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Since $\\lim_{\\sigma d \\to 2-} p^* = 2$, these solutions can collapse at any $2<p \\le \\infty$, and in particular for $p = 2 \\sigma+2$."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1004.1827","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-04-11T17:56:23Z","cross_cats_sorted":["nlin.PS"],"title_canon_sha256":"b45d6257fe2f6dfda2cc44f45d498a57c0bd1c07d1332a186429305b626a76b1","abstract_canon_sha256":"a1672a10ad7ca223e013e6d97879561e347a04818246c60ff883f65799b5412c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:08:06.980990Z","signature_b64":"I0z/4hkhlkr+WDxvUN5JGoeYm5mqsJDjBw7/VNgVm5zjisOj1OBdyED1ncg4Q0BLsiBM7cfU1VIYo1JIReSnAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1c09994e2581a73336c5d27db5cfe20895dd3860a5ab07e1c76cc6459b9cd520","last_reissued_at":"2026-05-18T02:08:06.980210Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:08:06.980210Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $p^*:=\\frac{\\sigma d}{\\sigma d -1}$. 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