{"paper":{"title":"Singular solutions of the subcritical nonlinear Schrodinger equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["nlin.PS"],"primary_cat":"math.AP","authors_text":"Gadi Fibich","submitted_at":"2010-04-11T17:56:23Z","abstract_excerpt":"We show that the subcritical $d$-dimensional nonlinear Schr\\\"odinger equation $i \\psi_t + \\Delta \\psi + |\\psi|^{2 \\sigma} \\psi = 0$, where $1<\\sigma d<2$, admits smooth solutions that become singular in~$L^p$ for $p^*<p \\le \\infty$, where $p^*:=\\frac{\\sigma d}{\\sigma d -1}$. Since $\\lim_{\\sigma d \\to 2-} p^* = 2$, these solutions can collapse at any $2<p \\le \\infty$, and in particular for $p = 2 \\sigma+2$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.1827","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":""},"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"}