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...
| Main Authors: | , , |
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| Format: | Journal article |
| Language: | English |
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Taylor & Francis
2021
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| _version_ | 1797075931258421248 |
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| author | Aftalion, A Farina, A Nguyen, L |
| author_facet | Aftalion, A Farina, A Nguyen, L |
| author_sort | Aftalion, A |
| collection | OXFORD |
| description | 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.
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| first_indexed | 2024-03-06T23:57:11Z |
| format | Journal article |
| id | oxford-uuid:74a3388c-6105-4c2e-b6dd-e5760b8094f0 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T23:57:11Z |
| publishDate | 2021 |
| publisher | Taylor & Francis |
| record_format | dspace |
| spelling | oxford-uuid:74a3388c-6105-4c2e-b6dd-e5760b8094f02022-03-26T20:04:20ZMoving planes for domain walls in a coupled systemJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:74a3388c-6105-4c2e-b6dd-e5760b8094f0EnglishSymplectic ElementsTaylor & Francis2021Aftalion, AFarina, ANguyen, LThe 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. |
| spellingShingle | Aftalion, A Farina, A Nguyen, L Moving planes for domain walls in a coupled system |
| title | Moving planes for domain walls in a coupled system |
| title_full | Moving planes for domain walls in a coupled system |
| title_fullStr | Moving planes for domain walls in a coupled system |
| title_full_unstemmed | Moving planes for domain walls in a coupled system |
| title_short | Moving planes for domain walls in a coupled system |
| title_sort | moving planes for domain walls in a coupled system |
| work_keys_str_mv | AT aftaliona movingplanesfordomainwallsinacoupledsystem AT farinaa movingplanesfordomainwallsinacoupledsystem AT nguyenl movingplanesfordomainwallsinacoupledsystem |