{"paper":{"title":"Axial Symmetry of Normalized Solutions for Magnetic Gross-Pitaevskii Equations with Anharmonic Potentials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Shuangjie Peng, Yan Li, Yong Luo, Yujin Guo","submitted_at":"2023-10-01T03:13:30Z","abstract_excerpt":"This paper is concerned with normalized solutions of the magnetic focusing Gross-Pitaevskii equations with anharmonic potentials in $\\mathbb{R}^N$, where $N=2$ or $3$. We construct axially symmetric normalized concentrating solutions as the parameter $a>0$ approaches $a_*(N)$, where $a_*(N)\\geq0$ is a critical constant depending only on $N$. We further prove that up to a constant phase (and a rotational transformation for $N=2$), normalized concentrating solutions are unique and axially symmetric as $a\\to a_*(N)$. When $N=3$, we also prove that the corresponding unique normalized concentrating"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2310.00556","kind":"arxiv","version":2},"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/2310.00556/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"}