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Cross-symmetry breaking of two-component discrete dipolar matter-wave solitons |
Yong-Yao Li1, Zhi-Wei Fan2, Zhi-Huan Luo2, Yan Liu2, He-Xiang He1, Jian-Tao Lü1, Jia-Ning Xie1, Chun-Qing Huang1( ), Hai-Shu Tan1 |
1. School of Physics and Optoelectronic Engineering, Foshan University, Foshan 528000, China
2. Department of Applied Physics, South China Agricultural University, Guangzhou 510642, China |
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Abstract We study the spontaneous symmetry breaking of dipolar Bose–Einstein condensates trapped in stacks of two-well systems, which may be effectively built as one-dimensional trapping lattices sliced by a repelling laser sheet. If the potential wells are sufficiently deep, the system is modeled by coupled discrete Gross–Pitaevskii equations with nonlocal self- and cross-interaction terms representing dipole–dipole interactions. When the dipoles are not polarized perpendicular or parallel to the lattice, the crossinteraction is asymmetric, replacing the familiar symmetric two-component solitons with a new species of cross-symmetric or-asymmetric ones. The orientation of the dipole moments and the interwell hopping rate strongly affect the shapes of the discrete two-component solitons as well as the characteristics of the cross-symmetry breaking and the associated phase transition. The sub- and super-critical types of cross-symmetry breaking can be controlled by either the hopping rate between the components or the total norm of the solitons. The effect of the interplay between the contact nonlinearity and the dipole angle on the cross-symmetry breaking is also discussed.
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| Keywords
discrete matter-wave solitons
two-component systems
dipole–dipole interactions
cross-symmetry breaking
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Corresponding Author(s):
Chun-Qing Huang
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Issue Date: 22 September 2017
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| 1 |
A.Griesmaier, Generation of a dipolar Bose–Einstein condensate, J. Phys. B40(14), R91 (2007)
https://doi.org/10.1088/0953-4075/40/14/R01
|
| 2 |
T.Lahaye, C.Menotti, L.Santos, M.Lewenstein, and T.Pfau, The physics of dipolar bosonic quantum gases, Rep. Prog. Phys. 72(12), 126401(2009)
https://doi.org/10.1088/0034-4885/72/12/126401
|
| 3 |
M. A.Baranov, Theoretical progress in many-body physics with ultracold dipolar gases, Phys. Rep. 464(3), 71(2008)
https://doi.org/10.1016/j.physrep.2008.04.007
|
| 4 |
S.Giovanazzi,A.Görlitz, and T.Pfau, Tuning the dipolar interaction in quantum gases, Phys. Rev. Lett. 89(13), 130401(2002)
https://doi.org/10.1103/PhysRevLett.89.130401
|
| 5 |
Y.Li, J.Liu, W.Pang, and B. A.Malomed, Matterwave solitons supported by field-induced dipole–dipole repulsion with spatially modulated strength, Phys. Rev. A88(5), 053630(2013)
https://doi.org/10.1103/PhysRevA.88.053630
|
| 6 |
T.Lahaye, T.Koch, B.Fröhlich, M.Fattori, J.Metz, A.Griesmaier, S.Giovanazzi, and T.Pfau, Strong dipolar effects in a quantum ferrofluid, Nature448(7154), 672(2007)
https://doi.org/10.1038/nature06036
|
| 7 |
H.Saito, Y.Kawaguchi, and M.Ueda, Ferrofluidity in a two-component dipolar Bose–Einstein condensate, Phys. Rev. Lett. 102(23), 230403(2009)
https://doi.org/10.1103/PhysRevLett.102.230403
|
| 8 |
H.Kadau, M.Schmitt, M.Wenzel, C.Wink, T.Maier, I.Ferrier-Barbut, and T.Pfau, Observing the Rosensweig instability of a quantum ferrofluid, Nature530(7589), 194(2016)
https://doi.org/10.1038/nature16485
|
| 9 |
R.Richterand I. V.Barashenkov, Two-dimensional solitons on the surface of magnetic fluids, Phys. Rev. Lett. 94(18), 184503(2005)
https://doi.org/10.1103/PhysRevLett.94.184503
|
| 10 |
L.Santos, G. V.Shlyapnikov, and M.Lewenstein, Roton–Maxon spectrum and stability of trapped dipolar Bose–Einstein condensates, Phys. Rev. Lett. 90(25), 250403(2003)
https://doi.org/10.1103/PhysRevLett.90.250403
|
| 11 |
M.Klawunn, R.Nath, P.Pedri, andL.Santos, Transverse instability of straight vortex lines in dipolar Bose– Einstein condensates, Phys. Rev. Lett. 100(24), 240403(2008)
https://doi.org/10.1103/PhysRevLett.100.240403
|
| 12 |
R. M.Wilson, S.Ronen, J. L.Bohn, and H.Pu, Manifestations of the roton mode in dipolar Bose–Einstein condensates, Phys. Rev. Lett. 100(24), 245302(2008)
https://doi.org/10.1103/PhysRevLett.100.245302
|
| 13 |
D.Hufnagl, R.Kaltseis, V.Apaja, and R. E.Zillich, Roton–roton crossover in strongly correlated dipolar Bose–Einstein Condensates, Phys. Rev. Lett. 107(6), 065303(2011)
https://doi.org/10.1103/PhysRevLett.107.065303
|
| 14 |
R.Nathand L.Santos, Faraday patterns in twodimensional dipolar Bose–Einstein condensates, Phys. Rev. A81(3), 033626(2010)
https://doi.org/10.1103/PhysRevA.81.033626
|
| 15 |
K.komy, R.Nath, and L.Santos, Faraday patterns in coupled one-dimensional dipolar condensates, Phys. Rev. A86(2), 023620(2012)
https://doi.org/10.1103/PhysRevA.86.023620
|
| 16 |
A.Bühlerand H. P.Büchler, Supersolid phase in atomic gases with magnetic dipole interaction, Phys. Rev. A84(2), 023607(2011)
https://doi.org/10.1103/PhysRevA.84.023607
|
| 17 |
A.Maluckov, G.Gligoric, Lj.Hadžievski, B. A.Malomed, and T.Pfau, Stable periodic density waves in dipolar Bose–Einstein condensates trapped in optical lattices, Phys. Rev. Lett. 108(14), 140402(2012)
https://doi.org/10.1103/PhysRevLett.108.140402
|
| 18 |
C.Ticknor, R. M.Wilson, and J. L.Bohn, Anisotropic superfluidity in a dipolar Bose gas, Phys. Rev. Lett. 106(6), 065301(2011)
https://doi.org/10.1103/PhysRevLett.106.065301
|
| 19 |
A. A.Wood, B. H. J.McKellar, and A. M.Martin, Persistent superfluid flow arising from the He–McKellar– Wilkens effect in molecular dipolar condensates, Phys. Rev. Lett. 116(25), 250403(2016)
https://doi.org/10.1103/PhysRevLett.116.250403
|
| 20 |
P. M.Lushnikov, Collapse of Bose–Einstein condensates with dipole–dipole interactions, Phys. Rev. A66, 051601(2002)
https://doi.org/10.1103/PhysRevA.66.051601
|
| 21 |
D. C. E.Bortolotti, S.Ronen, J. L.Bohn, and D.Blume, Scattering length instability in dipolar Bose–Einstein condensates, Phys. Rev. Lett. 97(16), 160402(2006)
https://doi.org/10.1103/PhysRevLett.97.160402
|
| 22 |
C.Ticknor, N. G.Parker,A.Melatos, S. L.Cornish, D. H. J.O’Dell, and A. M.Martin, Collapse times of dipolar Bose–Einstein condensates, Phys. Rev. A78, 061607(2008)
https://doi.org/10.1103/PhysRevA.78.061607
|
| 23 |
T.Lahaye, J.Metz, B.Fröhlich, T.Koch, M.Meister, A.Griesmaier, T.Pfau, H.Saito, Y.Kawaguchi, and M.Ueda, d-wave collapse and explosion of a dipolar Bose– Einstein condensate, Phys. Rev. Lett. 101(8), 080401(2008)
https://doi.org/10.1103/PhysRevLett.101.080401
|
| 24 |
I.Ferrier-Barbut, H.Kadau, M.Schmitt, M.Wenzel, and T.Pfau, Observation of quantum droplets in a strongly dipolar Bose gas, Phys. Rev. Lett. 116(21), 215301(2016)
https://doi.org/10.1103/PhysRevLett.116.215301
|
| 25 |
K.-T.Xiand H.Saito, Droplet formation in a Bose– Einstein condensate with strong dipole–dipole interaction, Phys. Rev. A93, 011604(2016)
https://doi.org/10.1103/PhysRevA.93.011604
|
| 26 |
F.Wächtlerand L.Santos, Quantum filaments in dipolar Bose–Einstein condensates, Phys. Rev. A93, 061603(2016)
https://doi.org/10.1103/PhysRevA.93.061603
|
| 27 |
D.Baillie, R. M.Wilson, R. N.Bisset, and P. B.Blakie, Self-bound dipolar droplet: A localized matter wave in free space, Phys. Rev. A94, 021602(2016)
https://doi.org/10.1103/PhysRevA.94.021602
|
| 28 |
M.Klawunnand L.Santos, Hybrid multisite excitations in dipolar condensates in optical lattices, Phys. Rev. A80(1), 013611(2009)
https://doi.org/10.1103/PhysRevA.80.013611
|
| 29 |
S.Müller, J.Billy, E. A. L.Henn, H.Kadau, A.Griesmaier, M.Jona-Lasinio, L.Santos, and T.Pfau, Stability of a dipolar Bose–Einstein condensate in a onedimensional lattice, Phys. Rev. A84(5), 053601(2011)
https://doi.org/10.1103/PhysRevA.84.053601
|
| 30 |
R. M.Wilsonand J. L.Bohn, Emergent structure in a dipolar Bose gas in a one-dimensional lattice, Phys. Rev. A83(2), 023623(2011)
https://doi.org/10.1103/PhysRevA.83.023623
|
| 31 |
K.Gawryluk, K.Bongs, and M.Brewczyk, How to observe dipolar Effects in spinor Bose–Einstein condensates, Phys. Rev. Lett. 106(14), 140403(2011)
https://doi.org/10.1103/PhysRevLett.106.140403
|
| 32 |
Q.Zhaoand Q.Gu, Trapped Bose–Einstein condensates in synthetic magnetic field, Front. Phys. 10(5), 100306(2015)
https://doi.org/10.1007/s11467-015-0505-x
|
| 33 |
W.Królikowski, O.Bang, N. I.Nikolov, D.Neshev, J.Wyller, J. J.Rasmussen, andD.Edmundson, Modulational instability, solitons and beam propagation in spatially nonlocal nonlinear media, J. Opt. B Quantum Semiclassical Opt. 6(5), S288(2004)
https://doi.org/10.1088/1464-4266/6/5/017
|
| 34 |
M.Pecciantiand G.Assanto, Nematicons, Phys. Rep. 516(4–5), 147(2012)
https://doi.org/10.1016/j.physrep.2012.02.004
|
| 35 |
W.Królikowskiand O.Bang, Solitons in nonlocal nonlinear media: Exact solutions, Phys. Rev. E63(1), 016610(2000)
https://doi.org/10.1103/PhysRevE.63.016610
|
| 36 |
S.Skupin, O.Bang, D.Edmundson, and W.Krolikowski,Stability of two-dimensional spatial solitons in nonlocal nonlinear media, Phys. Rev. E73(6), 066603(2006)
https://doi.org/10.1103/PhysRevE.73.066603
|
| 37 |
P.Pedriand L.Santos, Two-dimensional bright solitons in dipolar Bose–Einstein condensates, Phys. Rev. Lett. 95(20), 200404(2005)
https://doi.org/10.1103/PhysRevLett.95.200404
|
| 38 |
I.Tikhonenkov, B. A.Malomed, and A.Vardi, Anisotropic solitons in dipolar Bose–Einstein condensates, Phys. Rev. Lett. 100(9), 090406(2008)
https://doi.org/10.1103/PhysRevLett.100.090406
|
| 39 |
J.Cuevas, B. A.Malomed, P. G.Kevrekidis, and D. J.Frantzeskakis, Solitons in quasi-one-dimensional Bose– Einstein condensates with competing dipolar and local interactions, Phys. Rev. A79(5), 053608(2009)
https://doi.org/10.1103/PhysRevA.79.053608
|
| 40 |
F.Kh. Abdullaev, A.Gammal, B. A.Malomed, and L.Tomio, Bright solitons in quasi-one dimensional dipolar condensates with spatially modulated interactions, Phys. Rev. A87(6), 063621(2013)
https://doi.org/10.1103/PhysRevA.87.063621
|
| 41 |
M.Raghunandan, C.Mishra, K.Lakomy, P.Pedri, L.Santos, and R.Nath, Two-dimensional bright solitons in dipolar Bose–Einstein condensates with titled dipoles, Phys. Rev. A92(1), 013637(2015)
https://doi.org/10.1103/PhysRevA.92.013637
|
| 42 |
S. K.Adhikariand L. E.Young-S, Statics and dynamics of a binary dipolar Bose–Einstein condensate soliton, J. Phys. B: At. Mol. Opt. Phys. 47(1), 015302(2014)
https://doi.org/10.1088/0953-4075/47/1/015302
|
| 43 |
J.Huang, X.Jiang, H.Chen, Z.Fan, W.Pang, and Y.Li, Quadrupolar matter-wave soliton in two-dimensional free space, Front. Phys. 10(4), 100507(2015)
https://doi.org/10.1007/s11467-015-0501-1
|
| 44 |
G.Chen, Y.Liu, and H.Wang, Mixed-mode solitons in quadrupolar BECs with spin–orbit coupling, Commun. Nonlinear Sci. Numer. Simul. 48, 318 (2017)
https://doi.org/10.1016/j.cnsns.2016.12.028
|
| 45 |
R.Nath, P.Pedri, and L.Santos, Stability of dark solitons in three dimensional dipolar Bose–Einstein condensates, Phys. Rev. Lett. 101(21), 210402(2008)
https://doi.org/10.1103/PhysRevLett.101.210402
|
| 46 |
T.Bland, M. J.Edmonds, N. P.Proukakis, A. M.Martin, D. H. J.O’Dell, and N. G.Parker, Controllable nonlocal interactions between dark solitons in dipolar condensates, Phys. Rev. A92(6), 063601(2015)
https://doi.org/10.1103/PhysRevA.92.063601
|
| 47 |
K.Pawłowskiand K.Rza ¸żewski, Dipolar dark solitons, New J. Phys. 17(10), 105006(2015)
https://doi.org/10.1088/1367-2630/17/10/105006
|
| 48 |
M. J.Edmonds, T.Bland, D. H. J.O’Dell, and N. G.Parker, Exploring the stability and dynamics of dipolar matter-wave dark solitons, Phys. Rev. A93(6), 063617(2016)
https://doi.org/10.1103/PhysRevA.93.063617
|
| 49 |
V. M.Lashkin, Two-dimensional nonlocal vortices, multipole solitons, and rotating multisolitons in dipolar Bose–Einstein condensates,Phys. Rev. A75(4), 043607(2007)
https://doi.org/10.1103/PhysRevA.75.043607
|
| 50 |
I.Tikhonenkov, B. A.Malomed, and A.Vardi, Vortex solitons in dipolar Bose–Einstein condensates, Phys. Rev. A78, 043614(2008)
https://doi.org/10.1103/PhysRevA.78.043614
|
| 51 |
G.Gligorić, A.Maluckov, L.Hadžievski, and B. A.Malomed, Bright solitons in the one-dimensional discrete Gross–Pitaevskii equation with dipole–dipole interactions, Phys. Rev. A78(6), 063615(2008)
https://doi.org/10.1103/PhysRevA.78.063615
|
| 52 |
G.Gligorić, A.Maluckov, M.Stepič L.Hadžievski, and B. A.Malomed, Two-dimensional discrete solitons in dipolar Bose–Einstein condensates, Phys. Rev. A81(1), 013633(2010)
https://doi.org/10.1103/PhysRevA.81.013633
|
| 53 |
H.Chen, Y.Liu, Q.Zhang, Y.Shi, W.Pang, and Y.Li, Dipolar matter-wave solitons in two-dimensional anisotropic discrete lattices, Phys. Rev. A93(5), 053608(2016)
https://doi.org/10.1103/PhysRevA.93.053608
|
| 54 |
Z.Luo, Y.Li, W.Pang, and Y.Liu, Dipolar matterwave soliton in one-dimensional optical lattice with tunable local and nonlocal nonlinearities, J. Phys. Soc. Jpn. 82(9), 094401(2013)
https://doi.org/10.7566/JPSJ.82.094401
|
| 55 |
Y.Xu, Y.Zhang, and C.Zhang, Bright solitons in a twodimensional spin–orbit-coupled dipolar Bose–Einstein condensate, Phys. Rev. A92(1), 013633(2015)
https://doi.org/10.1103/PhysRevA.92.013633
|
| 56 |
X.Jiang, Z.Fan, Z.Chen, W.Pang, Y.Li, and B. A.Malomed, Two-dimensional solitons in dipolar Bose– Einstein condensates with spin–orbit-coupling, Phys. Rev. A93(2), 023633(2016)
https://doi.org/10.1103/PhysRevA.93.023633
|
| 57 |
Y.Li, Y.Liu, Z.Fan, W.Pang, S.Fu, and B. A.Malomed, Two-dimensional dipolar gap solitons in free space with spin–orbit coupling, Phys. Rev. A95(6), 063613(2017)
https://doi.org/10.1103/PhysRevA.95.063613
|
| 58 |
Y.Zhang, M. E.Mossman, T.Busch, P.Engels, and C.Zhang, Properties of spin–orbit-coupled Bose–Einstein condensates, Front. Phys. 11(3), 118103(2016)
https://doi.org/10.1007/s11467-016-0560-y
|
| 59 |
B. B.Baizakov, F. Kh.Abdullaev, B. A.Malomed, and M.Salerno, Solitons in Tonks–Girardeau gas with dipolar interactions, J. Phys. At. Mol. Opt. Phys. 42(17), 175302(2009)
https://doi.org/10.1088/0953-4075/42/17/175302
|
| 60 |
Z.Fan, Y.Shi, Y.Liu, W.Pang, Y.Li, and B. A.Malomed, Cross-symmetric dipolar-matter-wave solitons in double-well chains, Phys. Rev. E95(3), 032226(2017)
https://doi.org/10.1103/PhysRevE.95.032226
|
| 61 |
B. A.Malomed(Ed.), Spontaneous Symmetry Breaking, Self-Trapping, and Josephson Oscillations, Berlin: Springer, 2013
https://doi.org/10.1007/978-3-642-21207-9
|
| 62 |
B. A.Malomed, Spontaneous symmetry breaking in nonlinear systems: An overview and a simple model, in: Nonlinear Dynamics: Materials, Theory and Experiments, edited by M. Tlidi and M. Clerc, Springer Proceedings in PhysicsVol. 173, Berlin: Springer, 2016 pp 97–112
|
| 63 |
S.Trillo, E. M.Wright, G. I.Stegeman, and S.Wabnitz, Soliton switching in fiber nonlinear directional couplers, Opt. Lett. 13(8), 672(1988)
https://doi.org/10.1364/OL.13.000672
|
| 64 |
S. R.Friberg, A. M.Weiner, Y.Silberberg, B. G.Sfez, and P. S.Smith, Femtosecond switching in a dual-corefiber nonlinear coupler, Opt. Lett. 13(10), 904(1988)
https://doi.org/10.1364/OL.13.000904
|
| 65 |
F. Kh.Abdullaev, R. M.Abrarov, and S. A.Darmanyan, Dynamics of solitons in coupled optical fibers, Opt. Lett. 14(2), 131(1989)
https://doi.org/10.1364/OL.14.000131
|
| 66 |
E. M.Wright, G. I.Stegeman, and S.Wabnitz, Solitarywave decay and symmetry-breaking instabilities in twomode fibers, Phys. Rev. A40(8), 4455(1989)
https://doi.org/10.1103/PhysRevA.40.4455
|
| 67 |
C.Paréand M.Florjańczyk, Approximate model of soliton dynamics in all-optical couplers, Phys. Rev. A41(11), 6287(1990)
https://doi.org/10.1103/PhysRevA.41.6287
|
| 68 |
N.Akhmedievand A.Ankiewicz, Novel soliton states and bifurcation phenomena in nonlinear fiber couplers, Phys. Rev. Lett. 70(16), 2395(1993)
https://doi.org/10.1103/PhysRevLett.70.2395
|
| 69 |
P. L.Chu, B. A.Malomed, and G. D.Peng, Soliton switching and propagation in nonlinear fiber couplers: Analytical results, J. Opt. Soc. Am. B10(8), 1379(1993)
https://doi.org/10.1364/JOSAB.10.001379
|
| 70 |
J. M.Soto-Crespoand N.Akhmediev, Stability of the soliton states in a nonlinear fiber coupler, Phys. Rev. E48(6), 4710(1993)
https://doi.org/10.1103/PhysRevE.48.4710
|
| 71 |
M.Matuszewski, B. A.Malomed, and M.Trippenbach, Spontaneous symmetry breaking of solitons trapped in a double-channel potential, Phys. Rev. A75(6), 063621(2007)
https://doi.org/10.1103/PhysRevA.75.063621
|
| 72 |
Y. J.Tsofeand B. A.Malomed, Quasisymmetric and asymmetric gap solitons in linearly coupled Bragg gratings with a phase shift, Phys. Rev. E75(5), 056603(2007)
https://doi.org/10.1103/PhysRevE.75.056603
|
| 73 |
S. K.Adhikariand B. A.Malomed, Two-component gap solitons with linear interconversion, Phys. Rev. A79(1), 015602(2009)
https://doi.org/10.1103/PhysRevA.79.015602
|
| 74 |
H.Sakaguchiand B. A.Malomed, Symmetry breaking of solitons in two-component Gross–Pitaevskii equations, Phys. Rev. E83(3), 036608(2011)
https://doi.org/10.1103/PhysRevE.83.036608
|
| 75 |
Y.Li, B. A.Malomed, M.Feng, and J.Zhou, Double symmetry breaking of solitons in one-dimensional virtual photonic crystals, Phys. Rev. A83(5), 053832(2011)
https://doi.org/10.1103/PhysRevA.83.053832
|
| 76 |
I. M.Merhasin, B. A.Malomed, and R.Driben, Transition to miscibility in a binary Bose–Einstein condensate induced by linear coupling, J. Phys. B38(7), 877(2005)
https://doi.org/10.1088/0953-4075/38/7/009
|
| 77 |
G.Herring, P. G.Kevrekidis, B. A.Malomed, R.Carretero-González, and D. J.Frantzeskakis, Symmetry breaking in linearly coupled dynamical lattices, Phys. Rev. E76(6), 066606(2007)
https://doi.org/10.1103/PhysRevE.76.066606
|
| 78 |
Y.Liu, Y.Guan, H.Li,Z.Luo, and Z.Mai, Nonlinear defect localized modes and composite gray and anti-gray solitons in one-dimensional waveguide arrays with dualflip defects, Opt. Commun. 397, 105(2017)
https://doi.org/10.1016/j.optcom.2017.04.013
|
| 79 |
X.Shi, B. A.Malomed, F.Ye, and X.Chen, Symmetric and asymmetric solitons in a nonlocal nonlinear coupler, Phys. Rev. A85(5), 053839(2012)
https://doi.org/10.1103/PhysRevA.85.053839
|
| 80 |
Y.Li, J.Liu, W.Pang, and B. A.Malomed, Symmetry breaking in dipolar matter-wave solitons in dual-core couplers, Phys. Rev. A87(1), 013604(2013)
https://doi.org/10.1103/PhysRevA.87.013604
|
| 81 |
V. A.Brazhnyiand V. V.Konotop, Theory of nonlinear matter waves in optical lattices, Mod. Phys. Lett. B18(14), 627(2004)
https://doi.org/10.1142/S0217984904007190
|
| 82 |
O.Morschand M.Oberthaler, Dynamics of Bose– Einstein condensates in optical lattices, Rev. Mod. Phys. 78(1), 179(2006)
https://doi.org/10.1103/RevModPhys.78.179
|
| 83 |
A.Trombettoniand A.Smerzi, Discrete solitons and breathers with dilute Bose–Einstein condensates, Phys. Rev. Lett. 86(11), 2353(2001)
https://doi.org/10.1103/PhysRevLett.86.2353
|
| 84 |
G. L.Alfimov, P. G.Kevrekidis, V. V.Konotop, and M.Salerno, Wannier functions analysis of the nonlinear Schrödinger equation with a periodic potential, Phys. Rev. E66(4), 046608(2002)
https://doi.org/10.1103/PhysRevE.66.046608
|
| 85 |
R.Carretero-González, and K.Promislow, Nonlinear excitations in arrays of Bose–Einstein condensates, Phys. Rev. A66, 033610(2002)
https://doi.org/10.1103/PhysRevA.66.033610
|
| 86 |
P. G.Kevrekidis, The Discrete Nonlinear Schrödinger Equation: Mathematical Analysis, Numerical Computations, and Physical Perspectives, Springer: Berlin and Heidelberg, 2009
https://doi.org/10.1007/978-3-540-89199-4
|
| 87 |
F. K.Abdullaev, B. B.Baizakov, S. A.Darmanyan, V. V.Konotop, and M.Salerno, Nonlinear excitations in arrays of Bose–Einstein condensates, Phys. Rev. A64(4), 043606(2001)
https://doi.org/10.1103/PhysRevA.64.043606
|
| 88 |
Y.Li, W.Pang, J.Xu, C.Lee, B. A.Malomed, and L.Santos, Long-range transverse Ising model built with dipolar condensates in two-well arrays, New J. Phys. 19(1), 013030(2017)
https://doi.org/10.1088/1367-2630/aa58b3
|
| 89 |
M. L.Chiofalo,S.Succi, and M. P.Tosi, Ground state of trapped interacting Bose–Einstein condensates by an explicit imaginary-time algorithm, Phys. Rev. E62(5), 7438(2000)
https://doi.org/10.1103/PhysRevE.62.7438
|
| 90 |
J.Yangand T. I.Lakoba, Accelerated imaginarytime evolution methods for the computation of solitary waves, Stud. Appl. Math. 120(3), 265(2008)
https://doi.org/10.1111/j.1467-9590.2008.00398.x
|
| 91 |
J.Yangand T. I.Lakoba, Universally-convergent squared-operator iteration methods for solitary waves in general nonlinear wave equations, Stud. Appl. Math. 118(2), 153(2007)
|
| 92 |
G.Ioossand D. D.Joseph, Elementary Stability Bifurcation Theory, New York: Springer, 1980
|
| 93 |
Y.Li, W.Pang, S.Fu, and B. A.Malomed, Twocomponent solitons with a spatially modulated linear coupling: Inverted photonic crystals and fused couplers, Phys. Rev. A85(5), 053821(2012)
https://doi.org/10.1103/PhysRevA.85.053821
|
| 94 |
M.Vakhitovand A.Kolokolov, Stationary solutions of the wave equation in a medium with nonlinearity saturation, Radiophys. Quantum Electron. 16(7), 783(1973)
https://doi.org/10.1007/BF01031343
|
| 95 |
L.Bergé, Wave collapse in physics: principles and applications to light and plasma waves, Phys. Rep. 303(5–6), 259(1998)
|
| 96 |
E. A.Kuznetsovand F.Dias, Bifurcations of solitons and their stability, Phys. Rep. 507(2–3), 43(2011)
https://doi.org/10.1016/j.physrep.2011.06.002
|
| 97 |
S.Inouye, M. R.Andrews, J.Stenger, H. J.Miesner, D. M.Stamper-Kurn, and W.Ketterle, Observation of Feshbach resonances in a Bose–Einstein condensate, Nature392(6672), 151(1998)
https://doi.org/10.1038/32354
|
| 98 |
Z.Chen, J.Liu, S.Fu, Y.Li, and B. A.Malomed, Discrete solitons and vortices on two-dimensional lattices of PT-symmetric couplers, Opt. Express22(24), 29679 (2014)
https://doi.org/10.1364/OE.22.029679
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