Solution of the Riemann problem for polarization waves in a two-component Bose-Einstein condensate

S. K. Ivanov, A. M. Kamchatnov, T. Congy, and N. Pavloff
Phys. Rev. E 96, 062202 – Published 11 December 2017

Abstract

We provide a classification of the possible flows of two-component Bose-Einstein condensates evolving from initially discontinuous profiles. We consider the situation where the dynamics can be reduced to the consideration of a single polarization mode (also denoted as “magnetic excitation”) obeying a system of equations equivalent to the Landau-Lifshitz equation for an easy-plane ferromagnet. We present the full set of one-phase periodic solutions. The corresponding Whitham modulation equations are obtained together with formulas connecting their solutions with the Riemann invariants of the modulation equations. The problem is not genuinely nonlinear, and this results in a non-single-valued mapping of the solutions of the Whitham equations with physical wave patterns as well as the appearance of interesting elements—contact dispersive shock waves—that are absent in more standard, genuinely nonlinear situations. Our analytic results are confirmed by numerical simulations.

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  • Received 14 September 2017

DOI:https://doi.org/10.1103/PhysRevE.96.062202

©2017 American Physical Society

Physics Subject Headings (PhySH)

  1. Research Areas
  1. Physical Systems
Nonlinear Dynamics

Authors & Affiliations

S. K. Ivanov1,2, A. M. Kamchatnov1,2, T. Congy3, and N. Pavloff3

  • 1Institute of Spectroscopy, Russian Academy of Sciences, Troitsk, Moscow 108840, Russia
  • 2Moscow Institute of Physics and Technology, Institutsky lane 9, Dolgoprudny, Moscow region 141700, Russia
  • 3LPTMS, CNRS, Univ. Paris-Sud, Université Paris-Saclay, 91405 Orsay, France

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Issue

Vol. 96, Iss. 6 — December 2017

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