{"paper":{"title":"Vortex Collapse for the L2-Critical Nonlinear Schr\\\"odinger Equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Gideon Simpson, Ian Zwiers","submitted_at":"2010-10-28T05:31:45Z","abstract_excerpt":"The focusing cubic nonlinear Schr\\\"odinger equation in two dimensions admits vortex solitons, standing wave solutions with spatial structure, Qm(r,theta) = e^{i m theta} Rm(r). In the case of spin m = 1, we prove there exists a class of data that collapse with the vortex soliton profile at the log-log rate. This extends the work of Merle and Rapha\\\"el, (the case m = 0,) and suggests that the L2 mass that may be concentrated at a point during generic collapse may be unbounded. Difficulties with m >= 2 or when breaking the spin symmetry are discussed."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.5864","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":""},"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"}