Optimal pinwheel partitions and pinwheel solutions to a nonlinear Schrödinger system
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916196247404544 |
|---|---|
| author | Clapp, Mónica Saldaña, Alberto Soares, Mayra Vicente-Benítez, Víctor A. |
| author_facet | Clapp, Mónica Saldaña, Alberto Soares, Mayra Vicente-Benítez, Víctor A. |
| contents | We establish the existence of a solution to a nonlinear competitive Schrödinger system whose scalar potential tends to a positive constant at infinity with an appropriate rate. This solution has the property that all components are invariant under the action of a group of linear isometries and each component is obtained from the previous one by composing it with some fixed linear isometry. We call it a pinwheel solution. We describe the asymptotic behavior of the least energy pinwheel solutions when the competing parameter tends to zero and to minus infinity. In the latter case the components are segregated and give rise to an optimal pinwheel partition for the Schrödinger equation, that is, a partition formed by invariant sets that are mutually isometric through a fixed isometry. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_04448 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Optimal pinwheel partitions and pinwheel solutions to a nonlinear Schrödinger system Clapp, Mónica Saldaña, Alberto Soares, Mayra Vicente-Benítez, Víctor A. Analysis of PDEs 35J47, 35J50, 35B06, 35B40 We establish the existence of a solution to a nonlinear competitive Schrödinger system whose scalar potential tends to a positive constant at infinity with an appropriate rate. This solution has the property that all components are invariant under the action of a group of linear isometries and each component is obtained from the previous one by composing it with some fixed linear isometry. We call it a pinwheel solution. We describe the asymptotic behavior of the least energy pinwheel solutions when the competing parameter tends to zero and to minus infinity. In the latter case the components are segregated and give rise to an optimal pinwheel partition for the Schrödinger equation, that is, a partition formed by invariant sets that are mutually isometric through a fixed isometry. |
| title | Optimal pinwheel partitions and pinwheel solutions to a nonlinear Schrödinger system |
| topic | Analysis of PDEs 35J47, 35J50, 35B06, 35B40 |
| url | https://arxiv.org/abs/2404.04448 |