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Using variational and numerical solutions of the mean field Gross-Pitaevskii equation, we investigate the stabilities of nonrotating and vortex solitons in Bessel optical lattice by spatial modulation of the nonlinearity(nonlinear optical lattice). It is demonstrated that there exist the stable matter-wave solitons in a combination of optical lattices with linear Bessel optical lattices and nonlinear optical lattice. Using the time-dependent variational approach, we derive the odinary differential equations for the time evolutions of the width and phase of solitons. Through an effective potential, we obtain the stable criteria for all kinds of combinations of the system parameters. We perform direct numerical simulations to support our analytical results, and find that they are in goog agreement.
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Keywords:
- Bessel optical lattice /
- nonlinear optical lattices /
- solitons /
- stability
[1] Morsh O, Oberthaler M 2006 Rev. Mod. Phys. 78 179
[2] Brazhnyi V A, Konotop V V 2004 Mod. Phys. Lett. B 18 627
[3] Yang H S, Xu Z J, Cheng C, Wu Q, Xiong H W 2004 Acta Phys. Sin. 53 2835 (in Chinese) [杨欢耸, 徐志君, 程成, 武强, 熊宏伟 2004 53 2835]
[4] 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 59 3720]
[5] Vogels J M, Freeland R S, Tsai C C, Verhaar B J, Heinzen D J 2000 Phys. Rev. A 61 043407
[6] Modugno G, Modugno M, Riboli F, Roati G, Inguscio M 2002 Phys. Rev. Lett. 89 190404
[7] da Luz H L F, Abdullaev F K, Gammal A, Sarlerno M, Tomio L 2010 Phys. Rev. A 82 043618
[8] Ji S T, Yan P G, Liu X S 2014 Chin. Phys. B 23 030311
[9] Li Z J, Hai W H, Deng Y 2013 Chin. Phys. B 22 090505
[10] Wang X M, Li Q Y, Li Z D 2013 Chin. Phys. B 22 050311
[11] Baizakov B B, Malomed B A, Salerno M 2006 Phys. Rev. E 74 066615
[12] Baizakov B B, Malomed B A, Salerno M 2003 Europhys. Lett. 63 642
[13] Trombettoni A, Smerzi A 2001 Phys. Rev. Lett. 86 2353
[14] Abdullaev F K H, Baizakov B B, Darmanyan S A, Konotop V V, Salerno M 2001 Phys. Rev. A 64 043606
[15] Sakaguchi H, Malomed B A 2005 Phys. Rev. E 72 046610
[16] Abdullaev F K H, Garnier J 2005 Phys. Rev. A 72 061605
[17] Abdullaev F, Abdumalikov A, Galimzyanov R 2007 Phys. Lett. A 367 149
[18] Chen H J, Li X F 2013 Acta Phys. Sin. 62 070302 (in Chinese) [陈海军, 李向富 2013 62 070302]
[19] Dong L W, Wang J D, Wang H, Yin G Y 2009 Phys. Rev. A 79 013807
[20] Kartashov Y V, Dholakia K, Egorov A E, Vysloukh V A, Torner L 2009 Phys. Rev. E 70 065602
[21] Kartashov Y V, Vysloukh V A, Torner L 2004 Phys. Rev. Lett. 93 093904
[22] Kartashov Y V, Vysloukh V A, Torner L 2009 Phys. Rev. E 71 036621
[23] Adhikaria S K 2004 Phys. Rev. E 65 016703
[24] Adhikaria S K 2004 Phys. Rev. A 69 3613-1
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[1] Morsh O, Oberthaler M 2006 Rev. Mod. Phys. 78 179
[2] Brazhnyi V A, Konotop V V 2004 Mod. Phys. Lett. B 18 627
[3] Yang H S, Xu Z J, Cheng C, Wu Q, Xiong H W 2004 Acta Phys. Sin. 53 2835 (in Chinese) [杨欢耸, 徐志君, 程成, 武强, 熊宏伟 2004 53 2835]
[4] 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 59 3720]
[5] Vogels J M, Freeland R S, Tsai C C, Verhaar B J, Heinzen D J 2000 Phys. Rev. A 61 043407
[6] Modugno G, Modugno M, Riboli F, Roati G, Inguscio M 2002 Phys. Rev. Lett. 89 190404
[7] da Luz H L F, Abdullaev F K, Gammal A, Sarlerno M, Tomio L 2010 Phys. Rev. A 82 043618
[8] Ji S T, Yan P G, Liu X S 2014 Chin. Phys. B 23 030311
[9] Li Z J, Hai W H, Deng Y 2013 Chin. Phys. B 22 090505
[10] Wang X M, Li Q Y, Li Z D 2013 Chin. Phys. B 22 050311
[11] Baizakov B B, Malomed B A, Salerno M 2006 Phys. Rev. E 74 066615
[12] Baizakov B B, Malomed B A, Salerno M 2003 Europhys. Lett. 63 642
[13] Trombettoni A, Smerzi A 2001 Phys. Rev. Lett. 86 2353
[14] Abdullaev F K H, Baizakov B B, Darmanyan S A, Konotop V V, Salerno M 2001 Phys. Rev. A 64 043606
[15] Sakaguchi H, Malomed B A 2005 Phys. Rev. E 72 046610
[16] Abdullaev F K H, Garnier J 2005 Phys. Rev. A 72 061605
[17] Abdullaev F, Abdumalikov A, Galimzyanov R 2007 Phys. Lett. A 367 149
[18] Chen H J, Li X F 2013 Acta Phys. Sin. 62 070302 (in Chinese) [陈海军, 李向富 2013 62 070302]
[19] Dong L W, Wang J D, Wang H, Yin G Y 2009 Phys. Rev. A 79 013807
[20] Kartashov Y V, Dholakia K, Egorov A E, Vysloukh V A, Torner L 2009 Phys. Rev. E 70 065602
[21] Kartashov Y V, Vysloukh V A, Torner L 2004 Phys. Rev. Lett. 93 093904
[22] Kartashov Y V, Vysloukh V A, Torner L 2009 Phys. Rev. E 71 036621
[23] Adhikaria S K 2004 Phys. Rev. E 65 016703
[24] Adhikaria S K 2004 Phys. Rev. A 69 3613-1
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