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Solitons and rogue waves in spinor Bose-Einstein condensates

Sitai Li1, Barbara Prinari2, and Gino Biondini1,3

  • 1Department of Mathematics, State University of New York at Buffalo, Buffalo, New York 14260, USA
  • 2Department of Mathematics, University of Colorado Colorado Springs, Colorado Springs, Colorado 80918, USA
  • 3Department of Physics, State University of New York at Buffalo, Buffalo, New York 14260, USA

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Phys. Rev. E 97, 022221 – Published 23 February, 2018

DOI: https://doi.org/10.1103/PhysRevE.97.022221

Abstract

We present a general classification of one-soliton solutions as well as families of rogue-wave solutions for F=1 spinor Bose-Einstein condensates (BECs). These solutions are obtained from the inverse scattering transform for a focusing matrix nonlinear Schrödinger equation which models condensates in the case of attractive mean-field interactions and ferromagnetic spin-exchange interactions. In particular, we show that when no background is present, all one-soliton solutions are reducible via unitary transformations to a combination of oppositely polarized solitonic solutions of single-component BECs. On the other hand, we show that when a nonzero background is present, not all matrix one-soliton solutions are reducible to a simple combination of scalar solutions. Finally, by taking suitable limits of all the solutions on a nonzero background we also obtain three families of rogue-wave (i.e., rational) solutions.

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Phys. Rev. E 97, 022221– Published 23 February, 2018
  • Received 19 August 2017
  • Revised 10 January 2018
Article part of CHORUS
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