Soliton of Bose–Einstein condensate in a trap with rapidly oscillating walls: II. Analysis of the soliton behavior upon a decrease in the wall oscillation frequency

详细信息    查看全文

• 作者：N. A. Veretenov ; N. V. Vysotina ; L. A. Nesterov ; N. N. Rosanov
• 刊名：Optics and Spectroscopy
• 出版年：2016
• 出版时间：January 2016
• 年：2016
• 卷：120
• 期：1
• 页码：120-133
• 全文大小：1,442 KB
• 参考文献：1.N. A. Veretenov, N. V. Vysotina, L. A. Nesterov, and N. N. Rozanov, Opt. Spektrosk. 119 (2015, in press).
  2.A. Nayfeh, Perturbation Methods (Wiley, New York, 1973).
  3.A. J. Lichtenberg and M. A. Lieberman, Regular and Stochastic Motion (Springer, New York, 1983).CrossRef
  
• 作者单位：N. A. Veretenov (1) (2)
  N. V. Vysotina (1)
  L. A. Nesterov (1) (2)
  N. N. Rosanov (1) (2) (3)
  
  1. Vavilov State Optical Institute, St. Petersburg, 199053, Russia
  2. ITMO University, St. Petersburg, 197101, Russia
  3. Ioffe Physical Technical Institute, Russian Academy of Sciences, St. Petersburg, 194021, Russia
  
• 刊物类别：Physics and Astronomy
• 刊物主题：Physics
  Optical Spectroscopy and Ultrafast Optics
  Russian Library of Science
• 出版者：MAIK Nauka/Interperiodica distributed exclusively by Springer Science+Business Media LLC.
• ISSN：1562-6911

文摘

This work is a continuation of our study [1], in which a two-scale analytical approach to the investigation of a soliton oscillon in a trap with rapidly oscillating walls has been developed. In terms of this approach, the solution to the equation of motion of the soliton center is sought as a series expansion in powers of a small parameter, which is a ratio of the intrinsic frequency of slow soliton oscillations to the frequency of fast trap wall oscillations. In [1], we have examined the case ε ≪ 1, in which, to describe the motion of the soliton, it is sufficient to restrict the consideration to the zero approximation of the sought solution. However, when the frequency of wall oscillations begins to decrease, while the parameter begins to increase, it is necessary to take into account corrections to the zero approximation. In this work, we have calculated corrections of the first and second orders in to this approximation. We have shown that, with an increase in, the role played by the corrections related to fast oscillations of the trap walls increases, which results in a complex shape of the envelope of oscillations of the soliton center. It follows from our calculations that, if the difference between the amplitudes of wall oscillations is not too large, the analytical solution of the equation of motion of the soliton center will coincide very well with the numerical solution. However, with an increase in this difference, as well as with a decrease in the wall oscillation frequency, the discrepancy between the numerical and analytical solutions generally begins to increase. Regimes of irregular oscillations of the soliton center arise. With a decrease in the frequency of wall oscillations, the instability boundary shows a tendency toward a smaller difference between the wall oscillation amplitudes. In general, this leads to enlargement of the range of irregular regimes. However, at the same time, stability windows can arise in this range in which the analytical and numerical solutions correlate rather well with each other. Our comparative analysis of the analytical and numerical solutions has allowed us not only to study their properties in detail, but also to draw conclusions on the limits of applicability of the analytical approach. Original Russian Text © N.A. Veretenov, N.V. Vysotina, L.A. Nesterov, N.N. Rosanov, 2016, published in Optika i Spektroskopiya, 2016, Vol. 120, No. 1, pp. 135-148.