Moving planes for domain walls in a coupled system
Analysis of PDEs
2019-07-24 v1
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.
Cite
@article{arxiv.1907.09777,
title = {Moving planes for domain walls in a coupled system},
author = {Amandine Aftalion and Alberto Farina and Luc Nguyen},
journal= {arXiv preprint arXiv:1907.09777},
year = {2019}
}