Exact stationary wave patterns in three coupled nonlinear Schrödinger/Gross–Pitaevskii equations

The evolution of a Bose–Einstein condensate (BEC) with an internal degree of freedom, i.e., spinor BEC, is governed by a system of three coupled mean-field equations. The system admits the application of the inverse scattering transform and Hirota bilinear method under appropriate conditions, which makes it possible to generate exact analytical solutions relevant to physical applications. Here, we produce six families of exact periodic solutions, directly constructed in terms of Jacobi elliptic functions. Solitary-wave limit forms, obtained from these solutions in the long-wave limit, are presented too.