Dark solitons in atomic Bose-Einstein condensates: From theory to experiments

Journal of Physics A: Mathematical and Theoretical

Volumn 43, Issue 21, 2010, Pages

  Frantzeskakis, D J ^a  

^a UNIVERSITY OF ATHENS   (Greece)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 77952576864     PISSN: 17518113     EISSN: 17518121     Source Type: Journal    
DOI: 10.1088/1751-8113/43/21/213001     Document Type: Review

References (396)

1. Emplit Ph, Hamaide J P, Reynaud F, Froehly C and Barthelemy A 1987 Opt. Commun. 62 374
2. Krökel D, Halas N J, Giuliani G and Grischkowsky D 1988 Phys. Rev. Lett. 60 29
3. Swartzlander G A Jr, Andersen D R, Regan J J, Yin H and Kaplan A E 1991 Phys. Rev. Lett. 66 1583
4. Allan G R, Skinner S R, Andersen D R and Smirl A L 1991 Opt. Lett. 16 156
5. Denardo B, Wright W, Putterman S and Larraza A 1990 Phys. Rev. Lett. 64 1518
6. Denardo B, Galvin B, Greenfield A, Larraza A, Putterman S and Wright W 1992 Phys. Rev. Lett. 68 1730
7. Chen M, Tsankov M A, Nash J M and Patton C E 1993 Phys. Rev. Lett. 70 1707
8. Heidemann R, Zhdanov S, Sütterlin R, Thomas H M and Morfill G E 2009 Phys. Rev. Lett. 102 135002
9. Tsuzuki T 1971 J. Low Temp. Phys. 4 441
10. Pitaevskii L P 1961 Zh. Eksp. Teor. Fiz. 40 646
11. Pitaevskii L P 1961 Sov. Phys.-JETP 13 451 (Engl. Transl.)
12. Gross E P 1961 Nuovo Cimento 20 454
13. Zakharov V E and Shabat A B 1971 Zh. Eksp. Teor. Fiz. 61 118
14. Zakharov V E and Shabat A B 1971 Sov. Phys.-JETP 34 62 (Engl. Transl.)
15. Zakharov V E and Shabat A B 1973 Zh. Eksp. Teor. Fiz. 64 1627
16. Zakharov V E and Shabat A B 1973 Sov. Phys.-JETP 37 823 (Engl. Transl.)
17. Ablowitz M J and Segur H 1981 Solitons and the Inverse Scattering Transform (Philadelphia, PA: SIAM)
18. Gredeskul S A and Kivshar Yu S 1989 Phys. Rev. Lett. 62 977
19. Gredeskul S A, Kivshar Yu S and Yanovskaya M V 1990 Phys. Rev. A 41 3994
20. Zhao W and Bourkoff E 1989 Opt. Lett. 14 703
21. Zhao W and Bourkoff E 1989 Opt. Lett. 14 1371
22. Konotop V V and Vekslerchik V E 1991 J. Phys. A: Math. Gen. 24 767
23. Slavin A N, Kivshar Yu S, Ostrovskaya E A and Benner H 1999 Phys. Rev. Lett. 82 2583
24. Blow K J and Doran N J 1985 Phys. Lett. A 107 55
25. Akhmediev N N and Ankiewich A 1993 Phys. Rev. A 47 3213
26. Gagnon L 1993 J. Opt. Soc. Am. B 10 469
27. Thurston R N and Weiner A M 1991 J. Opt. Soc. Am. B 8 471
28. Lerner L, Mitchell D J and Snyder A W 1994 Opt. Lett. 19 1302
29. Kivshar Yu S and Królikowski W 1995 Opt. Commun. 114 353
30. Foursa D and Emplitt P 1996 Phys. Rev. Lett. 77 4011
31. Uzunov I M and Gerdjikov V S 1993 Phys. Rev. A 47 1582
32. Kivshar Yu S and Yang X 1994 Phys. Rev. E 49 1657
33. Konotop V V and Vekslerchik V E 1994 Phys. Rev. E 49 2397
34. Chen X J, Chen Z D and Huang N N 1998 J. Phys. A: Math. Gen. 31 6929
35. Huang N N, Chi S and Chen X J 1999 J. Phys. A: Math. Gen. 32 3939
36. Lashkin V M 2004 Phys. Rev. E 70 066620
37. Hasegawa A and Tappert F 1973 Appl. Phys. Lett. 23 171
38. Kivshar Yu S and Luther-Davies B 1998 Phys. Rep. 298 81
39. Kivshar Yu S and Agrawal G P 2003 Optical Solitons: From Fibers to Photonic Crystals (New York: Academic)
40. Anderson M H J, Ensher J R, Matthews M R, Wieman C E and Cornell E A 1995 Science 269 198
41. Davis K B, Mewes M-O, Andrews M R, van Druten N J, Durfee D S, Kurn D M and Ketterle W 1995 Phys. Rev. Lett. 75 3969
42. Bradley C C, Sackett C A, Tollett J J and Hulet R G 1995 Phys. Rev. Lett. 75 1687
43. Bradley C C, Sackett C A, Tollett J J and Hulet R G 1997 Phys. Rev. Lett. 79 1170
44. Cornell E A and Wieman C E 2002 Rev. Mod. Phys. 74 875
45. Ketterle W 2002 Rev. Mod. Phys. 74 1131
46. Pethick C J and Smith H 2001 Bose-Einstein Condensation in Dilute Gases (Cambridge: Cambridge University Press)
47. Pitaevskii L P and Stringari S 2003 Bose-Einstein Condensation (Oxford: Oxford University Press)
48. Kevrekidis P G, Frantzeskakis D J and Carretero-Gonzlez R (ed) 2007 Emergent Nonlinear Phenomena in Bose-Einstein Condensates: Theory and Experiment (Springer Series on Atomic, Optical, and Plasma Physics vol 45) (Heidelberg: Springer)
49. Carretero-Gonzlez R, Frantzeskakis D J and Kevrekidis P G 2008 Nonlinearity 21 R139
50. Burger S, Bongs K, Dettmer S, Ertmer W, Sengstock K, Sanpera A, Shlyapnikov G V and Lewenstein M 1999 Phys. Rev. Lett. 83 5198
51. Denschlag J et al 2000 Science 287 97
52. Dutton Z, Budde M, Slowe C and Hau L V 2001 Science 293 663
53. Anderson B P, Haljan P C, Regal C A, Feder D L, Collins L A, Clark C W and Cornell E A 2001 Phys. Rev. Lett. 86 2926
54. Bongs K, Burger S, Dettmer S, Hellweg D, Arlt J, Ertmer W and Sengstock K 2001 C. R. Acad. Sci. Paris 2 671
55. Kivshar Yu S, Alexander T J and Turitsyn S K 2001 Phys. Lett. A 278 225
56. Kevrekidis P G, Konotop V V, Rodrigues A and Frantzeskakis D J 2005 J. Phys. B: At. Mol. Opt. Phys. 38 1173
57. Landau L D and Lifshitz E M 1987 Quantum Mechanics (Oxford: Pergamon)
58. Pismen L M 1999 Vortices in Nonlinear fields (Oxford: Clarendon)
59. Kibble T W B 1976 J. Phys. A: Math. Gen. 9 1387
60. Zurek W H 1985 Nature 317 505
61. Weiler C N, Neely T W, Scherer D R, Bradley A S, Davis M J and Anderson B P 2008 Nature 455 948
62. Zurek W H 2009 Phys. Rev. Lett. 102 105702
63. Damski B and Zurek W H 2010 Phys. Rev. Lett. (arXiv:0909.0761) at press
64. Anglin J 2008 Nature Phys. 4 437
65. Negretti A and Henkel C 2004 J. Phys. B: At. Mol. Opt. Phys. 37 L385
66. Negretti A, Henkel C and Mølmer K 2008 Phys. Rev. A 78 023630
67. Jo G-B, Choi J-H, Christensen C A, Pasquini T A, Lee Y-R, Ketterle W and Pritchard D E 2007 Phys. Rev. Lett. 98 180401
68. Scott R G, Judd T E and Fromhold T M 2008 Phys. Rev. Lett. 100 100402
69. Scott R G, Martin A M, Fromhold T M, Bujkiewicz S, Sheard F W and Leadbeater M 2003 Phys. Rev. Lett. 90 110404
70. Ginsberg N J, Brand J and Hau L V 2005 Phys. Rev. Lett. 94 040403
71. Engels P and Atherton C 2007 Phys. Rev. Lett. 99 160405
72. Becker C, Stellmer S, Soltan-Panahi P, Dörscher S, Baumert M, Richter E-M, Kronjäger J, Bongs K and Sengstock K 2008 Nature Phys. 4 496
73. Stellmer S, Becker C, Soltan-Panahi P, Richter E-M, Dörscher S, Baumert M, Kronjäger J, Bongs K and Sengstock K 2008 Phys. Rev. Lett. 101 120406
74. Weller A, Ronzheimer J P, Gross C, Frantzeskakis D J, Theocharis G, Kevrekidis P G, Esteve J and Oberthaler M K 2008 Phys. Rev. Lett. 101 130401
75. Shomroni I, Lahoud E, Levy S and Steinhauer J 2008 Nature Phys. 5 193
76. Theocharis G, Weller A, Ronzheimer J P, Gross C, Oberthaler M K, Kevrekidis P G and Frantzeskakis D J 2009 arXiv:0909.2122
77. Chang J J, Engels P and Hoefer M A 2008 Phys. Rev. Lett. 101 170404
78. Proukakis N P, Parker N G, Frantzeskakis D J and Adams C S 2004 J. Opt. B: Quantum Semiclass. Opt. 6 S380
79. Fetter A L and Svidzinksy A A 2001 J. Phys.: Condens. Matter 13 R135
80. Kevrekidis P G, Frantzeskakis D J, Carretero-Gonzlez R and Kevrekidis I G 2004 Mod. Phys. Lett. B 18 1481
81. Komineas S 2007 Eur. Phys. J. Spec. Top. 147 133
82. Barenghi C F and R J Donnelly R J 2009 Fluid Dyn. Res. 41 051401
83. Bloch I, Dalibard J and Zwerger W 2008 Rev. Mod. Phys. 80 885
84. Bogoliubov N N 1947 J. Phys. (Moscow) 11 23
85. Lieb E H, Seiringer R and Yngvason J 2000 Phys. Rev. A 61 043602
86. Lieb E H, Seiringer R, Solovej J P and Yngvason J 2005 The Mathematics of the Bose Gas and Its Condensation (Oberwolfach Seminar Series vol 34) (Basel: Birkhauser)
87. Elgart A, Erdös L, Schlein B and Yau H T 2006 Arch. Ration. Mech. Anal. 179 265
88. Kevrekidis P G and Frantzeskakis D J 2004 Mod. Phys. Lett. B 18 173
89. Strecker K E, Partridge G B, Truscott A G and Hulet R G 2002 Nature 417 150
90. Khaykovich L, Schreck F, Ferrari G, Bourdel T, Cubizolles J, Carr L D, Castin Y and Salomon C 2002 Science 296 1290
91. Cornish S L, Thompson S T and Wieman C E 2006 Phys. Rev. Lett. 96 170401
92. Abdullaev F Kh, Gammal A, Kamchatnov A M and Tomio L 2005 Int. J. Mod. Phys. B 19 3415
93. Menotti C and Stringari S 2002 Phys. Rev. A 66 043610
94. Pérez-García V M, Michinel H and Herrero H 1998 Phys. Rev. A 57 3837
95. Jackson A D, Kavoulakis G M and Pethick C J 1998 Phys. Rev. A 58 2417
96. Muryshev A E, Shlyapnikov G V, Ertmer W, Sengstock K and Lewenstein M 2002 Phys. Rev. Lett. 89 110401
97. Salasnich L, Parola A and Reatto L 2002 Phys. Rev. A 65 043614
98. Gerbier F 2004 Europhys. Lett. 66 771
99. Mũoz Mateo A and Delgado V 2007 Phys. Rev. A 75 063610
100. Mũoz Mateo A and Delgado V 2008 Phys. Rev. A 77 013617
101. Mũoz Mateo A and Delgado V 2009 Ann. Phys. 324 709
102. Theocharis G, Kevrekidis P G, Oberthaler M K and Frantzeskakis D J 2007 Phys. Rev. A 76 045601
103. Moerdijk A J, Boesten H M J M and Verhaar B J 1996 Phys. Rev. A 53 916
104. Köhler T 2002 Phys. Rev. Lett. 89 210404
105. Tonks L 1936 Phys. Rev. 50 955
106. Girardeau M 1060 J. Math. Phys. (NY) 1 516
107. Paredes B, Widera A, Murg V, Mandel O, Folling S, Cirac I, Shlyapnikov G V, Häansch T W and Bloch I 2004 Nature 429 277
108. Kinoshita T, Wenger T and Weiss D S 2004 Science 305 1125
109. Kolomeisky E B and Straley J P 1992 Phys. Rev. B 46 11749
110. Kolomeisky E B, Newman T J, Straley J P and Qi X 2000 Phys. Rev. Lett. 85 1146
111. Girardeau M D and Wright E M 2000 Phys. Rev. Lett. 84 5691
112. Dunjko V, Lorent V and Olshanii M 2001 Phys. Rev. Lett. 86 5413
113. hberg P and Santos L 2002 Phys. Rev. Lett. 89 240402
114. Lieb E H, Seiringer R and Yngvason J 2003 Phys. Rev. Lett. 91 150401
115. Abdullaev F Kh, Nigmanov N K and Tsoy E N 1997 Phys. Rev. E 56 3638
116. Kamchatnov A M, Kraenkel R A and Umarov B A 2002 Phys. Rev. E 66 036609
117. Brazhnyi V A and Kamchatnov A M 2003 Phys. Rev. A 68 043614
118. Kivshar Yu S 1989 J. Phys. A: Math. Gen. 22 337
119. Weiner A M, Heritage J P, Hawkins R J, Thurston R N, Kirsschner E M, Learid D E and Tomlinson W J 1988 Phys. Rev. Lett. 61 2445
120. Barashenkov I V and Panova E Y 1993 Physica D 69 114
121. Barashenkov I V and Harin A O 1994 Phys. Rev. Lett. 72 1575
122. Fedichev P O, Muryshev A E and Shlyapnikov G V 1999 Phys. Rev. A 60 3220
123. Jeffrey A and Kawahara T 1982 Asymptotic Methods in Nonlinear Wave Theory (Boston, MA: Pitman)
124. Infeld E and Rowlands G 1990 Nonlinear Waves, Solitons, and Chaos (Cambridge: Cambridge University Press)
125. Zakharov V E and Kuznetsov E A 1986 Physica D 18 445
126. Bass F G, Konotop V V and Puzenko S A 1992 Phys. Rev. A 46 4185
127. Kivshar Yu S and Afanasjev V V 1991 Phys. Rev. A 44 R1446
128. Frantzeskakis D J 1996 J. Phys. A: Math. Gen. 29 3631
129. Leblond H 2008 J. Phys. B: At. Mol. Opt. Phys. 41 043001
130. Huang G X, Makarov V A and Velarde M G 2003 Phys. Rev. A 67 023604
131. Huang G X, Deng L and Hang C 2005 Phys. Rev. E 72 036621
132. Brazhnyi V A and Konotop V V 2005 Phys. Rev. E 72 026616
133. Nistazakis H E, Frantzeskakis D J, Kevrekidis P G, Malomed B A and Carretero-Gonzlez R 2008 Phys. Rev. A 77 033612
134. Aguero M, Frantzeskakis D J and Kevrekidis P G 2006 J. Phys. A: Math. Gen. 39 7705
135. Dobrek L, Gajda M, Lewenstein M, Sengstock K, Birkl G and Ertmer W 1999 Phys. Rev. A 60 R3381
136. Wu B, Liu J and Niu Q 2002 Phys. Rev. Lett. 88 034101
137. Shvartsburg A B, Stenflo L and Shukla P K 2002 Phys. Scr. 65 164
138. Grimm R, Weidemüller M and Ovchinnikov Y B 2000 Adv. At. Mol. Opt. Phys. 42 95
139. Burger S, Carr L D, hberg P, Sengstock K and Sanpera A 2002 Phys. Rev. A 65 043611
140. Carr L D, Brand J, Burger S and Sanpera A 2001 Phys. Rev. A 63 051601
141. Busch Th and Anglin J R 2001 Phys. Rev. Lett. 87 010401
142. Matthews M R, Anderson B P, Haljan P C, Hall D S, Wieman C E and Cornell E A 1999 Phys. Rev. Lett. 83 2498
143. Matthews M R, Anderson B P, Haljan P C, Hall D S, Holland M J, Williams J E, Wieman C E and Cornell E A 1999 Phys. Rev. Lett. 83 3358
144. Huang G, Velarde M G and Makarov V A 2001 Phys. Rev. A 64 013617
145. Alfimov G L and Zezyulin D A 2007 Nonlinearity 20 2075
146. Kivshar Yu S and Malomed B A 1989 Rev. Mod. Phys. 61 763
147. Parker N G, Proukakis N P, Leadbeater M and Adams C S 2003 Phys. Rev. Lett. 90 220401
148. Parker N G, Proukakis N P, Leadbeater M and Adams C S 2003 J. Phys. B: At. Mol. Opt. Phys. 36 2891
149. Reinhardt W P and Clark C W 1997 J. Phys. B: At. Mol. Opt. Phys. 30 L785
150. Morgan S A, Ballagh R J and Burnett K 1997 Phys. Rev. A 55 4338
151. Jackson A D, Kavoulakis G M and Pethick C J 1998 Phys. Rev. A 58 2417
152. Hong T, Wang Y Z and Huo Y S 1998 Phys. Rev. A 58 3128
153. Chen X-J, Zhang J-Q and Wong H-C 2000 Phys. Lett. A 268 306
154. Busch Th and Anglin J R 2000 Phys. Rev. Lett. 84 2298
155. Muryshev A E, van Linden van den Heuvel H B and Shlyapnikov G V 1999 Phys. Rev. A 60 R2665
156. Frantzeskakis D J, Theocharis G, Diakonos F K, Schmelcher P and Kivshar Yu S 2002 Phys. Rev. A 66 053608
157. Huang G, Szeftel J and Zhu S 2002 Phys. Rev. A 65 053605
158. Brazhnyi V A and Konotop V V 2003 Phys. Rev. A 68 043613
159. Konotop V V and Pitaevskii L 2004 Phys. Rev. Lett. 93 240403
160. Brazhnyi V A, Konotop V V and Pitaevskii L P 2006 Phys. Rev. A 73 053601
161. Frantzeskakis D J, Proukakis N P and Kevrekidis P G 2004 Phys. Rev. A 70 015601
162. Frantzeskakis D J, Kevrekidis P G and Proukakis N P 2007 Phys. Lett. A 364 129
163. Girardeau M D and Wright E M 2000 Phys. Rev. Lett. 84 5691
164. Girardeau M D 2003 Phys. Rev. Lett. 91 040401
165. gren M, Kavoulakis G M and Jackson A D 2005 Phys. Rev. A 72 021603
166. Baizakov B B, Abdullaev F Kh, Malomed B A and Salerno M 2009 J. Phys. B: At. Mol. Opt. Phys. 42 175302
167. Girardeau M D and Minguzzi A 2009 Phys. Rev. A 79 033610
168. Theocharis G, Schmelcher P, Oberthaler M K, Kevrekidis P G and Frantzeskakis D J 2005 Phys. Rev. A 72 023609
169. Bilas N and Pavloff N 2005 Phys. Rev. A 72 033618
170. Pelinovsky D E, Frantzeskakis D J and Kevrekidis P G 2005 Phys. Rev. E 72 016615
171. Pelinovsky D E and Kevrekidis P G 2008 Z. Angew. Math. Phys. 59 559
172. Kamchatnov A M and Salerno M 2009 J. Phys. B: At. Mol. Opt. Phys. 42 185303
173. Asano N 1974 Prog. Theor. Phys. Suppl. 55 52
174. Ko K and Kuehl H H 1978 Phys. Rev. Lett. 40 233
175. Karpman V I and Maslov E M 1982 Phys. Fluids 25 1686
176. Busch Th and Huyet G 2003 J. Phys. B: At. Mol. Opt. Phys. 36 2553
177. Feder D L, Pindzola M S, Collins L A, Schneider B I and Clark C W 2000 Phys. Rev. A 62 053606
178. Brand J and Reinhardt W P 2002 Phys. Rev. A 65 043612
179. Dziarmaga J and Sacha K 2002 Phys. Rev. A 66 043620
180. Kohn W 1961 Phys. Rev. 123 1242
181. Dobson J F 1994 Phys. Rev. Lett. 73 2244
182. MacKay R S 1987 Hamiltonian Dynamical Systems ed R S MacKay and J Meiss (Bristol: Hilger)
183. Kapitula T, Kevrekidis P G and Sandstede B 2004 Physica D 195 263
184. Fedichev P O, Shlyapnikov G V and Walraven J T M 1998 Phys. Rev. Lett. 80 2269
185. Wu B and Niu Q 2003 New J. Phys. 5 104
186. Law C K, Leung P T and Chu M-C 2002 J. Phys. B: At. Mol. Opt. Phys. 35 3583
187. Kapitula T and Kevrekidis P G 2005 Chaos 15 037114
188. Carr L D, Kutz J N and Reinhardt W P 2001 Phys. Rev. E 63 066604
189. Zezyulin D A, Alfimov G L, Konotop V V and Pérez-Garcia V M 2008 Phys. Rev. A 78 013606
190. Radouani A 2004 Phys. Rev. A 70 013602
191. Bilas N and Pavloff N 2005 Phys. Rev. Lett. 95 130403
192. Sacha K, Müller C A, Delande D and Zakrzewski J 2009 Phys. Rev. Lett. 103 210402
193. Parker N G, Proukakis N P and Adams C S 2010 Phys. Rev. A 81 033606
194. Parker N G, Proukakis N P, Barenghi C F and Adams C S 2004 J. Phys. B: At. Mol. Opt. Phys. 37 S175
195. Theocharis G, Frantzeskakis D J, Kevrekidis P G, Carretero-Gonzlez R and Malomed B A 2005 Math. Comput. Simul. 69 537
196. Proukakis N P, Parker N G, Barenghi C F and Adams C S 2004 Phys. Rev. Lett. 93 130408
197. Menza L Di and Gallo C 2007 Nonlinearity 20 461
198. Onofrio R, Raman C, Vogels J M, Abo-Shaeer J R, Chikkatur A P and Ketterle W 2000 Phys. Rev. Lett. 85 2228
199. Rodrigues A S, Kevrekidis P G, Porter M A, Frantzeskakis D J, Schmelcher P and Bishop A R 2008 Phys. Rev. A 78 013611
200. Theocharis G, Schmelcher P, Kevrekidis P G and Frantzeskakis D J 2005 Phys. Rev. A 72 033614
201. Abdullaev F Kh and Salerno M 2003 J. Phys. B: At. Mol. Opt. Phys. 36 2851
202. Rodas-Verde M I, Michinel H and Pérez-García V M 2005 Phys. Rev. Lett. 95 153903
203. Theocharis G, Schmelcher P, Kevrekidis P G and Frantzeskakis D J 2006 Phys. Rev. A 74 053614
204. Dong G, Hu B and Lu W 2006 Phys. Rev. A 74 063601
205. Sivan Y, Fibich G and Weinstein M I 2006 Phys. Rev. Lett. 97 193902
206. Bludov Yu V, Brazhnyi V A and Konotop V V 2007 Phys. Rev. A 76 023603
207. Niarchou P, Theocharis G, Kevrekidis P G, Schmelcher P and Frantzeskakis D J 2007 Phys. Rev. A 76 023615
208. Belmonte-Beitia J, Pérez-García V M, Vekslerchik V and Torres P J 2007 Phys. Rev. Lett. 98 064102
209. Rapti Z, Kevrekidis P G, Konotop V V and Jones C K R T 2007 J. Phys. A: Math. Theor. 40 14151
210. Kuznetsov E A and Turitsyn S K 1988 Zh. Eksp. Teor. Fiz. 94 119
211. Kuznetsov E A and Turitsyn S K 1988 Sov. Phys.-JETP 67 1583 (Engl. Transl.)
212. Kuznetsov E A and Rasmussen J J 1995 Phys. Rev. E 51 4479
213. Pelinovsky D E, Stepanyants Yu A and Kivshar Yu S 1995 Phys. Rev. E 51 5016
214. Kivshar Yu S and Pelinovsky D E 2000 Phys. Rep. 331 117
215. Tikhonenko V, Christou J, Luther-Davies B and Kivshar Yu S 1996 Opt. Lett. 21 1129
216. Mamaev A V, Saffman M and Zozulya A A 1996 Phys. Rev. Lett. 76 2262
217. Kevrekidis P G, Theocharis G, Frantzeskakis D J and Trombettoni A 2004 Phys. Rev. A 70 023602
218. Nath R, Pedri P and Santos L 2008 Phys. Rev. Lett. 101 210402
219. Lahaye T, Menotti C, Santos L, Lewenstein M and Pfau T 2009 Rep. Prog. Phys. 72 126401
220. Bang O, Królikowski W, Wyller J and Rasmussen J J 2002 Phys. Rev. E 66 046619
221. Armaroli A, Trillo S and Fratalocchi A 2009 Phys. Rev. A 80 053803
222. Malomed B A, Nistazakis H E, Frantzeskakis D J and Kevrekidis P G 2004 Phys. Rev. A 70 043616
223. Malomed B A, Nistazakis H E, Frantzeskakis D J and Kevrekidis P G 2005 Math. Comput. Simul. 69 400
224. Kivshar Yu S and Yang X 1994 Phys. Rev. E 50 R40
225. Frantzeskakis D J and Malomed B A 2000 Phys. Lett. A 264 179
226. Nistazakis H E, Frantzeskakis D J, Malomed B A and Kevrekidis P G 2001 Phys. Lett. A 285 157
227. Dreischuh W, Fliesser A, Velchev I, Dinev S and Windholz L 1996 Appl. Phys. B 62 139
228. Neshev D, Dreischuh A, Kamenov V, Stefanov I, Dinev S, Fliesser W and Windholz L 1997 Appl. Phys. B 64 429
229. Dreischuh A, Neshev D, Paulus G G, Grasbon F and Walther H 2002 Phys. Rev. E 66 066611
230. Theocharis G, Frantzeskakis D J, Kevrekidis P G, Malomed B A and Kivshar Yu S 2003 Phys. Rev. Lett. 90 120403
231. Carr L D and Clark C W 2006 Phys. Rev. A 74 043613
232. Ruostekoski J, Kneer B, Schleich W P and Rempe G 2001 Phys. Rev. A 63 043613
233. Yang S-J, Wu Q-S, Zhang S-N, Feng S, Guo W, Wen Y-C and Yu Y 2007 Phys. Rev. A 76 063606
234. Yang S-J, Wu Q-S, Feng S, Wen Y-C and Yu Y 2008 Phys. Rev. A 77 035602
235. Carretero-Gonzlez R, Whitaker N, Kevrekidis P G and Frantzeskakis D J 2008 Phys. Rev. A 77 023605
236. Xue J-K 2004 J. Phys. A: Math. Gen. 37 11223
237. Xue J-K and Peng P 2006 Chin. Phys. 15 1149
238. Herring G, Carr L D, Carretero-Gonzlez R, Kevrekidis P G and Frantzeskakis D J 2008 Phys. Rev. A 77 023625
239. Hu X-H, Zhang X-F, Zhao D, Luo H-G and Liu W M 2009 Phys. Rev. A 79 023619
240. Kevrekidis P G, Theocharis G, Frantzeskakis D J and Malomed B A 2003 Phys. Rev. Lett. 90 230401
241. Saito H and Ueda M 2003 Phys. Rev. Lett. 90 040403
242. Abdullaev F Kh, Caputo J G, Kraenkel R A and Malomed B A 2003 Phys. Rev. A 67 013605
243. Abdullaev F Kh, Kamchatnov A M, Konotop V V and Brazhnyi V A 2003 Phys. Rev. Lett. 90 230402
244. Pelinovsky D E, Kevrekidis P G and Frantzeskakis D J 2003 Phys. Rev. Lett. 91 240201
245. Pelinovsky D E, Kevrekidis P G, Frantzeskakis D J and Zharnitsky V 2004 Phys. Rev. E 70 047604
246. Komineas S and Brand J 2005 Phys. Rev. Lett. 95 110401
247. Komineas S and Papanicolaou N 2003 Phys. Rev. A 68 043617
248. Brand J and Reinhardt W P 2002 Phys. Rev. A 65 043612
249. Komineas S and Papanicolaou N 2002 Phys. Rev. Lett. 89 070402
250. Tang X Y and Shukla P K 2007 Phys. Rev. A 76 013612
251. Myatt C J, Burt E A, Ghrist R W, Cornell E A and Wieman C E 1997 Phys. Rev. Lett. 78 586
252. Hall D S, Matthews M R, Ensher J R, Wieman C E and Cornell E A 1998 Phys. Rev. Lett. 81 1539
253. Stamper-Kurn D M, Andrews M R, Chikkatur A P, Inouye S, Miesner H-J, Stenger J and Ketterle W 1998 Phys. Rev. Lett. 80 2027
254. Stenger J, Inouye S, Stamper-Kurn D M, Miesner H-J, Chikkatur A P and Ketterle W 1998 Nature 396 345
255. Modugno G, Ferrari G, Roati G, Brecha R J, Simoni A and Inguscio M 2001 Science 294 1320
256. DeMarco B and Jin D S 1999 Science 285 1703
257. O'Hara K M, Hemmer S L, Gehm M E, Granade S R and Thomas J E 2002 Science 298 2179
258. Ballagh R J, Burnett K and Scott T F 1997 Phys. Rev. Lett. 78 1607
259. Amoruso A, Meccoli I, Minguzzi A and Tosi M P 2000 Eur. Phys. J. D 8 361
260. Roth R and Feldmeier H 2001 J. Phys. B: At. Mol. Opt. Phys. 34 4629
261. Capuzzi P, Minguzzi A and Tosi M P 2003 Phys. Rev. A 67 053605
262. Mineev V P 1974 Zh. Eksp. Teor. Fiz. 67 263
263. Mineev V P 1974 Sov. Phys.-JETP 40 132 (Engl. Transl.)
264. Pu H and Bigelow N P 1998 Phys. Rev. Lett. 80 1130
265. Ho T-L and Shenoy V B 1996 Phys. Rev. Lett. 77 3276
266. Esry B D, Greene C H, Burke J P Jr and Bohn J L 1997 Phys. Rev. Lett. 78 3594
267. Timmermans E 1998 Phys. Rev. Lett. 81 5718
268. Trippenbach M, Goral K, Rzazewski K, Malomed B and Band Y B 2000 J. Phys. B: At. Mol. Opt. Phys. 33 4017
269. Coen S and Haelterman M 2001 Phys. Rev. Lett. 87 140401
270. Merhasin M I, Malomed B A and Driben R 2005 J. Phys. B: At. Mol. Opt. Phys. 38 877
271. Kasamatsu K and Tsubota M 2006 Phys. Rev. A 74 013617
272. Navarro R, Carretero-Gonzlez R and Kevrekidis P G 2009 Phys. Rev. A 80 023613
273. Deconinck B, Kevrekidis P G, Nistazakis H E and Frantzeskakis D J 2004 Phys. Rev. A 70 063605
274. Nistazakis H E, Rapti Z, Frantzeskakis D J, Kevrekidis P G, Sodano P and Trombettoni A 2008 Phys. Rev. A 78 023635
275. Mertes K M, Merrill J, Carretero-Gonzlez R, Frantzeskakis D J, Kevrekidis P G and Hall D S 2007 Phys. Rev. Lett. 99 190402
276. Thalhammer G, Barontini G, De Sarlo L, Catani J, Minardi F and Inguscio M 2008 Phys. Rev. Lett. 100 210402
277. Papp S B, Pino J M and Wieman C E 2008 Phys. Rev. Lett. 101 040402
278. hberg P and Santos L 2001 Phys. Rev. Lett. 86 2918
279. hberg P and Santos L 2001 J. Phys. B: At. Mol. Opt. Phys. 34 4721
280. Kevrekidis P G, Nistazakis H E, Frantzeskakis D J, Malomed B A and Carretero-Gonzlez R 2004 Eur. Phys. J. D 28 181
281. Zhang X-F, Hu X-H, Liu X-X and Liu W M 2009 Phys. Rev. A 79 033630
282. Liu X X, Pu H, Xiong B, Liu W M and Gong J B 2009 Phys. Rev. A 79 013423
283. Susanto H, Kevrekidis P G, Carretero-Gonzlez R, Malomed B A, Frantzeskakis D J and Bishop A R 2007 Phys. Rev. A 75 055601
284. Gladush Yu G, Kamchatnov A M, Shi Z, Kevrekidis P G, Frantzeskakis D J and Malomed B A 2009 Phys. Rev. A 79 033623
285. Schumayer D and Apagyi B 2004 Phys. Rev. A 69 043620
286. Li H, Wang D N and Cheng Y S 2009 Chaos Solitons Fractals 39 1988
287. Rajendran S, Muruganandam P and Lakshmanan M 2009 J. Phys. B: At. Mol. Opt. Phys. 42 145307
288. Manakov S V 1973 Zh. Eksp. Teor. Fiz. 65 505
289. Manakov S V 1974 Sov. Phys.-JETP 38 248 (Engl. Transl.)
290. Zakharov V E and Manakov S V 1976 Zh. Eksp. Teor. Fiz. 71 203
291. Zakharov V E and Manakov S V 1976 Sov. Phys.-JETP 42 842 (Engl. Transl.)
292. Zakharov V E and Schulman E I 1982 Physica D 4 270
293. Makhankov V G and Pashaev O K 1982 Theor. Math. Phys. 53 979
294. Radhakrishnan R and Lakshmanan M 1995 J. Phys. A: Math. Gen. 28 2683
295. Sheppard A P and Kivshar Yu S 1997 Phys. Rev. E 55 4773
296. Park Q H and Shin H J 2000 Phys. Rev. E 61 3093
297. Leanhardt A E, Shin Y, Kielpinski D, Pritchard D E and Ketterle W 2003 Phys. Rev. Lett. 90 140403
298. Sadler L E, Higbie J M, Leslie S R, Vengalattore M and Stamper-Kurn D M 2006 Nature 443 312
299. Chang M S, Qin Q S, Zhang W X, You L and Chapman M S 2005 Nature Phys. 1 111
300. Dabrowska-Wüster B J, Ostrovskaya E A, Alexander T J and Kivshar Yu S 2007 Phys. Rev. A 75 023617
301. Nistazakis H E, Frantzeskakis D J, Kevrekidis P G, Malomed B A, Carretero-Gonzlez R and Bishop A R 2007 Phys. Rev. A 76 063603
302. van Kempen E G M, Kokkelmans S J J M F, Heinzen D J and Verhaar B J 2002 Phys. Rev. Lett. 88 093201
303. Klausen N N, Bohn J L and Greene C H 2001 Phys. Rev. A 64 053602
304. Bergeman T, Moore M G and Olshanii M 2003 Phys. Rev. Lett. 91 163201
305. Ieda J, Miyakawa T and Wadati M 2004 Phys. Rev. Lett. 93 194102
306. Ieda J, Uchiyama M and Wadati M 2007 J. Math. Phys. 48 013507
307. Uchiyama M, Ieda J and Wadati M 2006 J. Phys. Soc. Japan 75 064002
308. Ieda J and Wadati M 2007 J. Low Temp. Phys. 148 405
309. Yajima N and Oikawa M 1976 Prog. Theor. Phys. 56 1719
310. Andrews M R, Townsend C G, Miesner H-J, Durfee D S, Kurn D M and Ketterle W 1997 Science 275 637
311. Castin Y and Dalibard J 1997 Phys. Rev. A 55 4330
312. Röhrl A, Naraschewski M, Schenzle A and Wallis H 1997 Phys. Rev. Lett. 78 4143
313. Scott T F, Ballagh R J and Burnett K 1998 J. Phys. B: At. Mol. Opt. Phys. 31 L329
314. Lee C, Ostrovskaya E A and Kivshar Yu S 2007 J. Phys. B: At. Mol. Opt. Phys. 40 4235
315. Scherer D R, Weiler C N, Neely T W and Anderson B P 2007 Phys. Rev. Lett. 98 110402
316. Carretero-Gonzlez R, Anderson B P, Kevrekidis P G, Frantzeskakis D J and Weiler C N 2008 Phys. Rev. A 77 033625
317. Ruben G, Paganin D M and Morgan M J 2008 Phys. Rev. A 78 013631
318. Landau L D 1941 J. Phys. (Moscow) 5 71
319. Raman C, Köhl M, Onofrio R, Durfee D S, Kuklewicz C E, Hadzibabic Z and Ketterle W 1999 Phys. Rev. Lett. 83 2502
320. Frisch T, Pomeau Y and Rica S 1992 Phys. Rev. Lett. 69 1644
321. Hakim V 1997 Phys. Rev. E 55 2835
322. Pavloff N 2002 Phys. Rev. A 66 013610
323. Leboeuf P and Pavloff N 2001 Phys. Rev. A 64 033602
324. Radouani A 2003 Phys. Rev. A 68 043620
325. Theocharis G, Kevrekidis P G, Nistazakis H E, Frantzeskakis D J and Bishop A R 2005 Phys. Lett. A 337 441
326. Carretero-Gonzlez R, Kevrekidis P G, Frantzeskakis D J, Malomed B A, Nandi S and Bishop A R 2007 Math. Comput. Simul. 74 361
327. Leszczyszyn A M, El G A, Gladush Yu G and Kamchatnov A M 2009 Phys. Rev. A 79 063608
328. Astrakharchik G E and Pitaevskii L P 2004 Phys. Rev. A 70 013608
329. Carusotto I, Hu S X, Collins L A and Smerzi A 2006 Phys. Rev. Lett. 97 260403
330. Gladush Yu G, El G A, Gammal A and Kamchatnov A M 2007 Phys. Rev. A 75 033619
331. Gladush Yu G and Kamchatnov A M 2007 Zh. Eksp. Teor. Fiz. 132 589
332. Gladush Yu G and Kamchatnov A M 2007 Sov. Phys.-JETP 105 520 (Engl. Transl.)
333. Gladush Yu G, Smirnov L A and Kamchatnov A M 2008 J. Phys. B: At. Mol. Opt. Phys. 41 165301
334. El G A and Kamchatnov A M 2006 Phys. Lett. A 350 192
335. El G A and Kamchatnov A M 2006 Phys. Lett. A 352 554 (erratum)
336. El G A, Gammal A and Kamchatnov A M 2006 Phys. Rev. Lett. 97 180405
337. El G A, Gladush Yu G and Kamchatnov A M 2007 J. Phys. A: Math. Theor. 40 611
338. Cornell E A 2005 Report at Conference on Nonlinear Waves, Integrable Systems and their Applications (Colorado Springs) (http://jilawww.colorado.edu/ bec/papers.html)
339. Kamchatnov A M and Pitaevskii L P 2008 Phys. Rev. Lett. 100 160402
340. Kravchenko L Y and Fil D V 2009 J. Low Temp. Phys. 155 219
341. Rodrigues A S, Kevrekidis P G, Carretero-Gonzlez R, Frantzeskakis D J, Schmelcher P, Alexander T J and Kivshar Yu S 2009 Phys. Rev. A 79 043603
342. Brazhnyi V A and Konotop V V 2004 Mod. Phys. Lett. B 18 627
343. Bloch I 2005 J. Phys. B: At. Mol. Opt. Phys. 38 S629
344. Morsch O and Oberthaler M K 2006 Rev. Mod. Phys. 78 179
345. Lewenstein M, Sanpera A, Ahufinger V, Damski B, Sen(De) A and Sen U 2007 Adv. Phys. 56 243
346. Eiermann B, Anker Th, Albiez M, Taglieber M, Treutlein P, Marzlin K P and Oberthaler M K 2004 Phys. Rev. Lett. 92 230401
347. Anker Th, Albiez M, Eiermann B, Taglieber M and Oberthaler M K 2004 Opt. Express 12 11
348. Alfimov G L, Kevrekidis P G, Konotop V V and Salerno M 2002 Phys. Rev. E 66 046608
349. Kevrekidis P G, Rasmussen K and Bishop A R 2001 Int. J. Mod. Phys. B 15 2833
350. Kevrekidis P G 2009 The Discrete Nonlinear Schrödinger Equation (Heidelberg: Springer)
351. Kevrekidis P G, Carretero-Gonzlez R, Theocharis G, Frantzeskakis D J and Malomed B A 2003 Phys. Rev. A 68 035602
352. Kevrekidis P G, Carretero-Gonzlez R, Theocharis G, Frantzeskakis D J and Malomed B A 2005 Phys. Rev. A 72 069908 (erratum)
353. Theocharis G, Frantzeskakis D J, Kevrekidis P G, Carretero-Gonzlez R and Malomed B A 2005 Phys. Rev. E 71 017602
354. Abdullaev F Kh, Baizakov B B, Darmanyan S A, Konotop V V and Salerno M 2001 Phys. Rev. A 64 043606
355. Yulin A V and Skryabin D V 2003 Phys. Rev. A 67 023611
356. Alfimov G L, Konotop V V and Salerno M 2002 Europhys. Lett. 58 7
357. Konotop V V and Salerno M 2002 Phys. Rev. A 65 021602
358. Louis P J Y, Ostrovskaya E A and Kivshar Yu S 2004 J. Opt. B: Quantum Semiclass. Opt. 6 S309
359. Porter M A, Kevrekidis P G, Carretero-Gonzlez R and Frantzeskakis D J 2006 Phys. Lett. A 352 210
360. Peil S, Porto J V, Tolra B L, Obrecht J M, King B E, Subbotin M, Rolston S L and Phillips W D 2003 Phys. Rev. A 67 051603
361. Feng J H and Kneubühl F K 1993 IEEE J. Quantum Electron. 29 590
362. Kivshar Yu S, Królikowski W and Chubykalo O A 1994 Phys. Rev. E 50 5020
363. Johansson M and Kivshar Yu S 1999 Phys. Rev. Lett. 82 85
364. Sukhorukov A A and Kivshar Yu S 2002 Phys. Rev. E 65 036609
365. Susanto H and Johansson M 2005 Phys. Rev. E 72 016605
366. Fitrakis E P, Kevrekidis P G, Susanto H and Frantzeskakis D J 2007 Phys. Rev. E 75 066608
367. Konotop V V and Takeno S 1999 Phys. Rev. E 60 1001
368. Pelinovsky D E and Kevrekidis P G 2008 J. Phys. A: Math. Theor. 41 185206
369. Braun O M and Kivshar Yu S 1998 Phys. Rep. 306 1
370. Greiner M, Mandel O, Esslinger T, Hansch T W and Bloch I 2002 Nature 415 39
371. Jaksch D, Bruder C, Cirac J I, Gardiner C W and Zoller P 1998 Phys. Rev. Lett. 81 3108
372. Mishmash R V and Carr L D 2009 Phys. Rev. Lett. 103 140403
373. Mishmash R V, Danshita I, Clark C W and Carr L D 2009 Phys. Rev. A 80 053612
374. Krutitsky K V, Larson J and Lewenstein M 2009 arXiv:0907.0625
375. Pitaevskii L P 1958 Zh. Eksp. Teor. Fiz. 35 408
376. Pitaevskii L P 1959 Sov. Phys.-JETP 35 282 (Engl. Transl.)
377. Jackson B and Proukakis N P 2008 Finite-temperature models of Bose-Einstein condensation J. Phys. B: At. Mol. Opt. Phys. 41 203002
378. Jackson B, Proukakis N P and Barenghi C F 2007 Phys. Rev. A 75 051601
379. Jackson B, Barenghi C F and Proukakis N P 2007 J. Low Temp. Phys. 148 387
380. Cockburn S P, Nistazakis H E, Horikis T P, Kevrekidis P G, Proukakis N P and Frantzeskakis D J 2010 Phys. Rev. Lett. (arXiv:0909.1660) at press
381. Martin A D and Ruostekoski J 2010 Phys. Rev. Lett. (arXiv:0909.2621) at press
382. Steel M J, Olsen M K, Plimak L I, Drummond P D, Tan S M, Collett M J, Walls D F and Graham R 1998 Phys. Rev. A 58 4824
383. Sinatra A, Lobo C and Castin Y 2002 J. Phys. B: At. Mol. Opt. Phys. 35 3599
384. Gangardt D M and Kamenev A 2010 Phys. Rev. Lett. (arXiv:0908.4513) at press
385. Kevrekidis P G and Frantzeskakis D J 2009 Discrete Cont. Dyn. Syst. S (at press)
386. Dziarmaga J, Karkuszewski Z P and Sacha K 2002 Phys. Rev. A 66 043615
387. Law C K 2003 Phys. Rev. A 68 015602
388. Dalvit D A R, Dziarmaga J and Onofrio R 2002 Phys. Rev. A 65 053604
389. El G A and Kamchatnov A M 2005 Phys. Rev. Lett. 95 204101
390. Fratalocchi A, Conti C, Ruocco G and Trillo S 2008 Phys. Rev. Lett. 101 044101
391. Luther-Davies B and Yang X 1992 Opt. Lett. 17 496
392. Giorgini S, Pitaevskii L P and Stringari S 2008 Rev. Mod. Phys. 80 1215
393. Ketterle W and Zwierlein M W 2008 Riv. Nuovo Cimento 31 247
394. Adhikari S K 2005 J. Phys. B: At. Mol. Opt. Phys. 38 3607
395. Antezza M, Dalfovo F, Pitaevskii L P and Stringari S 2007 Phys. Rev. A 76 043610
396. Wen W and Huang G X 2009 Phys. Rev. A 79 023605