Solitons and rogue waves in spinor Bose-Einstein condensates

Abstract

We present a general classification of one-soliton solutions as well as novel 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 non-zero background is present, not all matrix one-soliton solutions are reducible to a simple combination of scalar solutions. We show that some solitons are topological ones and others are dark-bright solitons. Finally, by taking suitable limits of all the solutions on a non-zero background we also obtain three families of rogue-wave (i.e., rational) solutions, two of which are novel to the best of our knowledge.

arXiv comment19 pages, 10 figures, 3 tables, to appear in Phys. Rev. E

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• Multi-breathers and high order rogue waves for the nonlinear Schrödinger equation on the elliptic function background
• Bright Matter-Wave Bound Soliton Molecules in Spin-1 Bose-Einstein Condensates with Non-autonomous Nonlinearities
• Many-body effects on second-order phase transitions in spinor Bose-Einstein condensates and breathing dynamics
• On soliton solutions and soliton interactions of Kulish-Sklyanin and Hirota-Ohta systems
• Fundamental Analytic Solutions for the Kulish-Sklyanin Model with Constant Boundary Conditions