Solutions of multi-component NLS models and Spinor Bose–Einstein condensates

Three- and five-component nonlinear Schrödinger-type models, which describe spinor Bose–Einstein condensates (BEC’s) with hyperfine structures F = 1 and F = 2 , respectively, are studied. These models for particular values of the coupling constants are integrable by the inverse scattering method. They are related to symmetric spaces of BD.I-type ≃ SO(2r + 1) / SO(2) × SO(2r −1) for r = 2 and r = 3 . Using conveniently modified Zakharov–Shabat dressing procedure we obtain different types of soliton solutions.