Domain Walls in the Coupled Gross–Pitaevskii Equations

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 …