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In the focusing regime, we consider a family of solutions $\\{(u_{\\tau}, v_{\\tau})\\}_{\\tau>0}$ in $ H^1\\times H^1$ associated to an initial data family $\\{(u_{\\tau_0},v_{\\tau_0})\\}_{\\tau>0}$ uniformly bounded in $H^1\\times L^2$, where $\\tau$ is a small response time parameter. We prove prove that $(u_{\\tau}, v_{\\tau})$ converges to $(u, -|u|^2)$ in the space $L^{\\infty}_{[0, T]}L"},"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":"1705.01003","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-05-02T14:45:41Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"672c1fafd1815a6168da7bcc0f555fd3b48cf71c29cec83e7d1a1f4f31f1c2a0","abstract_canon_sha256":"c443bd5d4a25c57088d46412f9404831772764dfb321781c1b238d81db6b70f9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:19:30.596449Z","signature_b64":"/LPxyq9eitodQ982LjDxl08Ondvr5JOO5Fwksn4KC6KzK2s8XO2sSg+wOqK+ONLKAsc+JSn+4dQGObn/hOK5Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"06a59e1023e8a8f805f41bd496a4aa8d6d9c50a49439fc1bc1259fa15bf29304","last_reissued_at":"2026-05-18T00:19:30.595961Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:19:30.595961Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Asymptotic behavior of the Schr\\\"odinger-Debye system with refractive index of square wave amplitude","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Adan J. Corcho, Juan C. Cordero","submitted_at":"2017-05-02T14:45:41Z","abstract_excerpt":"We obtain local well-posedness for the one-dimensional Schr\\\"odinger-Debye interactions in nonlinear optics in the spaces $L^2\\times L^p,\\; 1\\le p < \\infty$. When $p=1$ we show that the local solutions extend globally. In the focusing regime, we consider a family of solutions $\\{(u_{\\tau}, v_{\\tau})\\}_{\\tau>0}$ in $ H^1\\times H^1$ associated to an initial data family $\\{(u_{\\tau_0},v_{\\tau_0})\\}_{\\tau>0}$ uniformly bounded in $H^1\\times L^2$, where $\\tau$ is a small response time parameter. 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