Metastable spin textures and Nambu-Goldstone modes of a ferromagnetic spin-1 Bose-Einstein condensate confined in a ring trap

We investigate the metastability of a ferromagnetic spin-1 Bose-Einstein condensate confined in a quasi-one-dimensional rotating ring trap by solving the spin-1 Gross-Pitaevskii equation. We find analytical solutions that exhibit spin textures. By performing linear stability analysis, it is shown that the solutions can become metastable states. We also find that the number of Nambu-Goldstone modes changes at a certain rotation velocity without changing the continuous symmetry of the order parameter.