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By means of variational solution and direct numerical simulation of the Gross-Pitaevskii equation (GPE), we have studied the stability of matter-wave solitons in two-dimensional (2D) Bose-Einstein condensations (BECs), with 2D linear and nonlinear optical lattices (OLs). Using the static variational approach and Vakhitov-Kolokolov criterion necessary for stability, we obtain the stability condition for solitons in different combinations of OL's parameters. We show that the 2D linear and nonlinear optical lattices allow us to stabilize 2D solitons for both attractive and repulsive interactions. We also study the time-evolution problems of 2D BECs, using the time-dependent variational approach and numerical solution of GPE for 2D linear and nonlinear OLs. Very good agreement between the results corresponding to both treatments is observed.
[1] Wang D S, Hu X H, Liu W M 2010 Phys. Rev. A 82 023612
[2] Zhao W L, Dou F Q, Wang J Z 2012 Acta Phys. Sin. 61 220503 (in Chinese) [赵文垒, 豆福全, 王建忠 2012 物理学报 61 220503]
[3] Xi Y D, Wang D L, She Y C, Wang F J, Ding J W 2010 Acta Phys. Sin. 59 3720 (in Chinese) [奚玉东, 王登龙, 佘彦超, 王凤姣, 丁建文 2010 物理学报 59 3720]
[4] Chen H F, Huang J S, Xie Z W 2008 Acta Phys. Sin. 57 3435 (in Chinese) [陈海峰, 黄劲松, 谢征微 2008 物理学报 57 3435]
[5] Salerno M, Konotop V V, Bludov Y V 2008 Phys. Rev. Lett. 101 030405
[6] Wimberger S, Mannella R, Morsch O, Arimondo E, Kolovsky A R, Buchleitner A 2005 Phys. Rev. A 72 063610
[7] Anderson B P, Kasevich M A 1998 Science 282 1686
[8] Xie Y D 2012 Acta Phys. Sin. 61 210305 (in Chinese) [谢元栋 2012 物理学报 61 210305]
[9] Baizakov B B, Malomed B A, Salerno M 2003 Europhys. Lett. 63 642
[10] Baizakov B B, Malomed B A, Salerno M 2004 Phys. Rev. A 70 053613
[11] Mihalache D, Mazilu D, Lederer F, Kartashov Y V, Crasovan L C, Torner L 2004 Phys. Rev. E 70 0556039(R)
[12] Yang L Y, Fang Y C, Yang Z A 2008 Acta Phys. Sin. 57 661 (in Chinese) [杨丽云, 房永翠, 杨志安 2008 物理学报 57 661]
[13] Abdullaev F K, Kamchatnov A M, Konotop V V, Brazhnyi V A 2003 Phys. Rev. Lett. 90 230402
[14] Belmonte-Beitia J, Perez-Garcia V M, Vekslerchik V, Torres P J 2007 Phys. Rev. Lett. 98 064102
[15] Belmonte-Beitia J, Perez-Garcia V M, Vekslerchik V, Konotop V V 2008 Phys. Rev. Lett. 100 164102
[16] da Luz H L F, Abdullaev F K, Gammal A, Salerno M, Tomio L 2010 Phys. Rev. A 82 043618
[17] Sakaguchi H, Malomed B A 2005 Phys. Rev. E 72 046610
[18] Sakaguchi H, Malomed B A 2010 Phys. Rev. A 81 013624
[19] Vakhitov N G, Kolokolov A A 1973 Izv. Vyssh. Uchebn. Zaved. Radiofiz. 16 1020
[20] Cheng Y S, Adhikari S K 2011 Phys. Rev. A 83 023620
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[1] Wang D S, Hu X H, Liu W M 2010 Phys. Rev. A 82 023612
[2] Zhao W L, Dou F Q, Wang J Z 2012 Acta Phys. Sin. 61 220503 (in Chinese) [赵文垒, 豆福全, 王建忠 2012 物理学报 61 220503]
[3] Xi Y D, Wang D L, She Y C, Wang F J, Ding J W 2010 Acta Phys. Sin. 59 3720 (in Chinese) [奚玉东, 王登龙, 佘彦超, 王凤姣, 丁建文 2010 物理学报 59 3720]
[4] Chen H F, Huang J S, Xie Z W 2008 Acta Phys. Sin. 57 3435 (in Chinese) [陈海峰, 黄劲松, 谢征微 2008 物理学报 57 3435]
[5] Salerno M, Konotop V V, Bludov Y V 2008 Phys. Rev. Lett. 101 030405
[6] Wimberger S, Mannella R, Morsch O, Arimondo E, Kolovsky A R, Buchleitner A 2005 Phys. Rev. A 72 063610
[7] Anderson B P, Kasevich M A 1998 Science 282 1686
[8] Xie Y D 2012 Acta Phys. Sin. 61 210305 (in Chinese) [谢元栋 2012 物理学报 61 210305]
[9] Baizakov B B, Malomed B A, Salerno M 2003 Europhys. Lett. 63 642
[10] Baizakov B B, Malomed B A, Salerno M 2004 Phys. Rev. A 70 053613
[11] Mihalache D, Mazilu D, Lederer F, Kartashov Y V, Crasovan L C, Torner L 2004 Phys. Rev. E 70 0556039(R)
[12] Yang L Y, Fang Y C, Yang Z A 2008 Acta Phys. Sin. 57 661 (in Chinese) [杨丽云, 房永翠, 杨志安 2008 物理学报 57 661]
[13] Abdullaev F K, Kamchatnov A M, Konotop V V, Brazhnyi V A 2003 Phys. Rev. Lett. 90 230402
[14] Belmonte-Beitia J, Perez-Garcia V M, Vekslerchik V, Torres P J 2007 Phys. Rev. Lett. 98 064102
[15] Belmonte-Beitia J, Perez-Garcia V M, Vekslerchik V, Konotop V V 2008 Phys. Rev. Lett. 100 164102
[16] da Luz H L F, Abdullaev F K, Gammal A, Salerno M, Tomio L 2010 Phys. Rev. A 82 043618
[17] Sakaguchi H, Malomed B A 2005 Phys. Rev. E 72 046610
[18] Sakaguchi H, Malomed B A 2010 Phys. Rev. A 81 013624
[19] Vakhitov N G, Kolokolov A A 1973 Izv. Vyssh. Uchebn. Zaved. Radiofiz. 16 1020
[20] Cheng Y S, Adhikari S K 2011 Phys. Rev. A 83 023620
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