed theoretically. The numerical simulation results show that 1 ＋ 1 dimensional nonlocal fundamental surface dark Solitons are always stable in the domain of their existence, while second-order surface dark solitons are oscillatorily unstable and the width of unstable domain depends more greatly on propagation constant than nonlocality degree of nonlocal nonlinear medium. The figure showing the propagation, with the initial input of noise added, confirms the correctness of stability analysis results.