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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 (1+1)-dimensional fundamental and second-order dark soliton in thermal nonlinear medium. Numerical results show that (1+1)-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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Keywords:
- nonlocal /
- linear stability /
- dark solitons
[1] Hu W, Zhang T, Guo Q, Xuan L, Lan S 2006 Appl. Phys. Lett. 89 071111
[2] Cao J N, Guo Q 2005 Acta Phys. Sin. 54 3688 (in Chinese) [曹觉能, 郭旗2005 物理学报 54 3688]
[3] Jiang D S, Ouyang S G, She W L 2004 Acta Phys. Sin. 53 3777 (in Chinese) [江德生, 欧阳世根, 佘卫龙 2004 物理学报 53 3777]
[4] Xu Z Y, Kartashov Y V, Torner L 2005 Opt. Lett. 30 3171
[5] Dong L W, Ye F W 2010 Phys. Rev. A 81 013815
[6] Kartashov Y V, Vysloukh V A, Torner L 2009 Opt. Lett. 34 283
[7] Kartashov Y V, Torner L 2006 Opt. Lett. 31 2172
[8] Yang Z J, Ma X K, Lu D Q, Zheng Y Z, Gao X H, Hu W 2011 Opt. Express 19 4890
[9] Ye F W, Kartashov Y V, Torner L 2008 Phys. Rev. A 77 033829
[10] Ma X K, Yang Z J, Lu D Q, Guo Q, Hu W 2011 Phys. Rev. A 83 033829
[11] Ma X K, Yang Z J, Lu D Q, Guo Q, Hu W 2011 Phys. Rev. A 83 053831
[12] Ma X K, Yang Z J, Lu D Q, Guo Q, Hu W 2011 Phys. Rev. A 83 033802
[13] Dreischuh A, Neshev D N, Petersen D E, Bang O, Krolikowski W 2006 Phys. Rev. Lett. 96 043901
[14] Nikolov N I, Neshev D, Krolikowski W, Bang O, Rasmussen J J, Christiansen P L 2004 Opt. Lett. 29 286
[15] Fischer R, Neshev D N, Krolikowski W, Kivshar Y S, Iturbe-Castillo D, Chavez-Cerda S, Meneghetti M R, Caetano D P, Hickman J M 2006 Opt. Lett. 31 3010
[16] Kong Q, Wang Q, Bang O, Krolikowski W 2010 Opt. Lett. 35 2152
[17] Gao X H, Yang Z J, Zhou L H, Zheng Y Z, Lu D Q, Hu W 2011 Acta Phys. Sin. 60 084213 (in Chinese) [高星辉, 杨振军, 周罗红, 郑一周, 陆大全, 胡巍 2011 物理学报 60 084213]
[18] Armaroli A, Trillo S, Fratalocchi A 2009 Phys. Rev. A 80 053803
[19] Krolikowski W, Bang O, Rasmussen J J, Wyller J 2001 Phys. Rev. E 64 016612
[20] Wyller J, Krolikowski W, Bang O, Rasmussen J J 2002 Phys. Rev. E 66 066615
[21] Krolikowski W, Bang O, Rasmussen J J, Wyller J 2001 Phys. Rev. E 64 016612
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[1] Hu W, Zhang T, Guo Q, Xuan L, Lan S 2006 Appl. Phys. Lett. 89 071111
[2] Cao J N, Guo Q 2005 Acta Phys. Sin. 54 3688 (in Chinese) [曹觉能, 郭旗2005 物理学报 54 3688]
[3] Jiang D S, Ouyang S G, She W L 2004 Acta Phys. Sin. 53 3777 (in Chinese) [江德生, 欧阳世根, 佘卫龙 2004 物理学报 53 3777]
[4] Xu Z Y, Kartashov Y V, Torner L 2005 Opt. Lett. 30 3171
[5] Dong L W, Ye F W 2010 Phys. Rev. A 81 013815
[6] Kartashov Y V, Vysloukh V A, Torner L 2009 Opt. Lett. 34 283
[7] Kartashov Y V, Torner L 2006 Opt. Lett. 31 2172
[8] Yang Z J, Ma X K, Lu D Q, Zheng Y Z, Gao X H, Hu W 2011 Opt. Express 19 4890
[9] Ye F W, Kartashov Y V, Torner L 2008 Phys. Rev. A 77 033829
[10] Ma X K, Yang Z J, Lu D Q, Guo Q, Hu W 2011 Phys. Rev. A 83 033829
[11] Ma X K, Yang Z J, Lu D Q, Guo Q, Hu W 2011 Phys. Rev. A 83 053831
[12] Ma X K, Yang Z J, Lu D Q, Guo Q, Hu W 2011 Phys. Rev. A 83 033802
[13] Dreischuh A, Neshev D N, Petersen D E, Bang O, Krolikowski W 2006 Phys. Rev. Lett. 96 043901
[14] Nikolov N I, Neshev D, Krolikowski W, Bang O, Rasmussen J J, Christiansen P L 2004 Opt. Lett. 29 286
[15] Fischer R, Neshev D N, Krolikowski W, Kivshar Y S, Iturbe-Castillo D, Chavez-Cerda S, Meneghetti M R, Caetano D P, Hickman J M 2006 Opt. Lett. 31 3010
[16] Kong Q, Wang Q, Bang O, Krolikowski W 2010 Opt. Lett. 35 2152
[17] Gao X H, Yang Z J, Zhou L H, Zheng Y Z, Lu D Q, Hu W 2011 Acta Phys. Sin. 60 084213 (in Chinese) [高星辉, 杨振军, 周罗红, 郑一周, 陆大全, 胡巍 2011 物理学报 60 084213]
[18] Armaroli A, Trillo S, Fratalocchi A 2009 Phys. Rev. A 80 053803
[19] Krolikowski W, Bang O, Rasmussen J J, Wyller J 2001 Phys. Rev. E 64 016612
[20] Wyller J, Krolikowski W, Bang O, Rasmussen J J 2002 Phys. Rev. E 66 066615
[21] Krolikowski W, Bang O, Rasmussen J J, Wyller J 2001 Phys. Rev. E 64 016612
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