Matter-wave solitons and finite-amplitude Bloch waves in optical lattices with spatially modulated nonlinearity

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 82, Issue 3, 2010, Pages

  Zhang, Jie Fang ^a   Li, Yi Shen ^b   Meng, Jianping ^a   Wu, Lei ^a   Malomed, Boris A ^c  

^a ZHEJIANG NORMAL UNIVERSITY   (China)

^b UNIVERSITY OF SCIENCE AND TECHNOLOGY OF CHINA   (China)

^c TEL AVIV UNIVERSITY   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

BLOCH WAVES; BOSE-EINSTEIN CONDENSATES; DIRECT SIMULATION; EIGENVALUES; ELLIPTIC FUNCTIONS; EXACT SOLUTION; MATTER WAVE SOLITONS; NON-LINEARITY; OPTICAL LATTICES; RELAXATION METHODS; SMALL PERTURBATIONS; SOLITON SOLUTIONS; SPATIAL MODULATIONS;

CRYSTAL LATTICES; EIGENVALUES AND EIGENFUNCTIONS; OPTICAL MATERIALS; STATISTICAL MECHANICS; STEAM CONDENSERS;

SOLITONS;

EID: 77957147162     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.82.033614     Document Type: Article

References (68)

1. O. Morsch and M. Oberthaler, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.78.179 78, 179 (2006).
2. B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, J. Optics B JOBOFD 1464-4266 10.1088/1464-4266/7/5/R02 7, R53 (2005). (Pubitemid 40665898)
3. G. Agrawal, Applications of Nonlinear Fiber Optics, 2nd ed. (Academic, San Diego, 2001).
4. B. P. Anderson and M. A. Kasevich, Science SCIEAS 0036-8075 10.1126/science.282.5394.1686 282, 1686 (1998).
5. K. Berg-Sørensen and K. Mølmer, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.58.1480 58, 1480 (1998).
6. D. I. Choi and Q. Niu, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.82.2022 82, 2022 (1999).
7. B. Wu and Q. Niu, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.61. 023402 61, 023402 (2000);
8. B. Wu and Q. Niu, Phys. Rev. A 1050-2947 10.1103/PhysRevA.64.061603 64, 061603 (R) (2001);
9. B. Wu, R. B. Diener, and Q. Niu, Phys. Rev. A 1050-2947 10.1103/PhysRevA.65.025601 65, 025601 (2002).
10. J. C. Bronski, L. D. Carr, B. Deconinck, and J. N. Kutz, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.86.1402 86, 1402 (2001); (Pubitemid 32873600)
11. J. C. Bronski, L. D. Carr, B. Deconinck, J. N. Kutz, and K. Promislow, Phys. Rev. E PRLTAO 1539-3755 10.1103/PhysRevE.63.036612 63, 036612 (2001);
12. J. C. Bronski, L. D. Carr, R. Carretero-González, B. Deconinck, J. N. Kutz, and K. Promislow, Phys. Rev. E 1539-3755 10.1103/PhysRevE.64.056615 64, 056615 (2001).
13. A. Trombettoni and A. Smerzi, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.86.2353 86, 2353 (2001). (Pubitemid 32277998)
14. P. J. Y. Louis, E. A. Ostrovskaya, C. M. Savage, and Y. S. Kivshar, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.67.013602 67, 013602 (2003).
15. D. N. Neshev, T. J. Alexander, E. A. Ostrovskaya, Y. S. Kivshar, H. Martin, I. Makasyuk, and Z. Chen, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.92.123903 92, 123903 (2004);
16. Z. Chen, H. Martin, E. D. Eugenieva, J. Xu, and A. Bezryadina, Phys. Rev. Lett. 0031-9007 10.1103/PhysRevLett.92.143902 92, 143902 (2004).
17. T. Anker, M. Albiez, R. Gati, S. Hunsmann, B. Eiermann, A. Trombettoni, and M. K. Oberthaler, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.94. 020403 94, 020403 (2005). (Pubitemid 40620121)
18. G. Theocharis, D. J. Frantzeskakis, R. Carretero-González, P. G. Kevrekidis, and B. A. Malomed, Phys. Rev. E PRLTAO 1539-3755 10.1103/PhysRevE.71.017602 71, 017602 (2005). (Pubitemid 40620083)
19. R. Scharf and A. R. Bishop, Phys. Rev. E PRLTAO 1539-3755 10.1103/PhysRevE.47.1375 47, 1375 (1993);
20. B. B. Baizakov, B. A. Malomed, and M. Salerno, Eur. Phys. J. D EPJDF6 1434-6060 10.1140/epjd/e2006-00004-8 38, 367 (2006). (Pubitemid 43572630)
21. X. F. Zang, C. Jiang, and H. B. Zhu, Phys. Rev. E EPJDF6 1539-3755 10.1103/PhysRevE.80.036604 80, 036604 (2009).
22. J. Wang, J. Yang, T. J. Alexander, and Y. S. Kivshar, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.79.043610 79, 043610 (2009).
23. V. A. Brazhnyi and V. V. Konotop, Mod. Phys. Lett. B MPLBET 0217-9849 10.1142/S0217984904007190 18, 627 (2004); (Pubitemid 40292032)
24. F. Kh. Abdullaev, A. Cammal, A. M. Kamchatnov, and L. Tomio, Int. J. Mod. Phys. B IJPBEV 0217-9792 10.1142/S0217979205032279 19, 3415 (2005). (Pubitemid 41261960)
25. Emergent Nonlinear Phenomena in Bose-Einstein Condensates, ed. by, P. G. Kevrekidis,,, D. J. Frantzeskakis,, and, R. Carretero-González, (Springer, Berlin, 2008).
26. Y. Zhang and B. Wu, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.102.093905 102, 093905 (2009);
27. Y. Zhang, Z. Liang, and B. Wu, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.80.063815 80, 063815 (2009).
28. S. Inouye, M. R. Andrews, J. Stenger, H.-J. Miesner, D. M. Stamper-Kurn, and W. Ketterle, Nature (London) NATUAS 0028-0836 10.1038/32354 392, 151 (1998). (Pubitemid 28162780)
29. M. Theis, G. Thalhammer, K. Winkler, M. Hellwig, G. Ruff, R. Grimm, and J. H. Denschlag, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93.123001 93, 123001 (2004).
30. I. Towers and B. A. Malomed, J. Opt. Soc. Am. 0740-3232 10.1364/JOSAB.19.000537 19, 537 (2002).
31. F. Kh. Abdullaev, J. G. Caputo, R. A. Kraenkel, and B. A. Malomed, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.67.013605 67, 013605 (2003);
32. H. Saito and M. Ueda, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.90.040403 90, 040403 (2003).
33. G. Theocharis, P. Schmelcher, P. G. Kevrekidis, and D. J. Frantzeskakis, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.72.033614 72, 033614 (2005). (Pubitemid 41782083)
34. M. I. Rodas-Verde, H. Michinel, and V. M. Pérez-García, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.95.153903 95, 153903 (2005). (Pubitemid 41777508)
35. J. Belmonte-Beitia, V. M. Pérez-García, V. Vekslerchik, and P. J. Torres, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.98.064102 98, 064102 (2007). (Pubitemid 46220449)
36. J. Belmonte-Beitia, V. M. Pérez-García, V. Vekslerchik, and V. V. Konotop, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.100.164102 100, 164102 (2008). (Pubitemid 351590587)
37. V. M. Pérez-García, P. J. Torres, and G. D. Montesinos, SIAM J. Appl. Math. SMJMAP 0036-1399 10.1137/050643131 67, 990 (2007). (Pubitemid 47317914)
38. H. Sakaguchi and B. A. Malomed, Phys. Rev. E SMJMAP 1539-3755 10.1103/PhysRevE.73.026601 73, 026601 (2006); (Pubitemid 43287676)
39. H. Sakaguchi and B. A. Malomed, Phys. Rev. A 1050-2947 10.1103/PhysRevA.75.063825 75, 063825 (2007). (Pubitemid 47139442)
40. H. Sakaguchi and B. A. Malomed, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.81.013624 81, 013624 (2010).
41. F. K. Abdullaev and J. Garnier, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.72.061605 72, 061605 (R) (2005); (Pubitemid 43272769)
42. F. Abdullaev, A. Abdumalikov, and R. Galimzyanov, Phys. Lett. A PYLAAG 0375-9601 10.1016/j.physleta.2007.02.067 367, 149 (2007);
43. F. K. Abdullaev, A. Gammal, M. Salerno, and L. Tomio, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.77.023615 77, 023615 (2008); (Pubitemid 351393352)
44. F. K. Abdullaev, R. M. Galimzyanov, M. Brtka, and L. Tomio, Phys. Rev. E SMJMAP 1539-3755 10.1103/PhysRevE.79.056220 79, 056220 (2009).
45. G. Theocharis, P. Schmelcher, P. G. Kevrekidis, and D. J. Frantzeskakis, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.72.033614 72, 033614 (2005); (Pubitemid 41782083)
46. G. Theocharis, P. Schmelcher, P. G. Kevrekidis, and D. J. Frantzeskakis, Phys. Rev. A 1050-2947 10.1103/PhysRevA.74.053614 74, 053614 (2006). (Pubitemid 44749243)
47. Y. Sivan, G. Fibich, and M. I. Weinstein, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.97.193902 97, 193902 (2006); (Pubitemid 44730143)
48. Y. Sivan, G. Fibich, B. Ilan, and M. I. Weinstein, Phys. Rev. E PRLTAO 1539-3755 10.1103/PhysRevE.78.046602 78, 046602 (2008);
49. Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Opt. Lett. OPLEDP 0146-9592 10.1364/OL.33.001747 33, 1747 (2008);
50. Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Opt. Lett. 0146-9592 10.1364/OL.33.002173 33, 2173 (2008);
51. Y. V. Kartashov, B. A. Malomed, V. A. Vysloukh, and L. Torner, Opt. Lett. 0146-9592 10.1364/OL.34.000770 34, 770 (2009);
52. C. Hang, V. V. Konotop, and G. Huang, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.79.033826 79, 033826 (2009).
53. Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Opt. Lett. OPLEDP 0146-9592 10.1364/OL.33.001747 33, 1747 (2008);
54. Y. V. Kartashov, V. A. Vysloukh, A. Szameit, F. Dreisow, M. Heinrich, S. Nolte, A. Tünnermann, T. Pertsch, and L. Torner, Opt. Lett. 0146-9592 10.1364/OL.33.001120 33, 1120 (2008);
55. Y. V. Kartashov, B. A. Malomed, V. A. Vysloukh, and L. Torner, Opt. Lett. 0146-9592 10.1364/OL.34.003625 34, 3625 (2009).
56. C. H. Tsang, B. Malomed, and K. W. Chow, DCDS-S (to be published).
57. B. A. Malomed, Soliton Management in Periodic Systems (Springer, New York, 2006).
58. L. Salasnich, A. Parola, and L. Reatto, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.65.043614 65, 043614 (2002);
59. A. E. Muryshev, G. V. Shlyapnikov, W. Ertmer, K. Sengstock, and M. Lewenstein, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.89.110401 89, 110401 (2002);
60. A. Muñoz Mateo and V. Delgado, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.77.013617 77, 013617 (2008). (Pubitemid 351161682)
61. V. P. Ermakov, Univ. Izv. Kiev 20, 1 (1880);
62. E. Pinney, Proc. Am. Math. Soc. 0002-9939 10.1090/S0002-9939-1950- 0037979-4 1, 681 (1950).
63. M. Abramowitz and I. Stegun, Handbook of Mathematical Functions (Dover, New York, 1965).
64. D. Frenkel and R. Portugal, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/34/17/302 34, 3541 (2001).
65. T. Anker, M. Albiez, R. Gati, S. Hunsmann, B. Eiermann, A. Trombettoni, and M. K. Oberthaler, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.94. 020403 94, 020403 (2005); (Pubitemid 40620121)
66. T. J. Alexander, E. A. Ostrovskaya, and Y. S. Kivshar, Phys. Rev. Lett. 0031-9007 10.1103/PhysRevLett.96.040401 96, 040401 (2006). (Pubitemid 43270835)
67. T. J. Alexander and Y. S. Kivshar, Appl. Phys. B APBOEM 0946-2171 10.1007/s00340-005-2071-3 82, 203 (2006). (Pubitemid 43078529)
68. M. G. Vakhitov and A. A. Kolokolov, Sov. J. Radiophys. Quantum Electron. RPQEAC 0033-8443 10.1007/BF01031343 16, 783 (1973).