A thorough study of domain wall solutions in coupled Gross–Pitaevskii equations on the real
line is carried out including existence of these solutions; their spectral and nonlinear
stability; their persistence and stability under a small localized potential. The proof of
existence is variational and is presented in a general framework: we show that the domain
wall solutions are energy minimizers within a class of vector-valued functions with nontrivial
conditions at infinity. The admissible energy functionals include those corresponding to …

We study the existence and variational characterization of steady states in a coupled system
of Gross–Pitaevskii equations modeling two-component Bose-Einstein condensates with the
magnetic field trapping. The limit with no trapping has been the subject of recent works
where domain walls have been constructed and several properties, including their orbital
stability have been derived. Here we focus on the full model with the harmonic trapping
potential and characterize minimizers according to the value of the coupling parameter γ …