Riccati generalization of self-similar solutions of nonautonomous Gross-Pitaevskii equation

Regular Article Integrable Systems and Solitons

Abstract

We present a systematic analytical approach to construct a family of self-similar waves, related through a free parameter, in quasi one-dimension Gross-Pitaevskii equation with time-varying parameters. This approach enables us to control the dynamics of dark and bright similaritons, and first- and second- order self-similar rogue waves in Bose-Einstein condensate through the modulation of time dependent trapping potential. The analysis is done for the sech2− type time-varying quadratic trapping potential for two different choices of linear potential.

Keywords

Soliton European Physical Journal Special Topic Rogue Wave Trapping Potential Dark Soliton 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    E.A. Cornell, C.E. Wieman, Rev. Mod. Phys. 74, 875 (2002)ADSCrossRefGoogle Scholar
  2. 2.
    F. Dalfovo, S. Giorgini, L.P. Pitaevskii, S. Stringari, Rev. Mod. Phys. 71, 463 (1999)ADSCrossRefGoogle Scholar
  3. 3.
    C.J. Pethick, H. Smith, Bose-Einstein Condensation in Dilute Gases (Cambridge University Press, Cambridge, UK, 2002)Google Scholar
  4. 4.
    S. Burger, et al., Phys. Rev. Lett. 83, 5198 (1999)ADSCrossRefGoogle Scholar
  5. 5.
    J. Denschlag, et al., Science 287, 97 (2000)ADSCrossRefGoogle Scholar
  6. 6.
    G. Huang, J. Szeftel, S. Zhu1, Phys. Rev. A 65, 053605 (2002)ADSCrossRefGoogle Scholar
  7. 7.
    K.E. Strecker, et al., Nature 417, 150 (2002)ADSCrossRefGoogle Scholar
  8. 8.
    L. Khaykovich, et al., Science 296, 1290 (2002)ADSCrossRefGoogle Scholar
  9. 9.
    M.R. Matthews, et al., Phys. Rev. Lett. 83, 2498 (1999)ADSCrossRefGoogle Scholar
  10. 10.
    L. Wu, et al., Phys. Rev. A 81, 061805 (2010)ADSCrossRefGoogle Scholar
  11. 11.
    H. Sakaguchi, B.A. Malomed, Europhys. Lett. 72, 698 (2005)MathSciNetADSCrossRefGoogle Scholar
  12. 12.
    X.H. Hu, et al., Phys. Rev. A 79, 023619 (2009)ADSCrossRefGoogle Scholar
  13. 13.
    J. Stockhofe, P.G. Kevrekidis, D.J. Frantzeskakis, P. Schmelcher, J. Phys. B: At. Mol. Opt. Phys. 44, 191003 (2011)ADSCrossRefGoogle Scholar
  14. 14.
    C. Sudheesh, N. Bar-Gill, B.A. Malomed, G. Kurizki, J. Phys. B: At. Mol. Opt. Phys. 43, 205304 (2010)ADSCrossRefGoogle Scholar
  15. 15.
    S. Middelkamp, Phys. Rev. A 81, 053618 (2010)ADSCrossRefGoogle Scholar
  16. 16.
    W. Ketterle, Rev. Mod. Phys. 74, 1131 (2002)ADSCrossRefGoogle Scholar
  17. 17.
    Yu. V. Bludov, V.V. Konotop, N. Akhmediev, Phys. Rev. A 80, 033610 (2009)ADSCrossRefGoogle Scholar
  18. 18.
    L. Wen, et al., Eur. Phys. J. D 64, 473 (2011)ADSCrossRefGoogle Scholar
  19. 19.
    N. Akhmediev, A. Ankiewicz, M. Taki, Phys. Lett. A 373, 675 (2009)ADSMATHCrossRefGoogle Scholar
  20. 20.
    D.H. Peregrine, J. Aust. Math. Soc. Ser. B 25, 16 (1983)MathSciNetMATHCrossRefGoogle Scholar
  21. 21.
    C. Kharif, E. Pelinovsky, A. Slyunyaev, Rogue Waves in the Ocean (Springer, Berlin, 2009)Google Scholar
  22. 22.
    D.R. Solli, C. Ropers, P. Koonath, B. Jalali, Nature 450, 1054 (2007)ADSCrossRefGoogle Scholar
  23. 23.
    B. Kibler, et al., Nat. Phys. 6, 790 (2010)CrossRefGoogle Scholar
  24. 24.
    T. Busch, J.R. Anglin, Phys. Rev. Lett. 87, 010401 (2001)ADSCrossRefGoogle Scholar
  25. 25.
    R. Atre, P.K. Panigrahi, G.S. Agarwal, Phys. Rev. E 73, 056611 (2006)MathSciNetADSCrossRefGoogle Scholar
  26. 26.
    Q.Y. Li, Z.D. Li, S.X. Wang, W.W. Song, G. Fu, Opt. Commun. 282, 1676 (2009)ADSCrossRefGoogle Scholar
  27. 27.
    S. Inouye, et al., Nature (London) 392, 151 (1998)ADSCrossRefGoogle Scholar
  28. 28.
    J.L. Roberts, et al., Phys. Rev. Lett. 85, 728 (2000)ADSCrossRefGoogle Scholar
  29. 29.
    M. Theis, et al., Phys. Rev. Lett. 93, 123001 (2004)ADSCrossRefGoogle Scholar
  30. 30.
    K. Enomoto, K. Kasa, M. Kitagawa, Y. Takahashi, Phys. Rev. Lett. 101, 203201 (2008)ADSCrossRefGoogle Scholar
  31. 31.
    V.N. Serkin, A. Hasegawa, T.L. Belyaeva, Phys. Rev. Lett. 98, 074102 (2007)ADSCrossRefGoogle Scholar
  32. 32.
    V.N. Serkin, A. Hasegawa, T.L. Belyaeva, Phys. Rev. A 81, 023610 (2010)ADSCrossRefGoogle Scholar
  33. 33.
    V.R. Kumar, R. Radha, P.K. Panigrahi, Phys. Rev. A 77, 023611 (2008)ADSCrossRefGoogle Scholar
  34. 34.
    B. Li, X.F. Zhang, Y.Q. Li, W.M. Liu, J. Phys. B: At. Mol. Opt. Phys. 44, 175301 (2011)ADSCrossRefGoogle Scholar
  35. 35.
    F. Cooper, A. Khare, U. Sukhatme, Supersymmetry in Quantum Mechanics (World Scientific, Singapore, 2001) Chaper 6 and references thereinGoogle Scholar
  36. 36.
    C.N. Kumar, J. Phys. A: Math. Gen. 20, 5397 (1987)ADSCrossRefGoogle Scholar
  37. 37.
    B. Dey, C.N. Kumar, Int. J. Mod. Phys. A 9, 2699 (1994)MathSciNetADSMATHCrossRefGoogle Scholar
  38. 38.
    E. Drigo Filho, J.R. Ruggiero, Phys. Rev. E 56, 4486 (1997)ADSCrossRefGoogle Scholar
  39. 39.
    W. Alka, A. Goyal, C.N. Kumar, Phys. Lett. A 375, 480 (2011)ADSMATHCrossRefGoogle Scholar
  40. 40.
    R. Gupta, S. Loomba, C.N. Kumar, IEEE J. Quantum Electronics 48, 847 (2012)ADSCrossRefGoogle Scholar
  41. 41.
    C.N. Kumar, R. Gupta, A. Goyal, S. Loomba, T.S. Raju, P.K. Panigrahi, Phys. Rev. A 86, 025802 (2012)ADSCrossRefGoogle Scholar
  42. 42.
    A. Goyal, R. Gupta, S. Loomba, C.N. Kumar, Phys. Lett. A 376, 3454 (2012)ADSCrossRefGoogle Scholar
  43. 43.
    L. Salasnich, A. Parola, L. Reatto, Phys. Rev. A 65, 043614 (2002)ADSCrossRefGoogle Scholar
  44. 44.
    C.Q. Dai, Q. Tian, S.Q. Zhu, J. Phys. B: At. Mol. Opt. Phys. 45, 085401 (2012)ADSCrossRefGoogle Scholar
  45. 45.
    V.I. Kruglov, A.C. Peacock, J.D. Harvey, Phys. Rev. Lett. 90, 113902 (2003)ADSCrossRefGoogle Scholar
  46. 46.
    Y. Liu, Appl. Math. Comp. 217, 5866 (2011)MATHCrossRefGoogle Scholar
  47. 47.
    X.G. He, D. Zhao, L. Li, H.G. Luo, Phys. Rev. E 79, 056610 (2009)ADSCrossRefGoogle Scholar
  48. 48.
    W.P. Zhong, M.R. Belić, Phys. Rev. E 81, 056604 (2010)ADSCrossRefGoogle Scholar

Copyright information

© EDP Sciences and Springer 2013

Authors and Affiliations

  1. 1.Indian Institute of Science Education and Research-KolkataMohanpurIndia
  2. 2.Department of PhysicsPanjab UniversityChandigarhIndia

Personalised recommendations