Abstract
In this paper, we construct a binary Darboux transformation for the three-component Gross–Pitaevskii equations, which describe the hyperfine spin F=1 spinor Bose–Einstein condensates. Single-, double-hump bright solitons and bright-two soliton are obtained via the binary Darboux transformation with a zero seed solution, in which the bright-two soliton describes interaction between two solitons with the same spectral variable. Kink-type, double-hump, double kink-type breathers, two-breather and kink-type two-breather are derived with a nonzero seed solution, in which the latter two kinks breathers describing the interactions between two breathers with the same spectral variable have not been reported before, to our knowledge. Based on the breather solution, we obtain the rogue-wave solution. Beak-type rogue wave is presented.
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