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=1F=1 and F=2F=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=2r=2 and r=3r=3. Using conveniently modified Zakharov–Shabat dressing procedure we obtain different types of soliton solutions.