Moving planes for domain walls in a coupled system

2019/07/23 by Aftalion, Amandine, Farina, Alberto, Nguyen, Luc · 2 citations
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1907.09777

Abstract

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 mono-tonicity 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.

Cited by

• Phase transitions in two-component Bose-Einstein condensates with Rabi frequency (II): The De Giorgi conjecture for the nonlocal problem in ℝ² or ℝ³
• Phase transitions in two-component Bose-Einstein condensates with Rabi frequency (I): The De Giorgi conjecture for the local problem in ℝ³

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