{"paper":{"title":"Optimal pinwheel partitions and pinwheel solutions to a nonlinear Schr\\\"odinger system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alberto Salda\\~na, Mayra Soares, M\\'onica Clapp, V\\'ictor A. Vicente-Ben\\'itez","submitted_at":"2024-04-05T23:31:26Z","abstract_excerpt":"We establish the existence of a solution to a nonlinear competitive Schr\\\"odinger 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 component"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.04448","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2404.04448/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}