Moving planes for domain walls in a coupled system

Author: 

Aftalion, A
Farina, A
Nguyen, L

Publication Date: 

14 February 2021

Journal: 

Communications in Partial Differential Equations

Last Updated: 

2021-10-19T13:24:05.847+01:00

DOI: 

10.1080/03605302.2021.1881112

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 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.

Symplectic id: 

1152016

Submitted to ORA: 

Submitted

Publication Type: 

Journal Article