JETP Letters

, Volume 100, Issue 8, pp 508–511 | Cite as

Soliton in stationary and dynamical traps

Plasma, Hydro- and Gas Dynamics

Abstract

Soliton dynamics in a one-dimensional trap with immobile and oscillating walls has been analyzed by the example of an atomic Bose-Einstein condensate. Agreement between the consequences of a simplified Newton’s equation describing the interaction of a soliton with its antiphase mirror reflections and the initial Gross-Pitaevskii equation has been demonstrated. Comparison with the dynamics of a classical point particle in the Fermi-Ulam problem has been carried out.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    E. Fermi, Phys. Rev. 75, 1169 (1949).ADSCrossRefMATHGoogle Scholar
  2. 2.
    S. Ulam, in Proceedings of the 4th Berkley Symposium on Mathematics, Statistics, and Probability (California Univ. Press, Berkeley, Los Angeles, 1961), Vol. 3, p. 315.Google Scholar
  3. 3.
    A. J. Lichtenberg and M. A. Lieberman, Regular and Stochastic Motion (Springer, Berlin, Heidelberg, New York, 1983; Mir, Moscow, 1984).CrossRefMATHGoogle Scholar
  4. 4.
    A. Yu. Loskutov, Phys. Usp. 50, 939 (2007).ADSCrossRefGoogle Scholar
  5. 5.
    N. N. Rosanov, Phys. Rev. A 88, 063616 (2013).ADSCrossRefGoogle Scholar
  6. 6.
    N. N. Rosanov, Phys. Rev. A 89, 035601 (2014).ADSCrossRefGoogle Scholar
  7. 7.
    P. E. Toshek, Usp. Fiz. Nauk 158, 451 (1989).CrossRefGoogle Scholar
  8. 8.
    V. E. Zakharov and A. B. Shabat, Sov. Phys. JETP 34, 62 (1971).ADSMathSciNetGoogle Scholar
  9. 9.
    K. A. Gorshkov and L. A. Ostrovsky, Physica D 3, 428 (1981).ADSCrossRefMATHGoogle Scholar
  10. 10.
    I. G. Malkin, Some Problems of Nonlinear Oscillation Theory (Gos. Izdat. Tekh.-Teor. Liter., Moscow, 1956) [in Russian].Google Scholar
  11. 11.
    V. D. Vinokurova and N. N. Rozanov, Pis’ma Zh. Tekh. Fiz. 40(21), 21 (2014).Google Scholar

Copyright information

© Pleiades Publishing, Inc. 2014

Authors and Affiliations

  1. 1.Vavilov State Optical InstituteSt. PetersburgRussia
  2. 2.National Research University of Information Technologies, Mechanics, and Optics (ITMO University)St. PetersburgRussia
  3. 3.Ioffe Physical Technical InstituteRussian Academy of SciencesSt. PetersburgRussia

Personalised recommendations