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Dark-soliton dynamics in a two-species Bose-Einstein condensate with the external potential and thermal cloud effects. (English) Zbl 1310.82009
Summary: Considering the time-dependent external potential and thermal cloud effects, this paper investigates via symbolic computation the dark-soliton dynamics in a two-species Bose-Einstein condensate (BEC), which can be described by the quasi-one-dimensional coupled Gross-Pitaevskii equations. Under the balance between the harmonic potential and thermal cloud effects, dark multi-soliton solutions are derived for the two-species BEC through the Hirota bilinear method. Regions of the \(s\)-wave scattering lengths are ascertained for the existence of the dark solitons in two species. Influence of the scattering lengths and external potential on the background density, soliton width and velocity is examined. Graphical analysis demonstrates that the harmonic and linear potentials can change the propagation paths, collision positions and collision time of the dark solitons, and that the thermal cloud effects can affect the number of atoms in the two-species BEC.
MSC:
82B10 Quantum equilibrium statistical mechanics (general)
35Q55 NLS equations (nonlinear Schrödinger equations)
35C08 Soliton solutions
68W30 Symbolic computation and algebraic computation
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[1] Achilleos, V.; Yan, D.; Kevrekidis, P. G.; Frantzeskakis, D. J., New J. Phys., 14, 055006, (2012)
[2] Albiez, M.; Gati, R.; Fölling, J.; Hunsmann, S.; Cristiani, M.; Oberthaler, M. K.; Lim, L.-K.; Troppenz, T.; Smith, C. M., Phys. Rev. Lett., Phys. Rev. A, 84, 053609, (2011)
[3] Anderson, M. H.; Ensher, J. R.; Matthews, M. R.; Wieman, C. E.; Cornell, A. E.; Davis, K. B.; Mewes, M. O.; Andrews, M. R.; van Druten, N. J.; Durfee, D. S.; Kurn, D. M.; Ketterle, W., Science, Phys. Rev. Lett., 75, 3969, (1995)
[4] Apagyi, B.; Schumayera, D., Eur. Phys. J. B, 45, 55, (2005)
[5] Bradley, C. C.; Sackett, C. A.; Hulet, R. G., Phys. Rev. Lett., 78, 985, (1997)
[6] Brazhnyi, V. A.; Konotop, V. V., Phys. Rev. E, 72, 026616, (2005)
[7] Březinová, I.; Collins, L. A.; Ludwig, K.; Schneider, B. I.; Burgdörfer, J., Phys. Rev. A, 83, 043611, (2011)
[8] Cockburn, S. P.; Nistazakis, H. E.; Horikis, T. P.; Kevrekidis, P. G.; Proukakis, N. P.; Frantzeskakis, D. J., Phys. Rev. Lett., Phys. Rev. A, 84, 043640, (2011)
[9] Csire, Gábor; Schumayer, Dániel; Apagyi, Barnabás, Phys. Rev. A, 82, 063608, (2010)
[10] Denschlag, J.; Simsarian, J. E.; Feder, D. L.; Clark, C. W.; Collins, L. A.; Cubizolles, J.; Deng, L.; Hagley, E. W.; Helmerson, K.; Reinhardt, W. P.; Rolston, S. L.; Schneider, B. I.; Phillips, W. D., Science, 287, 97, (2000)
[11] Frantzeskakis, D. J., J. Phys. A, 43, 213001, (2010)
[12] Hamner, C.; Chang, J. J.; Engels, P.; Hoefer, M. A., Phys. Rev. Lett., 106, 065302, (2011)
[13] Hennig, H.; Dorignac, J.; Campbell, D. K., Phys. Rev. A, 82, 053604, (2010)
[14] Hirota, R., The direct method in soliton theory, (2004), Cambridge University Press Cambridge
[15] Hoefer, M. A.; Chang, J. J.; Hamner, C.; Engels, P., Phys. Rev. A, 84, 041605(R), (2011)
[16] Huang, G.; Velarde, M. G.; Makarov, V. A., Phys. Rev. A, 64, 013617, (2001)
[17] Inouye, S.; Andrews, M. R.; Stenger, J.; Miesner, H. J.; Stamper-Kurn, D. M.; Ketterle, W., Nature, 392, 151, (1998)
[18] Kagan, Y.; Muryshev, A. E.; Shlyapnikov, G. V., Phys. Rev. Lett., 81, 933, (1998)
[19] Kamchatnov, A. M.; Salerno, M., J. Phys. B, 42, 185303, (2009)
[20] Kasamatsu, K.; Tsubota, M.; Xue, J. K.; Li, G. Q.; Zhang, A. X.; Peng, P., Phys. Rev. Lett., Phys. Rev. E, 77, 016606, (2008)
[21] Kasamatsu, K.; Tsubota, M., Phys. Rev. A, 74, 013617, (2006)
[22] Kevrekidis, P. G.; Nistazakis, H. E.; Frantzeskakis, D. J.; Malomed, B. A.; Carretero-González, R., Eur. Phys. J. D, 28, 181, (2004)
[23] Li, B.; Zhang, X. F.; Li, Y. Q.; Chen, Y.; Liu, W. M., Phys. Rev. A, 78, 023608, (2008)
[24] Liu, X. X.; Pu, H.; Xiong, B.; Liu, W. M.; Gong, J. B., Phys. Rev. A, 79, 013423, (2009)
[25] Matthews, M. R.; Anderson, B. P.; Haljan, P. C.; Hall, D. S.; Wieman, C. E.; Cornell, E. A., Phys. Rev. Lett., 83, 2498, (1999)
[26] Murali, R.; Senthilnathan, K.; Porsezian, K., J. Phys. B, 41, 025401, (2008)
[27] Myatt, C. J.; Burt, E. A.; Ghrist, R. W.; Cornell, E. A.; Wieman, C. E., Phys. Rev. Lett., 78, 586, (1997)
[28] Öhberg, P.; Sogo, T.; Fedorov, D. V.; Jensen, A. S.; Liu, C. F.; Tang, Y., Phys. Rev. A, Phys. Rev. A, Eur. Phys. J. B, 70, 193, (2009)
[29] Öhberg, P.; Santos, L., Phys. Rev. Lett., J. Phys. B, 34, 4721, (2001)
[30] Öhberg, P.; Stenholm, S., Phys. Rev. A, 57, 1272, (1998)
[31] Parker, N. G.; Proukakis, N. P.; Barenghi, C. F.; Adams, C. S., J. Phys. B, 37, S175, (2004)
[32] Parker, N. G.; Proukakis, N. P.; Leadbeater, M.; Adams, C. S., J. Phys. B, 36, 2891, (2003)
[33] Robert, A.; Sirjean, O.; Browaeys, A.; Poupard, J.; Nowak, S.; Boiron, D.; Westbrook, C. I.; Aspect, A., Science, 292, 461, (2001)
[34] Scott, R. G.; Dalfovo, F.; Pitaevskii, L. P.; Stringari, S., Phys. Rev. Lett., 106, 185301, (2011)
[35] Stellmer, S.; Becker, C.; Soltan-Panahi, P.; Richter, E.; Dorscher, S.; Baumert, M.; Kronjager, J.; Bongs, K.; Sengstock, K., Phys. Rev. Lett., 101, 120406, (2008)
[36] Stenger, J.; Inouye, S.; Stamper-Kurn, D. M.; Miesner, H. J.; Chikkatur, A. P.; Ketterle, W., Nature, 396, 345, (1998)
[37] Sun, Z. Y.; Gao, Y. T.; Yu, X.; Liu, W. J.; Liu, Y.; Sun, Z. Y.; Gao, Y. T.; Yu, X.; Meng, X. H.; Liu, Y.; Yu, X.; Gao, Y. T.; Sun, Z. Y.; Liu, Y.; Sun, Z. Y.; Gao, Y. T.; Yu, X.; Liu, Y., Phys. Rev. E, Wave Motion, Phys. Rev. E, Nonlinear Dyn., Colloid Surf. A, 366, 1, (2010)
[38] Thalhammer, G.; Barontini, G.; De Sarlo, L.; Catani, J.; Minardi, F.; Inguscio, M., Phys. Rev. Lett., 100, 210402, (2008)
[39] Tian, B.; Gao, Y. T., Phys. Lett. A, 340, 243, (2005), 349 (2006) 314; 362 (2007) 283
[40] Vijayajayanthi, M.; Kanna, T.; Lakshmanan, M., Phys. Rev. A, 77, 013820, (2008)
[41] Lü, X.; Peng, M., Chaos, Commun. Nonlinear Sci. Numer. Simul., Nonlinear Dyn., 73, 405, (2013)
[42] Wang, D. S.; Hu, X. H.; Liu, W. M., Phys. Rev. A, 82, 023612, (2010)
[43] Wang, P.; Tian, B.; Liu, W. J.; Li, M.; Sun, K.; Qin, B.; Tian, B.; Liu, W. J.; Liu, L. C.; Qu, Q. X.; Zhang, H. Q.; Qin, B.; Tian, B.; Liu, L. C.; Wang, M.; Lin, Z. Q.; Liu, W. J., Stud. Appl. Math., SIAM J. Appl. Math., J. Math. Phys., 52, 043523, (2011)
[44] Wang, D. S.; Zhang, X. F.; Zhang, P.; Liu, W. M., J. Phys. B, 42, 245303, (2009)
[45] Xu, T.; Li, J.; Zhang, H. Q.; Zhang, Y. X.; Hu, W.; Gao, Y. T.; Tian, B., Phys. Lett. A, 372, 1990, (2008)
[46] Yan, D.; Chang, J. J.; Hamner, C.; Hoefer, M.; Kevrekidis, P. G.; Engels, P.; Achilleos, V.; Frantzeskakis, D. J.; Cuevas, J., J. Phys. B, 45, 115301, (2012)
[47] Zhang, X. F.; Hu, X. H.; Liu, X. X.; Liu, W. M., Phys. Rev. A, 79, 033630, (2009)
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