Moving planes for domain walls in a coupled system

The system leading to phase segregation in two-component Bose-Einstein condensates can be generalized to hyperfine spin states with a Rabi term coupling. This leads to domain wall solutions having a monotone structure for a non-cooperative system. We use the moving plane method to prove monotonicity and one-dimensionality of the phase transition solutions. This relies on totally new estimates for a type of system for which no Maximum Principle a priori holds. We also derive that one dimensional solutions are unique up to translations. When the Rabi coefficient is large, we prove that no non-constant solutions can exist.

Automated summary

In this study, the system leading to phase segregation in two-component Bose-Einstein condensates was generalized to hyperfine spin states with a Rabi term coupling. Domain wall solutions with a monotone structure were found for a non-cooperative system, and the moving plane method was used to prove the monotonicity and one-dimensionality of the phase transition solutions. Unique one-dimensional solutions up to translations were derived, and it was proven that no non-constant solutions can exist when the Rabi coefficient is large.