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

S. K. Ivanov, A. M. Kamchatnov, T. Congy, N. Pavloff

Research output: Contribution to journalArticlepeer-review

25 Citations (Scopus)


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.

Original languageEnglish
Article number062202
Pages (from-to)1-24
Number of pages24
JournalPhysical Review E
Issue number6
Publication statusPublished - 11 Dec 2017
Externally publishedYes


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